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IPython Notebook on Logistic Regression
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"cell_type": "heading",
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"metadata": {},
"source": [
"Fun with Logistic Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook was derived from the [Caltech \"Learning from Data\" course](http://work.caltech.edu/telecourse.html), specifically [Lecture 9](http://www.youtube.com/watch?v=qSTHZvN8hzs&hd=1) on the logistic regression model. It is a simple Python implementation of the logistic regression model using [NumPy](http://numpy.scipy.org/).\n",
"\n",
"## Table of Contents\n",
"\n",
"* [Derivation](#Derivation)\n",
" * [Error Measure](#ErrorMeasure)\n",
" * [Learning Algorithm](#LearningAlgorithm)\n",
"* [Example](#Example)\n",
" * [Data Set](#Data-Set)\n",
" * [Learning a Hypothesis](#Learning-a-Hypothesis)\n",
" * [Learning with Less Data](#Learning-with-Less-Data)\n",
" * [Learning Curve](#Learning-Curve)\n",
" * [Visualizing the Error Surface](#Visualizing-the-Error-Surface)\n",
" * [Nonlinear Transformation](#Nonlinear-Transformation)"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Notation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The problem structure is the classic classification problem. Our data set $\\mathcal{D}$ is composed of $N$ samples. Each sample is a tuple containing a feature vector and a label. For any sample $n$ the feature vector is a $d+1$ dimensional column vector denoted by ${\\bf x}_n$ with $d$ real-valued components known as features. Samples are represented in homogeneous form with the first component equal to $1$: $x_0=1$. Vectors are bold-faced. The associated label is denoted $y_n$ and can take on only two values: $+1$ or $-1$.\n",
"\n",
"$$\n",
"\\mathcal{D} = \\lbrace ({\\bf x}_1, y_1), ({\\bf x}_2, y_2), ..., ({\\bf x}_N, y_N) \\rbrace \\\\\n",
"{\\bf x}_n = \\begin{bmatrix} 1 & x_1 & ... & x_d \\end{bmatrix}^T \n",
"$$"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Derivation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Despite the name logistic *regression* this is actually a probabilistic classification model. It is also a linear model which can be subjected to nonlinear transforms."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All linear models make use of a \"signal\" $s$ which is a linear combination of the input vector ${\\bf x}$ components weighed by the corresponding components in a weight vector ${\\bf w}$.\n",
"\n",
"$$\n",
"{\\bf w} = \\begin{bmatrix} w_0 & w_1 & ... & w_d \\end{bmatrix}^T \\\\\n",
"s = w_0 + w_1 x_1 + \\;...\\; + w_d x_d = \\sum_{i=0}^d w_i x_i = {\\bf w} \\cdot {\\bf x} = {\\bf w}^T {\\bf x}\n",
"$$\n",
"\n",
"Note that the homogeneous representation (with the $1$ at the first component) allows us to include a constant offset using a more compact vector-only notation (instead of ${\\bf w}^T {\\bf x}+b$)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Linear classification passes the signal through a harsh threshold:\n",
"\n",
"$$\n",
"h({\\bf x}) = \\operatorname{sign}(s)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Linear regression uses the signal directly without modification:\n",
"\n",
"$$\n",
"h({\\bf x}) = s\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Logistic regression passes the signal through the logistic/sigmoid but then treats the result as a probability:\n",
"\n",
"$$\n",
"h({\\bf x}) = \\theta(s)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The [logistic function](http://en.wikipedia.org/wiki/Logistic_function) is\n",
"\n",
"$$\n",
"\\theta(s) = \\frac{e^s}{1+e^s} = \\frac{1}{1+e^{-s}}\n",
"$$\n",
"\n",
"There are many other formulas that can achieve a soft threshold such as the hyperbolic tangent, but this function results in some nice simplification."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We say that the data is generated by a noisy target.\n",
"\n",
"$$\n",
"P(y\\mid{\\bf x})=\\begin{cases}\n",
"f({\\bf x}) & \\text{for }y=+1 \\\\\n",
"1-f({\\bf x}) & \\text{for }y=-1\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With this noisy target we want to learn a hypothesis $h({\\bf x})$ that best fits the above noisy target according to some error function.\n",
"\n",
"$$\n",
"h({\\bf x})=\\theta({\\bf w}^T {\\bf x})\\approx f({\\bf x})\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's important to note that the data does not tell you the probability of a label but rather what label the sample has after being generated by the target distribution."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Error Measure"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To learn a good hypothesis we want to find a hypothesis parameterization ${\\bf w}$ (the weight vector) that minimizes some in-sample error measure $E_\\text{in}$.\n",
"\n",
"$$\n",
"{\\bf w}_h = \\underset{{\\bf w}}{\\operatorname{argmin}} \\; E_\\text{in}({\\bf w})\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The error measure we will use is both plausible and nice. It is based on likelihood which is the probability of generating the data given a model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If our hypothesis is close to our target distribution ($h\\approx f$) then we expect that probability of generating the data to be high."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is some controversy with using likelihood. We are really looking for the most probable hypothesis given the data: $\\underset{h}{\\operatorname{argmax}} P(h\\mid{\\bf x})$. The likelihood approach is looking for the hypothesis that makes the data most probable: $\\underset{h}{\\operatorname{argmax}} P({\\bf x}\\mid h)$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Bayesian approach tackles this issue using [Bayes' Theorem](http://en.wikipedia.org/wiki/Bayes'_theorem) but introduces other issues such as choosing priors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To determine the likelihood we assume the data was generated with our hypothesis $h$:\n",
"\n",
"$$\n",
"P(y\\mid{\\bf x})=\\begin{cases}\n",
"h({\\bf x}) & \\text{for }y=+1 \\\\\n",
"1-h({\\bf x}) & \\text{for }y=-1\n",
"\\end{cases} \\\\\n",
"$$\n",
"\n",
"where $h({\\bf x})=\\theta({\\bf w}^T {\\bf x})$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We don't want to deal with cases so we take advantage of a nice property of the logistic function: $\\theta(-s)=1-\\theta(s)$.\n",
"\n",
"$$\n",
"\\text{if } y = +1 \\text{ then } h({\\bf x}) = \\theta({\\bf w}^T {\\bf x}) = \\theta(y \\; {\\bf w}^T {\\bf x}) \\\\\n",
"\\text{if } y = -1 \\text{ then } 1 - h({\\bf x}) = 1 - \\theta({\\bf w}^T {\\bf x}) = \\theta(- {\\bf w}^T {\\bf x}) = \\theta(y \\; {\\bf w}^T {\\bf x}) \\\\\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using this simplification,\n",
"\n",
"$$\n",
"P(y\\mid{\\bf x})=\\theta(y\\; {\\bf w}^T {\\bf x})\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The likelihood is defined for a data set $\\mathcal{D}$ with $N$ samples given a hypothesis (denoted arbitrarily $g$ here):\n",
"\n",
"$$\n",
"L(\\mathcal{D} \\mid g) =\n",
"\\prod_{n=1}^{N} P(y_n \\mid {\\bf x}_n) =\n",
"\\prod_{n=1}^{N} \\theta(y_n \\; {\\bf w}_g^T {\\bf x}_n)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now finding a good hypothesis is a matter of finding a hypothesis parameterization ${\\bf w}$ that maximizes the likelihood.\n",
"\n",
"$$\n",
"{\\bf w}_h =\n",
"\\underset{{\\bf w}}{\\operatorname{argmax}} \\; L(\\mathcal{D} \\mid h) = \n",
"\\underset{{\\bf w}}{\\operatorname{argmax}} \\; \\theta(y_n \\; {\\bf w}^T {\\bf x}_n)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Maximizing the likelihood is equivalent to maximizing the log of the function since the natural logarithm is a monotonically increasing function:\n",
"\n",
"$$\n",
"\\underset{{\\bf w}}{\\operatorname{argmax}} \\; \\ln \\left( \\prod_{n=1}^{N} \\theta(y_n \\; {\\bf w}^T {\\bf x}_n) \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can maximize the above proportional to a constant as well so we'll tack on a $\\frac{1}{N}$:\n",
"\n",
"$$\n",
"\\underset{{\\bf w}}{\\operatorname{argmax}} \\; \\frac{1}{N} \\ln \\left( \\prod_{n=1}^{N} \\theta(y_n \\; {\\bf w}^T {\\bf x}_n) \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now maximizing that is the same as minimizing its negative:\n",
"\n",
"$$\n",
"\\underset{{\\bf w}}{\\operatorname{argmin}} \\left[ -\\frac{1}{N} \\ln \\left( \\prod_{n=1}^{N} \\theta(y_n \\; {\\bf w}^T {\\bf x}_n) \\right) \\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we move the negative into the log and the log into the product we turn the product into a sum of logs:\n",
"\n",
"$$\n",
"\\underset{{\\bf w}}{\\operatorname{argmin}} \\;\\frac{1}{N} \\sum_{n=1}^{N} \\ln \\left( \\frac{1}{\\theta(y_n \\; {\\bf w}^T {\\bf x}_n)} \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Expanding the logistic function,\n",
"\n",
"$$\n",
"\\underset{{\\bf w}}{\\operatorname{argmin}} \\;\\frac{1}{N} \\sum_{n=1}^{N} \\ln \\left( 1 + e^{y_n \\; {\\bf w}^T {\\bf x}_n} \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we have a much nicer form for the error measure known as the \"cross-entropy\" error.\n",
"\n",
"$$\n",
"E_\\text{in}({\\bf w}) = \\frac{1}{N} \\sum_{n=1}^{N} \\ln \\left( 1+e^{-y_n \\; {\\bf w}^T {\\bf x}_n} \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is nice because it can be interpreted as the average point error where the point error function is\n",
"\n",
"$$\n",
"e(h({\\bf x}_n), y_n) = \\ln \\left( 1+e^{-y_n \\; {\\bf w}^T {\\bf x}_n} \\right) \\\\\n",
"E_\\text{in}({\\bf w}) = \\frac{1}{N} \\sum_{n=1}^{N} e(h({\\bf x}_n), y_n)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So to learn a hypothesis we'll want to perform the following optimization:\n",
"\n",
"$$\n",
"{\\bf w}_h =\n",
"\\underset{{\\bf w}}{\\operatorname{argmin}} \\; E_\\text{in}({\\bf w}) =\n",
"\\underset{{\\bf w}}{\\operatorname{argmin}} \\;\\frac{1}{N} \\sum_{n=1}^{N} \\ln \\left( 1 + e^{y_n \\; {\\bf w}^T {\\bf x}_n} \\right)\n",
"$$"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Learning Algorithm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The learning algorithm is how we search the set of possible hypotheses (hypothesis space $\\mathcal{H}$) for the best parameterization (in this case the weight vector ${\\bf w}$). This search is an optimization problem looking for the hypothesis that optimizes an error measure."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is no nice, closed-form solution like with [least-squares linear regression](http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse) so we will use [gradient descent](http://en.wikipedia.org/wiki/Gradient_descent) instead. Specifically we will use batch gradient descent which calculates the gradient from all data points in the data set."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Luckily, our \"cross-entropy\" error measure is [convex](http://en.wikipedia.org/wiki/Convex_optimization) so there is only one minimum. Thus the minimum we arrive at is the global minimum."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gradient descent is a general method and requires twice differentiability for [smoothness](http://en.wikipedia.org/wiki/Smooth_function). It updates the parameters using a first-order approximation of the error surface.\n",
"\n",
"$$\n",
"{\\bf w}_{i+1} = {\\bf w}_i + \\nabla E_\\text{in}({\\bf w}_i)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To learn we're going to minimize the following error measure using batch gradient descent.\n",
"\n",
"$$\n",
"e(h({\\bf x}_n), y_n) = \\ln \\left( 1+e^{-y_n \\; {\\bf w}^T {\\bf x}_n} \\right) \\\\\n",
"E_\\text{in}({\\bf w}) = \\frac{1}{N} \\sum_{n=1}^{N} e(h({\\bf x}_n), y_n) = \\frac{1}{N} \\sum_{n=1}^{N} \\ln \\left( 1+e^{-y_n \\; {\\bf w}^T {\\bf x}_n} \\right)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll need to the derivative of the point loss function and possibly some abuse of notation.\n",
"\n",
"$$\n",
"\\frac{d}{d{\\bf w}} e(h({\\bf x}_n), y_n)\n",
"= \\frac{-y_n \\; {\\bf x}_n \\; e^{-y_n {\\bf w}^T {\\bf x}_n}}{1 + e^{-y_n {\\bf w}^T {\\bf x}_n}}\n",
"= -\\frac{y_n \\; {\\bf x}_n}{1 + e^{y_n {\\bf w}^T {\\bf x}_n}}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the point loss derivative we can determine the gradient of the in-sample error:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\nabla E_\\text{in}({\\bf w})\n",
"&= \\frac{d}{d{\\bf w}} \\left[ \\frac{1}{N} \\sum_{n=1}^N e(h({\\bf x}_n), y_n) \\right] \\\\\n",
"&= \\frac{1}{N} \\sum_{n=1}^N \\frac{d}{d{\\bf w}} e(h({\\bf x}_n), y_n) \\\\\n",
"&= \\frac{1}{N} \\sum_{n=1}^N \\left( - \\frac{y_n \\; {\\bf x}_n}{1 + e^{y_n {\\bf w}^T {\\bf x}_n}} \\right) \\\\\n",
"&= - \\frac{1}{N} \\sum_{n=1}^N \\frac{y_n \\; {\\bf x}_n}{1 + e^{y_n {\\bf w}^T {\\bf x}_n}} \\\\\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our weight update rule per batch gradient descent becomes\n",
"\n",
"$$\n",
"\\begin{align}\n",
"{\\bf w}_{i+1} &= {\\bf w}_i - \\eta \\; \\nabla E_\\text{in}({\\bf w}_i) \\\\\n",
"&= {\\bf w}_i - \\eta \\; \\left( - \\frac{1}{N} \\sum_{n=1}^N \\frac{y_n \\; {\\bf x}_n}{1 + e^{y_n {\\bf w}_i^T {\\bf x}_n}} \\right) \\\\\n",
"&= {\\bf w}_i + \\eta \\; \\left( \\frac{1}{N} \\sum_{n=1}^N \\frac{y_n \\; {\\bf x}_n}{1 + e^{y_n {\\bf w}_i^T {\\bf x}_n}} \\right) \\\\\n",
"\\end{align}\n",
"$$\n",
"\n",
"where $\\eta$ is our learning rate."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we'll get the dependencies out of the way."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import itertools\n",
"import random\n",
"import time"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For pretty visualization we'll define some custom [color maps](http://matplotlib.org/api/cm_api.html)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"cdict = {'red': ((0.0, 0.0, 0.0),\n",
" (1.0, 1.0, 1.0)),\n",
" 'green': ((0.0, 0.0, 0.0),\n",
" (1.0, 0.0, 0.0)),\n",
" 'blue': ((0.0, 1.0, 1.0),\n",
" (1.0, 0.0, 0.0))}\n",
"BinaryRdBu = matplotlib.colors.LinearSegmentedColormap('BinaryRdBu', cdict, 2)\n",
"cdict = {'red': ((0.0, 0.9, 0.9),\n",
" (1.0, 1.0, 1.0)),\n",
" 'green': ((0.0, 0.9, 0.9),\n",
" (1.0, 0.9, 0.9)),\n",
" 'blue': ((0.0, 1.0, 1.0),\n",
" (1.0, 0.9, 0.9))}\n",
"LightRdBu = matplotlib.colors.LinearSegmentedColormap('LightRdBu', cdict)\n",
"cdict = {'red': ((0.0, 1.0, 1.0),\n",
" (0.4, 0.7, 0.7),\n",
" (0.5, 0.0, 0.0),\n",
" (0.6, 0.7, 0.7),\n",
" (1.0, 1.0, 1.0)),\n",
" 'green': ((0.0, 1.0, 1.0),\n",
" (0.4, 0.7, 0.7),\n",
" (0.5, 0.0, 0.0),\n",
" (0.6, 0.7, 0.7),\n",
" (1.0, 1.0, 1.0)),\n",
" 'blue': ((0.0, 1.0, 1.0),\n",
" (0.4, 0.7, 0.7),\n",
" (0.5, 0.0, 0.0),\n",
" (0.6, 0.7, 0.7),\n",
" (1.0, 1.0, 1.0))}\n",
"HalfContour = matplotlib.colors.LinearSegmentedColormap('HalfContour', cdict)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll define our [logistic/sigmoid function](http://en.wikipedia.org/wiki/Logistic_function) using the latter definition since it uses only one exponentiation.\n",
"\n",
"$$\n",
"\\theta(s)=\\frac{e^s}{1+e^s}=\\frac{1}{1+e^{-s}}\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"logistic = lambda s: 1.0 / (1.0 + np.exp(-s))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Data Set"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this example we'll create a toy data set."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To visualize this properly we'll set the input dimension size to $d=2$. For now we'll keep it linear ($\\phi({\\bf x})={\\bf x}$)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d_x = 2\n",
"\n",
"phi = lambda x: x\n",
"d_z = len( phi( np.ones((d_x+1,)) ) ) - 1"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For our data set we'll generate $N=100$ points."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = 100"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll define our input distribution $P({\\bf x})$ to be uniform within the intervals $\\left[-1, 1\\right]$ for visualization purposes. Note the homogeneous representation with $x_0=1$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"P_x = lambda: np.array( [1.0] + [np.random.uniform(-1, 1) for i in range(d_x)] ) # simulates P(x)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we need to create a fake, linear, noisy target $P(y\\mid{\\bf x})$. The target distribution is parameterized by a \"target function\" $f$ which will be drawn randomly from our hypothesis set (linear logistic probability models). The weights are randomly chosen for good visual effect (thus the `hardness` measure)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def generate_target(d, hardness=20.0, offset_ratio=0.25, w_f=None):\n",
" \n",
" # randomize target weights\n",
" if w_f is None:\n",
" w_f = np.array([np.random.uniform(-hardness * offset_ratio, hardness * offset_ratio)] +\n",
" [np.random.uniform(-hardness, hardness) for i in range(d)])\n",
" \n",
" # create target distribution simulator\n",
" f = lambda z: logistic(w_f.dot(z.T))\n",
" P_f = lambda z: ( np.array([np.random.uniform() for i in range(z.shape[0])]) <= f(z) )*2.0-1.0\n",
" # \"*2.0-1.0\" to scale from [0, 1] to [-1, 1] which are our actual label values\n",
" \n",
" return w_f, f, P_f"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w_f, f, P_f = generate_target(d_z, hardness=12.0)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With our target distribution we can generate our toy data set. Note that $\\mathcal{Z}$ is the same as $\\mathcal{X}$ in this linear example."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def generate_data_samples(N, P_x, phi, P_f):\n",
" \n",
" # create samples in our input space (x-space)\n",
" x = np.array([P_x() for i in range(N)])\n",
" \n",
" # transform x-space samples to z-space samples\n",
" z = np.apply_along_axis(phi, 1, x)\n",
" \n",
" # produce classification labels from target distribution\n",
" y = P_f(z)\n",
" \n",
" # create function to calculate cross-entropy error from a hypothesis weight vector\n",
" cross_entropy_error = lambda w: np.mean(np.log(1 + np.exp(-y * w.dot(z.T))))\n",
" \n",
" return x, z, y, cross_entropy_error"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x, z, y, cross_entropy_error = generate_data_samples(N, P_x, phi, P_f)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's visualize our data set. For our pretty fills and contours we need to define the entire grid to some level of detail. Here we'll use $s=300$ meaning 300 points per axis."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def generate_fill_data(s=300, phi=lambda x: x):\n",
" # create grid of points\n",
" x_1, x_2 = np.array(np.meshgrid(np.linspace(-1, 1, s), np.linspace(-1, 1, s)))\n",
" \n",
" # reshape the grid to an array of homogenized points\n",
" x_grid = np.hstack((np.ones((s*s, 1)), np.reshape(x_1, (s*s, 1)), np.reshape(x_2, (s*s, 1))))\n",
" \n",
" # transform homogenized points into z-space\n",
" z_grid = np.apply_along_axis(phi, 1, x_grid)\n",
" \n",
" return x_1, x_2, x_grid, z_grid"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def apply_to_fill(z_grid, func):\n",
" s = int(np.sqrt(z_grid.shape[0]))\n",
" \n",
" # calculate function at each point on the grid and reshape it back to a grid\n",
" return np.reshape(func(z_grid), (s, s))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x_1, x_2, x_grid, z_grid = generate_fill_data(300, phi)\n",
"f_grid = apply_to_fill(z_grid, f)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll plot our data set along with the background probability from the noisy target. Red points are classified as $+1$ and blue points are classified as $-1$. The background color denotes the probability of the data generating distribution. The black line is the decision boundary where the probability is equal to $0.5$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_data_set_and_hypothesis(x, y, x_1, x_2, f_grid=None, title=''):\n",
" start_time = time.time()\n",
" \n",
" fig = plt.figure(figsize=(6, 6))\n",
" ax = fig.add_subplot(1, 1, 1)\n",
" ax.set_aspect(1)\n",
" ax.set_xlabel(r'$x_1$', fontsize=18)\n",
" ax.set_ylabel(r'$x_2$', fontsize=18)\n",
" if not title == '':\n",
" ax.set_title(title, fontsize=18)\n",
" ax.xaxis.grid(color='gray', linestyle='dashed')\n",
" ax.yaxis.grid(color='gray', linestyle='dashed')\n",
" ax.set_axisbelow(True)\n",
" ax.set_xlim(-1, 1)\n",
" ax.set_ylim(-1, 1)\n",
" ax.autoscale(False)\n",
" \n",
" if not f_grid is None:\n",
" # plot background probability\n",
" ax.pcolor(x_1, x_2, f_grid, cmap=LightRdBu, vmin=0, vmax=1)\n",
" \n",
" # plot decision boundary\n",
" ax.contour(x_1, x_2, f_grid*2-1, cmap=HalfContour, levels=[-0.5, 0.0, 0.5], vmin=-1, vmax=1)\n",
" \n",
" # plot data set\n",
" ax.scatter(x[:, 1], x[:, 2], s=40, c=y, cmap=BinaryRdBu, vmin=-1, vmax=1)\n",
" \n",
" print('Plot took {:.2f} seconds.'.format(time.time()-start_time))\n",
" \n",
" return fig"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"target_fig = plot_data_set_and_hypothesis(x, y, x_1, x_2, f_grid,\n",
" title=r'Target, $N={:}$'.format(N))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 5.81 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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aru3bh6hTzeK7f1yuHCQNSle+uABN9r2xPOuSIgzoYqNxJKchO1w+9akfpTzS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nx0WQAllneTBYOJ8kEwfLmAoNehS07AnZGN1+EimgE9EgiOHT9G227teKLvQJ4a8FSUMAm/ESAf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\nwv8DR3Yqo1T5RX4AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x37a9950>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Learning a Hypothesis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's initialize our hypothesis parameters to zero and perform gradient descent with a learning rate of $\\eta=10.0$. We'll continue iteration for a maximum of $\\text{10,000}$ iterations or until the change in the weight vector's norm is smaller than $0.1\\%$, which ever comes first. As a reminder, our update rule is\n",
"\n",
"$$\n",
"{\\bf w}_{i+1} = {\\bf w}_i + \\eta \\; \\left( \\frac{1}{N} \\sum_{n=1}^N \\frac{y_n \\; {\\bf x}_n}{1 + e^{y_n {\\bf w}_i^T {\\bf x}_n}} \\right)\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def gradient_descent(z, y, w_h=None, eta=1.0, max_iterations=10000, epsilon=0.001):\n",
" if w_h == None:\n",
" w_h = np.array([0.0 for i in range(z.shape[1])])\n",
" \n",
" # save a history of the weight vectors into an array\n",
" w_h_i = [np.copy(w_h)]\n",
" \n",
" for i in range(max_iterations):\n",
" subset_indices = range(z.shape[0])\n",
" # subset_indices = np.random.permutation(z.shape[0])[:N/8] # uncomment for stochastic gradient descent\n",
" \n",
" grad_E_in = np.mean(np.tile(- y[subset_indices] /\n",
" ( 1.0 + np.exp(y[subset_indices] * w_h.dot(z[subset_indices].T)) ),\n",
" (z.shape[1], 1)).T * \n",
" z[subset_indices], axis=0)\n",
" \n",
" w_h -= eta * grad_E_in\n",
" w_h_i.append(np.copy(w_h))\n",
" \n",
" if np.linalg.norm(grad_E_in) <= np.linalg.norm(w_h) * epsilon:\n",
" break\n",
" \n",
" return np.array(w_h_i)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w_h_i = gradient_descent(z, y, eta=4.0)\n",
"w_h = w_h_i[-1]\n",
"print('Number of iterations: {:}'.format(w_h_i.shape[0]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of iterations: 73\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we'll visualize the final hypothesis $g$ in the input space $\\mathcal{X}$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = lambda z: logistic(w_h.dot(z.T))\n",
"h_grid = apply_to_fill(z_grid, h)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"full_N_fig = plot_data_set_and_hypothesis(x, y, x_1, x_2, h_grid,\n",
" title=r'Hypothesis, $N={:}$'.format(N))\n",
"target_fig.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 5.42 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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aru3bh6hTzeK7f1yuHCQNSle+uABN9r2xPOuSIgzoYqNxJKchO1w+9akfpTzS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nx0WQAllneTBYOJ8kEwfLmAoNehS07AnZGN1+EimgE9EgiOHT9G227teKLvQJ4a8FSUMAm/ESAf\nJi6RnMxLh4nSGaK6xKVKVexU5oGiwiTanVe+z4ePHKZtt3Y8M+gZBvR9QlGeRb6tQLsgCFhTdLgu\nwET+vAsKEzVfokpVcajMA6WsKhQmhaeDhw7SoXtHnhvyHI/1fLxQYwsCWMvpcDlEcrM8kSuoKtP6\n99/T/PDDtzidDpo1a0n16rWKu0uqLkFl/jkUr+KXQ17qFtFYzU4kdnMZ9OiSEnCnZ+N1usLWi3Z2\nsv/Afjp078jLL7xMz669wtaJHC/oHDRgTdHnwyQ4VqTzDokXwSYdN7Kv8vpyUmcnSjR79le88sow\noC1ebxwazSK6d+/F22+/L/sOP1VFI/XBRgkpB0rRw0TZICkFEwO6pHjc6Vl4ne6w9aJdpvrr77/o\n1PNhRr00im6du8v6BbYXDUwMOO1ebNkFhUl0yXlpv8j+yurLSR0IlejIkf+jWbMm2O2bgBoXStOw\nWO5iwoTRtGjRvji7d9lLfbCxwCp8mFzcVivtEw1M/GMJRh9MXGmBMBFl6oV+lrft+XMPHR/txFuv\nvh0RJmIE28V++MoEDSSWM+C0ewoIE4HCg0lorHBSYRIbLVw4C4+nFxdhApBMbu4LfPXVzOLqlqpL\n1GUOlNjAJJxPtDDJLzEa0CX6YCK63JI+ypPkgbadu3fycK/OjHlzLJ3bdw4bIzKcAtsTNGAtZ8Ce\n68GW7ZXsT2SYBOrSYBJZTqeT7ds3s/fPXVHcpakwiUbp6Rm4XBUkLOXJyMgs8v6UFdlsuRw6dIDs\n7Kxiaf8yBkpxwyTwTlkeJgKCyXgBJpkyMAk/+8j7LGXb9sc2HunThQ/f/Yj2rdsrmH2Eg1PgsaC9\nCBN7jjRMCKonFctfsYbJt9/OpW69KnTr/hQdOjzCrbfWZdeubRFqqTCJVs2aPUBc3DwCfzIXjMY5\ntGjRrHg6VYrl9Xp5553XqFv3Glq0eIh69SrzwgtDcTqdRdqPyzSHcikwKdzke6AtdHDWmAxorXG4\nUjMR3R7kBvfgMiUg+H3b7zzavyfjx02gxf0tCpAjkT/WaAWsKXpsOR4cueFgEnnpK9QmbZf2C+/r\nrx07fqfzIx2x2b4Hbr4QaT4JCUPZsmUfiYlJErVUmBREXq+XTp1asXu3Brt9OBCHwfAF5cr9wk8/\nbSYpKbm4u1iqNGbMm0ydugqbbTZwLf/f3pmHN1Gtf/wzWdp0C1DEguyyyF5c+KEiiwIiIhWQTdlE\nVBDQexVxw+vGFQEFl4uCIMqiUMDLLiiIIC4gCFdBQECkQNlpoXuSJpnfH6WlSWaSSUibNj2f58nz\nZM55z3veTKfzzTnvORM4i8n0KElJtXnvvY/89ieS8gooC0p4iUmgU14//7KNoSOHMvO9WXTp1MVP\nMfE+stLpJcxVjeRlB0dM/BGIQMUEYMSjw1i//kZk+WmX8qioB3n55XYMHz7Gb58CdaxWK3PnzmDR\nomRsNis9evTgySfHER9/TahDK1fYbDaaNatJbu52oEGxmnQiIxuwe/cRqlSJ98tnufoJ4NBRdsRE\nXQgKjnVRkejjojSKiX+jiq0/beWRMSP4ZMZcOt7RUcPoQ7uY6A0ScfFG8rIcWPNKT0z8+ZuptT96\nNAVZ9tx3k5fXmpSU4377FHgnMjKS0aPHMXr0uFCHUq5JT7+A02nAVUwA4omIqEdqaorfghIoFSSH\non1lT5kSk7RMZLuT4IhJwTnYvHUzw0c/wrxZ81TExN98THEx0WGON5Kb5cCiUUzUkvKu9sr16nbq\ntt7at27dCr3+O4/6mJjvaNWqpV8+BYKSJisrk/3796DT6dDp7MDfbhYXsdlSqFmzbqnFVEEEpfyg\ni45EH3tZTBzOoPre8N0GHnvqcRbOWUi7W+8AID09jS0/bGHfgX0BDXEL0RsKHqeSk+nAlhfcuEuL\nMWOeIjJyFrAQyAcy0etfwWxOoUePviGOTiAowG63M2HCeFq1qkuvXg/Rtm0Tate+HpNpCJB62eo8\nJtPDJCUNID6+aqnFVgEERfvIJFijE09fat/SXUcbuugo9DFR2NILxUT7iipfo5N1G9Yz+pkxLPp0\nEbf93+3IsswbE1+m9c03MO2xQTzY807uvqstx1OPq/pwfX8lNp2hIAGfk2nHZnEq2qiPqDzLletK\ndnQCcP31jVi6dDXNm8/BYKiEwVCDjh0PsHbtJkymKM0+BYKSZNKkV0lO3oXVeoDs7D+wWv/m2LFa\n1K6dj8nUipiYxkRGNqJ379pMnfp+qcZWAZLyp33aqZ8AX9NYnjb+JOCLl+liotBHm7ClZ4LDfZoL\nH8fep71Wr1vNuAnPsmTeEm5MvAmATxfMZcEbL7EuN5cEwAFM0+lYWKceW3/agyTpVP0VR2+UiKti\nJDvDjs1aGJ32zx3c1Vze7X23vUJ2dhZ6vYGoqCjNPgWCksZqtdKs2XXk5e0Gik9lXSQy8np++OE3\nLBYLCQk1iIszB9yP2CkfICUjJp7fqNVHFcXEJE1JTDxHMv6IyfLVy3n25fF8ufC/RWIiA598OJ3p\nl8UEQA+Mdzrh/Dm2/fKzqr/ilC0x0ZYnUx+JuhIbGxeQmGRmZnDgwF4yMi751U4g0EJ6+gVkOQJX\nMQGoQkREXS5eTKNhwxuuSkyuhgotKCUnJmptPZf66mKj0UdFYkvLAKdyAl7dh/cpryXLl/Li6y+x\n/IvltGrRyqXuxPlztFT4RC2A1JMnVMUkJzeHBYs+Y/anMzFE2TmdelFRTNSS7SUnJr7x//uWdjHJ\nz8/nhReeJjGxLvffP5DWrevxzDNjsFqtfvcqEKhRtWo19Ho7cNit5gI2Wwq1a9cPRVhFVFhBCVxM\nfI8+vNUVP9bHRqMzRRRMczllvIuFuw/vK7MWLV3Ea5NeY+XiVTRv2sJFdGSgVeOmbHSL1QZsdTpo\n2SJRsa/jJ45x8603s2FTKiMef5x+/d6jaYum/L5nN8qigUp5WRcT7asCC3njjQksW7Yfq/Ug2dn7\nsFr/YuXKE0yY8KxffgQCb0RERDBy5D+JihoCHLlcmkpU1GD69h0a8g2hFTKHEqzku2u9Wp3yDVUf\nF40UaSTfh5i49+1tGqrweP6i+Ux9721WLF5JwwaNFNrDlq2bGfVwfz6x5NGdgrUhz0SasN3WnvmL\nViv6T+rbh9i4wSxY8CD9+sHWrQDJ1K79b3Zt340kSRqWAAe2NNhfW+/tvOF/viQvL5fmzWthsewF\naharuUBkZCN+/z0Fs7mS334FAiWcTifTpk3i44/fR5ZNyHIOgwY9yiuvvInRaAxKHyKHopHSEBP3\nKSh32yIxSdMiJgXfln2t5Co8/mTBXN7+4B1WL13jIibuI52OHe7ivdmfM6F+A0w6HYmmKKo/OIxZ\nc5d4+AfIys4ivmokCxYMpHfvQjEBGEBaWg4HDx0oMTFRznuUDTEBOH/+LDpdHK5iAnANRmN1Tp9O\nVWomEASETqdj/PiX2bcvla1bf2LfvpNMnDg1aGJyNVSoEUppiYm3G6reHI1kNJCfngWybzHxZ5Qy\nc+4sZs6dyerkNdSpU1fVh3vseRYLERGR6HQ61Sk6mz0PfWQ+SUlV+OUX1wcsxMY2Z+V/P6NVyxu9\nfnblcuV6dTt1W21t1Qh8JZfFYqF585oKK2/OYDI1Zc+e48TGxgXsXyAobcQIpRygN8e4iUnw+GDW\nB8z+bDZrl62lbp26vhsUw2QyodOpXwoRJh0J11VizOjn+OWXpW61P2M0ZNKsqXuKv+JgMpl45JEx\nREUNBlIulxbMaz/44KNCTAQVhgrxLC9/EvCe9tr2mfj6Jq6vFItk0BfkTGSltoGPTqb9ZzqLli1i\nzbI11KxRS8WH76XHStN0ESYdMWYDmel2Hh0+gnXre2Oz7cNu74ROt4vIyHd5d/qHGAwGlfOhfk6U\n6tTtfNv7bqvG1e8zeeGFV5Ekiblzb0aSYpDlbAYPfpx//evfV+1bICgvhP2Ul0N1Y2Npikkckl5H\n/sVAxETdVpZh8rtTWLFmBauSV1E9oYaqj0AS/MXFxG4vsPj76BFmfjyT//22j0YN6/HEyFG0bNla\n5XyonxOlOmUb3/ba2wfuUysWi4Xz589wzTUJl/exCATlD/H4egXUBSV4+0zUb/wF6CvHIemkgmmu\nYnbeRg7ehKDwWJZh4tv/Zv2G9axcvIprq10bFDEptI2M0hEVZyArPR+73bWt5+cM3tLgqxmVqLdX\nI7hiIhCEC+Lx9ZopPTExVI4DSU1M/J/yKi4mr056je+2fsfqJWuoWvUaDWLirT9lMclMy8fh8P4Z\ny4qYBPBdyu8WAoHAOxVMUEpLTCQMVQoSsfkXr1ZMXOtkGV58/SW27djG6iVr3DYyqYuJtlEKREbr\niYrRh7GYCCERCEqKsF/l1euBPnzx3//iUHgUvOeNTptoaBITWfYqJrLCcaGt+/vCY6dT5tmXx7Nz\n105WLV59WUykotcVf4GJialQTNJ9iYnkpdwVX2Iie9io2yohxEQgKDuEvaA8uG0bHz7/HINHDHeZ\nE9Ryo3Ov0/Lt3BAfhyzL5F/KdrFTnmbSnj9xOmWeeWkcf+z/g/9+sRxzpUr4K05exSRGjylGT4bP\nkYn2EZz2c+yOEBNB+LBlyzckJd1Dq1YN6dcvie3bt/puVE4Jf0EBvs/N5Y8ff+K7H38ErlZMVL6d\nSxKGeDOyU8auSUw8/aq9dzicPDn+KQ4ePsiyhV9efoyHf+Lk2p+rbVSsHlN0gZg4nd7a+DsdqFyv\nbKNuq4QQE0F5IDl5PiNGPMavvw7hwoV1/PRTLwYNGsj69StDHVqJEParvAo/3FvA2YeHM33SW0EQ\nFDdbScJQxYzscGDPyPHwfTWCYrc7GDNuDKfOnGbxZ4uJiY4NyJ9r/ZW2UbF6IkwF01xOl1lB5TYe\nn12hTgiKQAA2m42WLeuSlbUeaF2sZjMJCSPZtetPrxuKQ4nYKe+DXJ2OyMjIkhGTeHcx8Ta95D5N\nVVCm9D4/387j/xjJuQvnSZ635KrERGlaLCpOT4RJ5yYmSiMwb9NZQkwEAiWOHDmILFfCVUwAOpGR\nkcGZM6dCEVaJUiEE5RzwaWQkffv0KVaq7SapSUzyC8VE/WasnOMoKFMSApstnxFjHyUrK4tFcxcT\nHRWtQZw8E/K41RUeR8fpiYjUkZlmV5zmcu/DtcybffE6dTH57bedPDx8EG1vvZlBgwawY8fPHrZK\nCDERlBfM5krk56dR8MMQxcnG6cwjJiY2FGGVKGEvKC/p9bQ2mXjs8ZHc1LLV5VJtN0k1gSkSk6qV\nkPPt2DNzlG18JuSVxETCarUx7ImHybfbWTjnc0wmk0Z/njErjWKizXqMEZfFRPa0d49f+XxoFxp3\nm02b1tHngSQ2bLiV48c/4bvNdzHwwf6sWu3+nDDl9toQYiIILTVr1qFp05bo9dOLlcoYDBNp1+5u\nKlWqHLLYSoqwz6G8OGYsD9zfi9YtWhSWutj4s3rJJQFftRKyNR97Vq6CjT+jFNc6i8XCkMeHYjKZ\n+GTGXIwREYp26n157y/GbEBvlMhKVxaTK2g7T77audvIsszNt7Tg9On3gbuLWWynSpX+7N3zN3q9\n3ot/LQgxEZQNUlOP0bv3PWRkVMFma4PR+CMJCTIrVqynWrUE3w5ChHj0igKSJGE/daZ4iUt9QGKi\n0xVMc1ls2LPzFGy0iomnXW5eLoMfHULlypWZ9d7HGIxGP/y5xqwoJpUM6A2+xER78l2tb282p06l\n0u6ONlgsZzzsY2Iase6rlTRu3EzFvxaEmAjKFna7nc2bv+bo0cM0btyMDh26ltlkfCHi0SteCWSF\nkrKYGOPNOCw2HF7ExPdIwbNdTm4OA4c/SPWEGnw0/SP0ik/vvUox0UtkptuLPTm/dMUEICoqGqfT\nAliA4g9PzMduzyC62LyymOIShAMGg4GuXe8LdRilQtmWyaCgfSWXuphIoNNjrFoJR54WMfFnlZdE\nVnYWfYf0o3at2sx8d6aLmPjOx/jqD2IrG9DpJTIvahcTtfPhWedZr2xTQJUqVQBibpUAABaDSURB\nVLn55vbo9W+7lOt0H9KoURNq1azjFpcWhJgIKg4Oh4OPPprOjTfeQP36Zu69tzPbtn0f6rCACjHl\nddalzOsIRLFcKhiZVDXjyLXgyLEq+PM++vD2PiMzg35D+9P0hqZMf+tdJJ3OD3++62MrG5B0BSMT\n98/o+1y41mmpV7ZxtT158gRJ999NZmZ1cnLaER29k+jov1i18hvq128oxEQg8MK4cWNZufJ38vLe\nAW4A1mIyjWPhwmTatbszKH2IHIoC7oLi/QaqsmRWf3maK8eCI9eq2i6QKa+MjAz6DH6AGxNvYurE\nqSApjzS0+fc8jq1sRJIg82LZEZNC8vPz+eabVRw+fID69RvRvXtvhX1CvhBiIqhYnDx5gjvuSMRq\nTQHMxWqSadlyFt98syUo/YgcSklQJCZ5l8UkeDew9Ivp9B7Uh9vb3s6br0xy2dUfDOKqFPxps1zE\npOxgNBq5776+oQ5DIChX7NnzKxERd2C1mt1qkti/f1hIYipOBcih+MqPuJYVlev1BdNc2a5iouTL\n3xzKhbQL9ByQRMd2Hd3ExHuuRSlmpf7iqhiQZYmsi3YveRa1c+HlnCj4UrdR96WGGJ0IBN6pWvVa\nnM6/8fxv+RuzOfTLkMNeULznR1zLisoNhgIxycrDkecqJu6+/M2hnDt/jp4DkrinS3dee+l1n2Ki\nLE7q/cXFG5FlyL7kLibqn9uXWASymsuXvfb2gfsUCMKNNm1uJz4eJGkWV/5rcjGZxjF8+OOhDA2o\nAIJSgOtN0tsqL8lgKJjmysxVERP/VnAVrztz9gz39e/J/T3uZ8L4CRrFBMU6j2MJzPFGZIdM9iWH\n4kjGnwUJhWRmZXLxYrpqvaeP4r583/jVVoOpI8REUHGRJInFi1dw3XUfEBt7I7Gx/TGZ6tGlS3X+\n8Y/nQx1e+Cfl80+dcynztjpKMugxxJtxZObgsNhQFhPXNt7eFz8+efokSQPu56F+D/HMk+M0J+41\nJeAlMFcx4nDI5GQoiwluZd7KAY4d+5sn//kUu3f/AOho0KAF09+Zxk03tXWxUxcT3wSwhsTvFgJB\nOOJ0Otm+fSvnzp0mMbEN9es3DKp/scpLAXdB8SomRj2GKmbsmTk4vYiJViEofnw89QRJA5MYPvgR\nnhr1VEDLi9X6lqSCaS5HvkxOpjcx0T6NlZOTzf/dmkj6xSdwOp8CjMASYqKf5rtNP1O37vUKPpR9\nqSFGJQJB2UU8vt4L3qd7JCSjoUBMMrI1iIl/U17Hjh/jvv73MXL4yBIQE4m4eCP2IIqJDHy5fDG5\neTfidD5PwW52AzAIq20Esz7+0Ms0lRATgaAiE/aC4n26p1BM4grExJqPbzHB41gtkf53yt/06H8f\nT416ilEjntCUZ1F6ryYm5qoG7LbgignAnj37yM3tiDt2eyf+99s+j3IlX2oIMREIwpewF5QClJLy\nElJEgZjkX8rGabWjRUy0CsHhI4fp2T+JZ58az4ihj2pcvaWWP3Etk3QFYpJvlcnJchTz5T3no0VM\nABo1qo/JtBt39PpdNG5U361UW/LdvY9CUlOP8cILT9Ohw23069eLb7/9SjE+gUBQ9qkgguKJFGHA\nUDkO+6UsZFt+UH3/eehPkgbcz4vjXmTYQ8OC6lvSgTnegM0ik5vlCKrvQvr1HYzRuAFI5ooM/EhE\nxPuMHPlE0Pr566+DdO58G4sWmfjrr2n89NMDjBr1NO++OzlofQgEgtIj7JPytlPnXcpkQIqIwFA5\nFvulLJy2KyOTwvrLrYsda5/22vfnPh4Y3JfXX3qd/n0GBORDKQ4AdGCOj8BmcZCX7fTwpdbO8w/s\nexrst99/5bHHHyEtLQedZCIiMpfp096nW7ckVT/eULrIhg4dyKZNNyPLzxUrPUVkZHN+/fUQVatW\n0+xfIBAED7HKSwF3QZEBKTICQ6VY7BezcOYrTXNBoGKy54899B3aj7dem0yfpD5effgWLtf+JB2Y\nq0ZgyXVgyQmOmPgUGlnm0OEDWK1WmjVrVeyHr/ybjlK7wK6/vgoWyyHgWpfy2Nj7mTZtMD179vOr\nH4FAEBzEs7y8UHhagiEmakKw+/fdDHh4INMmTadn954afHgTJ9djnb5gZKImJt4XHniW+6orKpUk\nlx+78marhrdLMiIiGovlEu6CIkmXiIqK9qsfgUAQesI+h1KUgDdFFohJeqaKmCgnyc9eOM+kqZNI\nurczIx4ZxNaffvCw27l7J/2HDeD9Ke/Ts3tPzYl75TrXY51eKhCTnNIVE08777ZKbX19v+nb9yEi\nIiYCzmKlm4E/ad++i+a+BBWPlJQjrFu3nN9//zWgb9KCkiHsp7yspy6gM0WgN8cUiIm9cFWU970p\nAMdPnqBrtzu5JzubXjYrR4G3o6IZ9czzjB3zT0Bi245tDHl8KB9O/4i777o74ByJupgYyctxYM31\nJia+p74865Trle282/puq0x2dha9e99LSkoeOTk9MZn+Qqf7mnnzlnLHHXdp7k9QcbBarTzxxCNs\n2bIRo/F2HI4/qFPnGhYtWk716teFOrywQeRQFJAkifyLmejjfIuJ0vETox+j9poV/NtxZTVVKtAy\nMpL//XqAPw/9ycNPDOfj92dzV8e7AtirUtzOtV6nlzBXNZKX5cCad/ViolUglC+G4ItJoV+Hw8GW\nLd/w66/bqFYtgV69HiQ+vqpfXgQVh1deeZ7PP/8TiyWZgk23TgyGN2jWbAtff70lxNGFD0JQFJAk\nCafdTn56FrJPMfEUgvqNa7MzO4s6bn77xMTSYMRIFixeyKcffUaHdh38TLh7FxO9QUdcvIG8LAeW\nPKdLvVIb7eXK9ep26rba26sh9pkI/MNisdC06bVYrZOBvlzJvdmJiqrHN998S8OGTUIYYfggHr2i\nQn5aJrLdib9iAmA0GMhV8HnC6eST+XNZMHuBipho27SoJibmeAO5mYVi4rpxUG2aToiJIJzZufNn\nbrqpIVZrHeAbCn769g0KrjwDBsP1nD17OqQxCirAKi/ZcUVM/OWBPv2Y8vk8PrXZijy8D/xms7J8\nfjK3t20XrDAB0BskzPEGcjId2CxO3w0EggpAVlYmgwb1Ijt7HnDv5dKzwJ1AM6AjNtsemjZtFaoQ\nw4Ljx4/y7bdfYTAELgthLyi+ppe8jVyef+5lkn7cSoeTJ+iVk8N3RiMbnE5eeeFVOt1xp4oPfxLy\nV8p0RglzFSM5mXZsFjnAfSbBWs3l3V5bezXE6ETgH2vXfonTeQdXxAQgAXgNmE5U1DQeemikyL1d\nBVOmvMGsWR8AvdHpbAH7qQCCoi0BryQElcyV2LjxR9asX8uixQvYtvtXFn80l26d7/Fo518OxbU/\nvVEiroqR7Aw7+dZAxCQ0q7mU23tDiInAfy5cOIvVqvR7H43Q6Q4yfvy/ePzxp0o9rnDhhx82MXv2\nfKzW/VzJSy0IyFfY51CUcxqgdVRhNEbglJ3sPfQnX6/4WqOYeMuhuPbnS0zU8iPlS0xc80ACgT/c\neGNbIiO/AlyfXafXr6FPnwcYNeqf6HRhfysrMRYsWEBe3tO4bzAOhArwV9A+5aUkDIu/TOblif9i\n+RcraNGsZVA3LeojLovJJXUx0fI5ilNa+0z8E5PwxW63i411JUy7dnfSpEl1IiMHA4eAdOA/mEwz\n+Mc/ng1xdOWf9PRLQPWg+KoAgqK+osrXqOLzJZ8zccpEViWvplmTZgGs4FL3b4zQEVfZSNYlO/k2\nb2Lie5WXZ51yvbKdd1vfbdUI71HJd9+tp337NtStG0mjRtV4/fUXsVqtoQ4rLJEkiaVLVzN0aB3M\n5k5ERNShQ4fNrF69iQYNGoc6vHLP3XfficmUHBRfYb8PJfdUevESQNuo4tOFnzJ9xrusTF5Fg/oN\n/Ey4K9sVHhsjdcRWMpB1yY7dp5jgR7lyfaC23tt5I3yFBGDr1o08/PBQLJbZFCSKj2IyPUOHDjHM\nm7c41OEJBH6RnZ1F5863cfbsrdhsTwBWoJ3Y2OjOFUHxZ+WVxOx5c/jPx/9h1eLV1K9X38+EuzYx\nybxox55f6K3kxeRqVnIJMXGlW7dO7N07GuhfrNSCyVSXDRu20rDhDaEKTSAIiIsX05kxYxqrVq3C\nYDBw/PjvQlDcKRCUi0XHWkYVH835iI/nzWZ18hrq1K5zlcuCr15MtC8L9qxXt1O31dZWjfAXE4B6\n9eKw2VKBSi7lsbH9mTq1D716DQxNYAJBkBA75b2gNZH+3kfv8cmCuaxZutZFTNzbe/Phni8pLIsw\nFYhJRnqhmPjOjWgXE/V8hRCT4FO1ai1gv1upjCzv57rraoUipHKDw+EgOfkz7rvvbu66qz3vvjuJ\njIxLoQ5LECQqxD4ULbz9wTssXb6UNcvWcF31mkH1HWHSEWM2kJlux2EP2wFhhWHUqNFMnvw0eXlf\nAVUBJzrddKpV09OmTXCfnhBOyLLMY48N4fvvU8jLexYwc/ToZyxZ0p4NG37EbK7k04egbBP2IxRf\nK7NkGd6a9hZfrvySNUuviEnx0QnubdyO1abEAIxRV8TEXiQm/m5a9DU6UUaMTkqGESPG8OCD7YmM\nbIjZ3JXo6EY0aLCEJUtWIUkV61z4w44dP7J166/k5X0H9AG6YLV+wdmzLfnss5mhDk8QBMI+h5Jz\n6spwWklM3pjyBt98u4GVyauodk01lxu52ns1f+431ogoHVFxBjLT8rnyBHx/xcSVkl4aHEAazu8W\nZY38/HzWrVvOV1+tJzo6igEDBnLbbR19trtw4Rx79+6mWrXqNG+eGHZiIssyqanHkGWZ2rXrXfXn\nmzRpAjNmGIDX3Wo20Lz5m2zc+P1V+RcEj7DJoSxbtozmzZuj1+vZvXu3qt3XX39NkyZNaNSoEVOm\nTPHqU2lUIcvw8sR/8e2WTaxeuoZrgiQmhX1FRHsXkysxKfl1LfOsU65XtvNu672dL8r/DdRqtdK3\nbw/GjXuftWtvY9myhgwZ8givvvqCz7bXXHMtd955Dy1atA47Mdm9+xfatbuJjh1vo1On22nX7iZ2\n7dp+VT6jo6MxGDIUajKIjo65Kt+CskGZE5SWLVuyYsUKOnTooGrjcDgYO3YsX3/9Nfv372fx4sUc\nOHBA0VZpykuW4YXXXuTnX35mdfIat4fKeRcT31NeYIrWExXjXUyK9+dZXtbFJHw2LSYnf8Yff8jk\n5v4AjESWx5Gbu5PPP/+cP/74LdThhYTTp08yYEBPUlJexGI5icVykpSUFxk4MIlTp1ID9tur10AM\nhi+AlGKleURHv8PQoQ9dbdiCMkCZE5QmTZrQuLH33a87duygYcOG1KtXD6PRyMCBA1m1apWKtesN\n2+mUGTfhWXb9bxcrFq2kUuXKxex8i4m3fAyAKUaPKUZPZrovMdG2A951JONZ727risiX+GLp0uXk\n5Y0F9MVK47Fah7B27fJQhRVSFiz4hPz8/hTss9FdfvUnP38A8+fPCdhvvXoNmDDhdUymWzAan0SS\nJhAd3YLOnZvQu7cQlLBALqN06tRJ3rVrl2LdsmXL5EcffbToeOHChfLYsWM97LhyPxYv8RIv8RIv\nP16BEJJlw127duXMmTMe5ZMmTaJnz54+22udr5bDd72BQCAQlDlCIigbN268qvY1a9bkxIkTRccn\nTpygVi2xoUwgEAhCSZnLoRRHbYRxyy23cPjwYVJSUrDZbCxZsoSkpKRSjk4gEAgExSlzgrJixQpq\n167N9u3b6dGjB927dwfg1KlT9OjRAwCDwcCMGTPo1q0bzZo1Y8CAATRt2jSUYQsEAoEgoMxLGWXp\n0qVys2bNZJ1Op5rQl2VZXr9+vXzDDTfIDRs2lCdPnlyKEZYv0tLS5C5dusiNGjWSu3btKl+8eFHR\nrm7dunLLli3l1q1by23atCnlKMs2Wq61J598Um7YsKHcqlUreffu3aUcYfnC1/ncvHmzbDab5dat\nW8utW7eWJ06cGIIoywfDhw+Xr732WrlFixaqNv5em2ElKAcOHJAPHjzodYWY3W6XGzRoIB89elS2\n2WxyYmKivH///lKOtHwwfvx4ecqUKbIsy/LkyZPl559/XtGuXr16clpaWmmGVi7Qcq199dVXcvfu\n3WVZluXt27fLbdu2DUWo5QIt53Pz5s1yz549QxRh+WLr1q3y7t27VQUlkGuzzE15XQ3B38NSsVm9\nejXDhg0DYNiwYaxcuVLVVhYr6jzQcq0VP8dt27bl0qVLnD17NhThlnm0/u+Ka1Eb7du3p0qVKqr1\ngVybYSUoWjh58iS1a9cuOq5VqxYnT54MYURll7Nnz5KQkABAQkKC6sUkSRJdunThlltuYc6cwDe+\nhRtarjUlm9TUwHejhzNazqckSfz8888kJiZy7733sn+/+88MCLQSyLVZ7h5fX1p7WCoKaufzzTff\ndDmWJEn13P3000/UqFGD8+fP07VrV5o0aUL79u1LJN7yRKD7pcQ1qoyW83LTTTdx4sQJoqOjWb9+\nPb169eLQoUOlEF144u+1We4ERexhCS7ezmdCQgJnzpyhevXqnD59mmuvvVbRrkaNGgBUq1aN3r17\ns2PHDiEoaLvW3G1SU1OpWTO4v8cTLmg5n3FxcUXvu3fvzujRo0lPTyc+Pr7U4gwXArk2w3bKS20e\nVexh0U5SUhLz588HYP78+fTq1cvDJjc3l6ysLABycnLYsGEDLVu2LNU4yyparrWkpCQWLFgAwPbt\n26lcuXLRNKPAFS3n8+zZs0X/+zt27ECWZSEmARLQtRmc9QJlg+XLl8u1atWSTSaTnJCQIN9zzz2y\nLMvyyZMn5XvvvbfIbt26dXLjxo3lBg0ayJMmTQpVuGWetLQ0uXPnzh7LhoufzyNHjsiJiYlyYmKi\n3Lx5c3E+3VC61mbNmiXPmjWryGbMmDFygwYN5FatWnld7i7wfT5nzJghN2/eXE5MTJRvu+02edu2\nbaEMt0wzcOBAuUaNGrLRaJRr1aolz50796qvzbD+gS2BQCAQlB5hO+UlEAgEgtJFCIpAIBAIgoIQ\nFIFAIBAEBSEoAoFAIAgKQlAEAoFAEBSEoAgEAoEgKJS7nfICQXlj9uzZXLhwgT///JOhQ4dy7Ngx\nzp07x969e5k6dWqFflKDILwQ+1AEghJkzpw5tG7dmjZt2rBz5066du3KvHnziImJoVu3bqxfv55u\n3bqFOkyBICiIEYpAUIKkpaXRpk0bAI4dO4ZOp6NXr17k5eXx/fffi2eeCcIKkUMRCEqQF154oej9\nli1b6NixIwBRUVEeYnLkyBEeeeSRUo1PIAgmYoQiEJQSmzZtYtSoUYp1M2bMYNeuXaSkpJRuUAJB\nEBEjFIGghHA4HGzcuBGn08mpU6c4ePBg0QgFYOrUqUXvx44dy8MPPxyCKAWC4CEERSAoIT7++GO6\ndevG4cOHWbJkCdHR0UUrutauXcsNN9zgYi/WxwjKO2LKSyAoIdq1a8egQYNYsmQJiYmJzJw5k+ee\ne4569epRr149hg4dGuoQBYKgIgRFICghEhMTWbhwoUvZkCFDQhSNQFDyiCkvgUAgEAQFISgCgUAg\nCApCUASCMsCcOXN455132Lt3Ly+//DKHDh0KdUgCgd+IR68IBAKBICiIEYpAIBAIgoIQFIFAIBAE\nBSEoAoFAIAgKQlAEAoFAEBSEoAgEAoEgKAhBEQgEAkFQEIIiEAgEgqAgBEUgEAgEQUEIikAgEAiC\nwv8DR3Yqo1T5RX4AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x37a9950>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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dyg8AckgIZf2cAQkCz19Hj9LUZHL6SjaTZQ7dvOHfrUAwZWKfIM7i5OnTNGz6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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0xc6020d0>"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we have the target distribution we can stochastically estimate the out-of-sample error. Classifying using the logistic regression is a matter of choosing the label that is most probable for a data point. So if the output of the hypothesis function $h$ is greater than $0.5$ we label the data point $y=+1$ and vice versa."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def in_sample_error(z, y, h):\n",
" y_h = (h(z) >= 0.5)*2-1\n",
" return np.sum(y != y_h) / float(len(y))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def estimate_out_of_sample_error(P_x, phi, P_f, h, N=10000, phi_h=None):\n",
" x = np.array([P_x() for i in range(N)])\n",
" z = np.apply_along_axis(phi, 1, x)\n",
" if not phi_h is None:\n",
" z_h = np.apply_along_axis(phi_h, 1, x)\n",
" else:\n",
" z_h = z\n",
" y = P_f(z)\n",
" y_h = (h(z_h) >= 0.5)*2-1\n",
" return np.sum(y != y_h) / float(N)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note the relatively high error rates for a toy data set due to treating the decision boundary as a hard threshold despite the noisy nature of the target distribution. The higher our `hardness` factor on our toy data set the smaller this error rate will be."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print('Target weights: {:}'.format(w_f))\n",
"print('Hypothesis weights: {:}'.format(w_h))\n",
"print('Hypothesis in-sample error: {:.2%}'.format(in_sample_error(z, y, h)))\n",
"print('Hypothesis out-of-sample error: {:.2%}'.format(estimate_out_of_sample_error(P_x, phi, P_f, h)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Target weights: [ 0.41537607 -7.94492 8.11922518]\n",
"Hypothesis weights: [ 0.72043721 -5.41271258 5.34073738]\n",
"Hypothesis in-sample error: 8.00%\n",
"Hypothesis out-of-sample error: 8.89%"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Learning with Less Data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we learn from a smaller set of data, say $N=10$, we should see a larger discrepancy in the out-of-sample error."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N_subset = 10\n",
"subset_indices = np.random.permutation(N)[:N_subset]\n",
"x_subset = x[subset_indices, :]\n",
"z_subset = z[subset_indices, :]\n",
"y_subset = y[subset_indices]\n",
"\n",
"w_h_i_subset = gradient_descent(z_subset, y_subset, eta=10.0)\n",
"w_h_subset = w_h_i_subset[-1]\n",
"print('Number of iterations: {:}'.format(w_h_i_subset.shape[0]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of iterations: 12\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h_subset = lambda z: logistic(w_h_subset.dot(z.T))\n",
"h_subset_grid = apply_to_fill(z_grid, h_subset)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"subset_N_fig = plot_data_set_and_hypothesis(x_subset, y_subset, x_1, x_2, h_subset_grid,\n",
" title=r'Hypothesis, $N={:}$'.format(N_subset))\n",
"target_fig.show()\n",
"full_N_fig.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 5.42 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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aru3bh6hTzeK7f1yuHCQNSle+uABN9r2xPOuSIgzoYqNxJKchO1w+9akfpTzS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nx0WQAllneTBYOJ8kEwfLmAoNehS07AnZGN1+EimgE9EgiOHT9G227teKLvQJ4a8FSUMAm/ESAf\nJi6RnMxLh4nSGaK6xKVKVexU5oGiwiTanVe+z4ePHKZtt3Y8M+gZBvR9QlGeRb6tQLsgCFhTdLgu\nwET+vAsKEzVfokpVcajMA6WsKhQmhaeDhw7SoXtHnhvyHI/1fLxQYwsCWMvpcDlEcrM8kSuoKtP6\n99/T/PDDtzidDpo1a0n16rWKu0uqLkFl/jkUr+KXQ17qFtFYzU4kdnMZ9OiSEnCnZ+N1usLWi3Z2\nsv/Afjp078jLL7xMz669wtaJHC/oHDRgTdHnwyQ4VqTzDokXwSYdN7Kv8vpyUmcnSjR79le88sow\noC1ebxwazSK6d+/F22+/L/sOP1VFI/XBRgkpB0rRw0TZICkFEwO6pHjc6Vl4ne6w9aJdpvrr77/o\n1PNhRr00im6du8v6BbYXDUwMOO1ebNkFhUl0yXlpv8j+yurLSR0IlejIkf+jWbMm2O2bgBoXStOw\nWO5iwoTRtGjRvji7d9lLfbCxwCp8mFzcVivtEw1M/GMJRh9MXGmBMBFl6oV+lrft+XMPHR/txFuv\nvh0RJmIE28V++MoEDSSWM+C0ewoIE4HCg0lorHBSYRIbLVw4C4+nFxdhApBMbu4LfPXVzOLqlqpL\n1GUOlNjAJJxPtDDJLzEa0CX6YCK63JI+ypPkgbadu3fycK/OjHlzLJ3bdw4bIzKcAtsTNGAtZ8Ce\n68GW7ZXsT2SYBOrSYBJZTqeT7ds3s/fPXVHcpakwiUbp6Rm4XBUkLOXJyMgs8v6UFdlsuRw6dIDs\n7Kxiaf8yBkpxwyTwTlkeJgKCyXgBJpkyMAk/+8j7LGXb9sc2HunThQ/f/Yj2rdsrmH2Eg1PgsaC9\nCBN7jjRMCKonFctfsYbJt9/OpW69KnTr/hQdOjzCrbfWZdeubRFqqTCJVs2aPUBc3DwCfzIXjMY5\ntGjRrHg6VYrl9Xp5553XqFv3Glq0eIh69SrzwgtDcTqdRdqPyzSHcikwKdzke6AtdHDWmAxorXG4\nUjMR3R7kBvfgMiUg+H3b7zzavyfjx02gxf0tCpAjkT/WaAWsKXpsOR4cueFgEnnpK9QmbZf2C+/r\nrx07fqfzIx2x2b4Hbr4QaT4JCUPZsmUfiYlJErVUmBREXq+XTp1asXu3Brt9OBCHwfAF5cr9wk8/\nbSYpKbm4u1iqNGbMm0ydugqbbTZwLf/f3pmHN1Gtf/wzWdp0C1DEguyyyF5c+KEiiwIiIhWQTdlE\nVBDQexVxw+vGFQEFl4uCIMqiUMDLLiiIIC4gCFdBQECkQNlpoXuSJpnfH6WlSWaSSUibNj2f58nz\nZM55z3veTKfzzTnvORM4i8n0KElJtXnvvY/89ieS8gooC0p4iUmgU14//7KNoSOHMvO9WXTp1MVP\nMfE+stLpJcxVjeRlB0dM/BGIQMUEYMSjw1i//kZk+WmX8qioB3n55XYMHz7Gb58CdaxWK3PnzmDR\nomRsNis9evTgySfHER9/TahDK1fYbDaaNatJbu52oEGxmnQiIxuwe/cRqlSJ98tnufoJ4NBRdsRE\nXQgKjnVRkejjojSKiX+jiq0/beWRMSP4ZMZcOt7RUcPoQ7uY6A0ScfFG8rIcWPNKT0z8+ZuptT96\nNAVZ9tx3k5fXmpSU4377FHgnMjKS0aPHMXr0uFCHUq5JT7+A02nAVUwA4omIqEdqaorfghIoFSSH\non1lT5kSk7RMZLuT4IhJwTnYvHUzw0c/wrxZ81TExN98THEx0WGON5Kb5cCiUUzUkvKu9sr16nbq\ntt7at27dCr3+O4/6mJjvaNWqpV8+BYKSJisrk/3796DT6dDp7MDfbhYXsdlSqFmzbqnFVEEEpfyg\ni45EH3tZTBzOoPre8N0GHnvqcRbOWUi7W+8AID09jS0/bGHfgX0BDXEL0RsKHqeSk+nAlhfcuEuL\nMWOeIjJyFrAQyAcy0etfwWxOoUePviGOTiAowG63M2HCeFq1qkuvXg/Rtm0Tate+HpNpCJB62eo8\nJtPDJCUNID6+aqnFVgEERfvIJFijE09fat/SXUcbuugo9DFR2NILxUT7iipfo5N1G9Yz+pkxLPp0\nEbf93+3IsswbE1+m9c03MO2xQTzY807uvqstx1OPq/pwfX8lNp2hIAGfk2nHZnEq2qiPqDzLletK\ndnQCcP31jVi6dDXNm8/BYKiEwVCDjh0PsHbtJkymKM0+BYKSZNKkV0lO3oXVeoDs7D+wWv/m2LFa\n1K6dj8nUipiYxkRGNqJ379pMnfp+qcZWAZLyp33aqZ8AX9NYnjb+JOCLl+liotBHm7ClZ4LDfZoL\nH8fep71Wr1vNuAnPsmTeEm5MvAmATxfMZcEbL7EuN5cEwAFM0+lYWKceW3/agyTpVP0VR2+UiKti\nJDvDjs1aGJ32zx3c1Vze7X23vUJ2dhZ6vYGoqCjNPgWCksZqtdKs2XXk5e0Gik9lXSQy8np++OE3\nLBYLCQk1iIszB9yP2CkfICUjJp7fqNVHFcXEJE1JTDxHMv6IyfLVy3n25fF8ufC/RWIiA598OJ3p\nl8UEQA+Mdzrh/Dm2/fKzqr/ilC0x0ZYnUx+JuhIbGxeQmGRmZnDgwF4yMi751U4g0EJ6+gVkOQJX\nMQGoQkREXS5eTKNhwxuuSkyuhgotKCUnJmptPZf66mKj0UdFYkvLAKdyAl7dh/cpryXLl/Li6y+x\n/IvltGrRyqXuxPlztFT4RC2A1JMnVMUkJzeHBYs+Y/anMzFE2TmdelFRTNSS7SUnJr7x//uWdjHJ\nz8/nhReeJjGxLvffP5DWrevxzDNjsFqtfvcqEKhRtWo19Ho7cNit5gI2Wwq1a9cPRVhFVFhBCVxM\nfI8+vNUVP9bHRqMzRRRMczllvIuFuw/vK7MWLV3Ea5NeY+XiVTRv2sJFdGSgVeOmbHSL1QZsdTpo\n2SJRsa/jJ45x8603s2FTKiMef5x+/d6jaYum/L5nN8qigUp5WRcT7asCC3njjQksW7Yfq/Ug2dn7\nsFr/YuXKE0yY8KxffgQCb0RERDBy5D+JihoCHLlcmkpU1GD69h0a8g2hFTKHEqzku2u9Wp3yDVUf\nF40UaSTfh5i49+1tGqrweP6i+Ux9721WLF5JwwaNFNrDlq2bGfVwfz6x5NGdgrUhz0SasN3WnvmL\nViv6T+rbh9i4wSxY8CD9+sHWrQDJ1K79b3Zt340kSRqWAAe2NNhfW+/tvOF/viQvL5fmzWthsewF\naharuUBkZCN+/z0Fs7mS334FAiWcTifTpk3i44/fR5ZNyHIOgwY9yiuvvInRaAxKHyKHopHSEBP3\nKSh32yIxSdMiJgXfln2t5Co8/mTBXN7+4B1WL13jIibuI52OHe7ivdmfM6F+A0w6HYmmKKo/OIxZ\nc5d4+AfIys4ivmokCxYMpHfvQjEBGEBaWg4HDx0oMTFRznuUDTEBOH/+LDpdHK5iAnANRmN1Tp9O\nVWomEASETqdj/PiX2bcvla1bf2LfvpNMnDg1aGJyNVSoEUppiYm3G6reHI1kNJCfngWybzHxZ5Qy\nc+4sZs6dyerkNdSpU1fVh3vseRYLERGR6HQ61Sk6mz0PfWQ+SUlV+OUX1wcsxMY2Z+V/P6NVyxu9\nfnblcuV6dTt1W21t1Qh8JZfFYqF585oKK2/OYDI1Zc+e48TGxgXsXyAobcQIpRygN8e4iUnw+GDW\nB8z+bDZrl62lbp26vhsUw2QyodOpXwoRJh0J11VizOjn+OWXpW61P2M0ZNKsqXuKv+JgMpl45JEx\nREUNBlIulxbMaz/44KNCTAQVhgrxLC9/EvCe9tr2mfj6Jq6vFItk0BfkTGSltoGPTqb9ZzqLli1i\nzbI11KxRS8WH76XHStN0ESYdMWYDmel2Hh0+gnXre2Oz7cNu74ROt4vIyHd5d/qHGAwGlfOhfk6U\n6tTtfNv7bqvG1e8zeeGFV5Ekiblzb0aSYpDlbAYPfpx//evfV+1bICgvhP2Ul0N1Y2Npikkckl5H\n/sVAxETdVpZh8rtTWLFmBauSV1E9oYaqj0AS/MXFxG4vsPj76BFmfjyT//22j0YN6/HEyFG0bNla\n5XyonxOlOmUb3/ba2wfuUysWi4Xz589wzTUJl/exCATlD/H4egXUBSV4+0zUb/wF6CvHIemkgmmu\nYnbeRg7ehKDwWJZh4tv/Zv2G9axcvIprq10bFDEptI2M0hEVZyArPR+73bWt5+cM3tLgqxmVqLdX\nI7hiIhCEC+Lx9ZopPTExVI4DSU1M/J/yKi4mr056je+2fsfqJWuoWvUaDWLirT9lMclMy8fh8P4Z\ny4qYBPBdyu8WAoHAOxVMUEpLTCQMVQoSsfkXr1ZMXOtkGV58/SW27djG6iVr3DYyqYuJtlEKREbr\niYrRh7GYCCERCEqKsF/l1euBPnzx3//iUHgUvOeNTptoaBITWfYqJrLCcaGt+/vCY6dT5tmXx7Nz\n105WLV59WUykotcVf4GJialQTNJ9iYnkpdwVX2Iie9io2yohxEQgKDuEvaA8uG0bHz7/HINHDHeZ\nE9Ryo3Ov0/Lt3BAfhyzL5F/KdrFTnmbSnj9xOmWeeWkcf+z/g/9+sRxzpUr4K05exSRGjylGT4bP\nkYn2EZz2c+yOEBNB+LBlyzckJd1Dq1YN6dcvie3bt/puVE4Jf0EBvs/N5Y8ff+K7H38ErlZMVL6d\nSxKGeDOyU8auSUw8/aq9dzicPDn+KQ4ePsiyhV9efoyHf+Lk2p+rbVSsHlN0gZg4nd7a+DsdqFyv\nbKNuq4QQE0F5IDl5PiNGPMavvw7hwoV1/PRTLwYNGsj69StDHVqJEParvAo/3FvA2YeHM33SW0EQ\nFDdbScJQxYzscGDPyPHwfTWCYrc7GDNuDKfOnGbxZ4uJiY4NyJ9r/ZW2UbF6IkwF01xOl1lB5TYe\nn12hTgiKQAA2m42WLeuSlbUeaF2sZjMJCSPZtetPrxuKQ4nYKe+DXJ2OyMjIkhGTeHcx8Ta95D5N\nVVCm9D4/387j/xjJuQvnSZ635KrERGlaLCpOT4RJ5yYmSiMwb9NZQkwEAiWOHDmILFfCVUwAOpGR\nkcGZM6dCEVaJUiEE5RzwaWQkffv0KVaq7SapSUzyC8VE/WasnOMoKFMSApstnxFjHyUrK4tFcxcT\nHRWtQZw8E/K41RUeR8fpiYjUkZlmV5zmcu/DtcybffE6dTH57bedPDx8EG1vvZlBgwawY8fPHrZK\nCDERlBfM5krk56dR8MMQxcnG6cwjJiY2FGGVKGEvKC/p9bQ2mXjs8ZHc1LLV5VJtN0k1gSkSk6qV\nkPPt2DNzlG18JuSVxETCarUx7ImHybfbWTjnc0wmk0Z/njErjWKizXqMEZfFRPa0d49f+XxoFxp3\nm02b1tHngSQ2bLiV48c/4bvNdzHwwf6sWu3+nDDl9toQYiIILTVr1qFp05bo9dOLlcoYDBNp1+5u\nKlWqHLLYSoqwz6G8OGYsD9zfi9YtWhSWutj4s3rJJQFftRKyNR97Vq6CjT+jFNc6i8XCkMeHYjKZ\n+GTGXIwREYp26n157y/GbEBvlMhKVxaTK2g7T77audvIsszNt7Tg9On3gbuLWWynSpX+7N3zN3q9\n3ot/LQgxEZQNUlOP0bv3PWRkVMFma4PR+CMJCTIrVqynWrUE3w5ChHj0igKSJGE/daZ4iUt9QGKi\n0xVMc1ls2LPzFGy0iomnXW5eLoMfHULlypWZ9d7HGIxGP/y5xqwoJpUM6A2+xER78l2tb282p06l\n0u6ONlgsZzzsY2Iase6rlTRu3EzFvxaEmAjKFna7nc2bv+bo0cM0btyMDh26ltlkfCHi0SteCWSF\nkrKYGOPNOCw2HF7ExPdIwbNdTm4OA4c/SPWEGnw0/SP0ik/vvUox0UtkptuLPTm/dMUEICoqGqfT\nAliA4g9PzMduzyC62LyymOIShAMGg4GuXe8LdRilQtmWyaCgfSWXuphIoNNjrFoJR54WMfFnlZdE\nVnYWfYf0o3at2sx8d6aLmPjOx/jqD2IrG9DpJTIvahcTtfPhWedZr2xTQJUqVQBibpUAABaDSURB\nVLn55vbo9W+7lOt0H9KoURNq1azjFpcWhJgIKg4Oh4OPPprOjTfeQP36Zu69tzPbtn0f6rCACjHl\nddalzOsIRLFcKhiZVDXjyLXgyLEq+PM++vD2PiMzg35D+9P0hqZMf+tdJJ3OD3++62MrG5B0BSMT\n98/o+1y41mmpV7ZxtT158gRJ999NZmZ1cnLaER29k+jov1i18hvq128oxEQg8MK4cWNZufJ38vLe\nAW4A1mIyjWPhwmTatbszKH2IHIoC7oLi/QaqsmRWf3maK8eCI9eq2i6QKa+MjAz6DH6AGxNvYurE\nqSApjzS0+fc8jq1sRJIg82LZEZNC8vPz+eabVRw+fID69RvRvXtvhX1CvhBiIqhYnDx5gjvuSMRq\nTQHMxWqSadlyFt98syUo/YgcSklQJCZ5l8UkeDew9Ivp9B7Uh9vb3s6br0xy2dUfDOKqFPxps1zE\npOxgNBq5776+oQ5DIChX7NnzKxERd2C1mt1qkti/f1hIYipOBcih+MqPuJYVlev1BdNc2a5iouTL\n3xzKhbQL9ByQRMd2Hd3ExHuuRSlmpf7iqhiQZYmsi3YveRa1c+HlnCj4UrdR96WGGJ0IBN6pWvVa\nnM6/8fxv+RuzOfTLkMNeULznR1zLisoNhgIxycrDkecqJu6+/M2hnDt/jp4DkrinS3dee+l1n2Ki\nLE7q/cXFG5FlyL7kLibqn9uXWASymsuXvfb2gfsUCMKNNm1uJz4eJGkWV/5rcjGZxjF8+OOhDA2o\nAIJSgOtN0tsqL8lgKJjmysxVERP/VnAVrztz9gz39e/J/T3uZ8L4CRrFBMU6j2MJzPFGZIdM9iWH\n4kjGnwUJhWRmZXLxYrpqvaeP4r583/jVVoOpI8REUHGRJInFi1dw3XUfEBt7I7Gx/TGZ6tGlS3X+\n8Y/nQx1e+Cfl80+dcynztjpKMugxxJtxZObgsNhQFhPXNt7eFz8+efokSQPu56F+D/HMk+M0J+41\nJeAlMFcx4nDI5GQoiwluZd7KAY4d+5sn//kUu3f/AOho0KAF09+Zxk03tXWxUxcT3wSwhsTvFgJB\nOOJ0Otm+fSvnzp0mMbEN9es3DKp/scpLAXdB8SomRj2GKmbsmTk4vYiJViEofnw89QRJA5MYPvgR\nnhr1VEDLi9X6lqSCaS5HvkxOpjcx0T6NlZOTzf/dmkj6xSdwOp8CjMASYqKf5rtNP1O37vUKPpR9\nqSFGJQJB2UU8vt4L3qd7JCSjoUBMMrI1iIl/U17Hjh/jvv73MXL4yBIQE4m4eCP2IIqJDHy5fDG5\neTfidD5PwW52AzAIq20Esz7+0Ms0lRATgaAiE/aC4n26p1BM4grExJqPbzHB41gtkf53yt/06H8f\nT416ilEjntCUZ1F6ryYm5qoG7LbgignAnj37yM3tiDt2eyf+99s+j3IlX2oIMREIwpewF5QClJLy\nElJEgZjkX8rGabWjRUy0CsHhI4fp2T+JZ58az4ihj2pcvaWWP3Etk3QFYpJvlcnJchTz5T3no0VM\nABo1qo/JtBt39PpdNG5U361UW/LdvY9CUlOP8cILT9Ohw23069eLb7/9SjE+gUBQ9qkgguKJFGHA\nUDkO+6UsZFt+UH3/eehPkgbcz4vjXmTYQ8OC6lvSgTnegM0ik5vlCKrvQvr1HYzRuAFI5ooM/EhE\nxPuMHPlE0Pr566+DdO58G4sWmfjrr2n89NMDjBr1NO++OzlofQgEgtIj7JPytlPnXcpkQIqIwFA5\nFvulLJy2KyOTwvrLrYsda5/22vfnPh4Y3JfXX3qd/n0GBORDKQ4AdGCOj8BmcZCX7fTwpdbO8w/s\nexrst99/5bHHHyEtLQedZCIiMpfp096nW7ckVT/eULrIhg4dyKZNNyPLzxUrPUVkZHN+/fUQVatW\n0+xfIBAED7HKSwF3QZEBKTICQ6VY7BezcOYrTXNBoGKy54899B3aj7dem0yfpD5effgWLtf+JB2Y\nq0ZgyXVgyQmOmPgUGlnm0OEDWK1WmjVrVeyHr/ybjlK7wK6/vgoWyyHgWpfy2Nj7mTZtMD179vOr\nH4FAEBzEs7y8UHhagiEmakKw+/fdDHh4INMmTadn954afHgTJ9djnb5gZKImJt4XHniW+6orKpUk\nlx+78marhrdLMiIiGovlEu6CIkmXiIqK9qsfgUAQesI+h1KUgDdFFohJeqaKmCgnyc9eOM+kqZNI\nurczIx4ZxNaffvCw27l7J/2HDeD9Ke/Ts3tPzYl75TrXY51eKhCTnNIVE08777ZKbX19v+nb9yEi\nIiYCzmKlm4E/ad++i+a+BBWPlJQjrFu3nN9//zWgb9KCkiHsp7yspy6gM0WgN8cUiIm9cFWU970p\nAMdPnqBrtzu5JzubXjYrR4G3o6IZ9czzjB3zT0Bi245tDHl8KB9O/4i777o74ByJupgYyctxYM31\nJia+p74865Trle282/puq0x2dha9e99LSkoeOTk9MZn+Qqf7mnnzlnLHHXdp7k9QcbBarTzxxCNs\n2bIRo/F2HI4/qFPnGhYtWk716teFOrywQeRQFJAkifyLmejjfIuJ0vETox+j9poV/NtxZTVVKtAy\nMpL//XqAPw/9ycNPDOfj92dzV8e7AtirUtzOtV6nlzBXNZKX5cCad/ViolUglC+G4ItJoV+Hw8GW\nLd/w66/bqFYtgV69HiQ+vqpfXgQVh1deeZ7PP/8TiyWZgk23TgyGN2jWbAtff70lxNGFD0JQFJAk\nCafdTn56FrJPMfEUgvqNa7MzO4s6bn77xMTSYMRIFixeyKcffUaHdh38TLh7FxO9QUdcvIG8LAeW\nPKdLvVIb7eXK9ep26rba26sh9pkI/MNisdC06bVYrZOBvlzJvdmJiqrHN998S8OGTUIYYfggHr2i\nQn5aJrLdib9iAmA0GMhV8HnC6eST+XNZMHuBipho27SoJibmeAO5mYVi4rpxUG2aToiJIJzZufNn\nbrqpIVZrHeAbCn769g0KrjwDBsP1nD17OqQxCirAKi/ZcUVM/OWBPv2Y8vk8PrXZijy8D/xms7J8\nfjK3t20XrDAB0BskzPEGcjId2CxO3w0EggpAVlYmgwb1Ijt7HnDv5dKzwJ1AM6AjNtsemjZtFaoQ\nw4Ljx4/y7bdfYTAELgthLyi+ppe8jVyef+5lkn7cSoeTJ+iVk8N3RiMbnE5eeeFVOt1xp4oPfxLy\nV8p0RglzFSM5mXZsFjnAfSbBWs3l3V5bezXE6ETgH2vXfonTeQdXxAQgAXgNmE5U1DQeemikyL1d\nBVOmvMGsWR8AvdHpbAH7qQCCoi0BryQElcyV2LjxR9asX8uixQvYtvtXFn80l26d7/Fo518OxbU/\nvVEiroqR7Aw7+dZAxCQ0q7mU23tDiInAfy5cOIvVqvR7H43Q6Q4yfvy/ePzxp0o9rnDhhx82MXv2\nfKzW/VzJSy0IyFfY51CUcxqgdVRhNEbglJ3sPfQnX6/4WqOYeMuhuPbnS0zU8iPlS0xc80ACgT/c\neGNbIiO/AlyfXafXr6FPnwcYNeqf6HRhfysrMRYsWEBe3tO4bzAOhArwV9A+5aUkDIu/TOblif9i\n+RcraNGsZVA3LeojLovJJXUx0fI5ilNa+0z8E5PwxW63i411JUy7dnfSpEl1IiMHA4eAdOA/mEwz\n+Mc/ng1xdOWf9PRLQPWg+KoAgqK+osrXqOLzJZ8zccpEViWvplmTZgGs4FL3b4zQEVfZSNYlO/k2\nb2Lie5WXZ51yvbKdd1vfbdUI71HJd9+tp337NtStG0mjRtV4/fUXsVqtoQ4rLJEkiaVLVzN0aB3M\n5k5ERNShQ4fNrF69iQYNGoc6vHLP3XfficmUHBRfYb8PJfdUevESQNuo4tOFnzJ9xrusTF5Fg/oN\n/Ey4K9sVHhsjdcRWMpB1yY7dp5jgR7lyfaC23tt5I3yFBGDr1o08/PBQLJbZFCSKj2IyPUOHDjHM\nm7c41OEJBH6RnZ1F5863cfbsrdhsTwBWoJ3Y2OjOFUHxZ+WVxOx5c/jPx/9h1eLV1K9X38+EuzYx\nybxox55f6K3kxeRqVnIJMXGlW7dO7N07GuhfrNSCyVSXDRu20rDhDaEKTSAIiIsX05kxYxqrVq3C\nYDBw/PjvQlDcKRCUi0XHWkYVH835iI/nzWZ18hrq1K5zlcuCr15MtC8L9qxXt1O31dZWjfAXE4B6\n9eKw2VKBSi7lsbH9mTq1D716DQxNYAJBkBA75b2gNZH+3kfv8cmCuaxZutZFTNzbe/Phni8pLIsw\nFYhJRnqhmPjOjWgXE/V8hRCT4FO1ai1gv1upjCzv57rraoUipHKDw+EgOfkz7rvvbu66qz3vvjuJ\njIxLoQ5LECQqxD4ULbz9wTssXb6UNcvWcF31mkH1HWHSEWM2kJlux2EP2wFhhWHUqNFMnvw0eXlf\nAVUBJzrddKpV09OmTXCfnhBOyLLMY48N4fvvU8jLexYwc/ToZyxZ0p4NG37EbK7k04egbBP2IxRf\nK7NkGd6a9hZfrvySNUuviEnx0QnubdyO1abEAIxRV8TEXiQm/m5a9DU6UUaMTkqGESPG8OCD7YmM\nbIjZ3JXo6EY0aLCEJUtWIUkV61z4w44dP7J166/k5X0H9AG6YLV+wdmzLfnss5mhDk8QBMI+h5Jz\n6spwWklM3pjyBt98u4GVyauodk01lxu52ns1f+431ogoHVFxBjLT8rnyBHx/xcSVkl4aHEAazu8W\nZY38/HzWrVvOV1+tJzo6igEDBnLbbR19trtw4Rx79+6mWrXqNG+eGHZiIssyqanHkGWZ2rXrXfXn\nmzRpAjNmGIDX3Wo20Lz5m2zc+P1V+RcEj7DJoSxbtozmzZuj1+vZvXu3qt3XX39NkyZNaNSoEVOm\nTPHqU2lUIcvw8sR/8e2WTaxeuoZrgiQmhX1FRHsXkysxKfl1LfOsU65XtvNu672dL8r/DdRqtdK3\nbw/GjXuftWtvY9myhgwZ8givvvqCz7bXXHMtd955Dy1atA47Mdm9+xfatbuJjh1vo1On22nX7iZ2\n7dp+VT6jo6MxGDIUajKIjo65Kt+CskGZE5SWLVuyYsUKOnTooGrjcDgYO3YsX3/9Nfv372fx4sUc\nOHBA0VZpykuW4YXXXuTnX35mdfIat4fKeRcT31NeYIrWExXjXUyK9+dZXtbFJHw2LSYnf8Yff8jk\n5v4AjESWx5Gbu5PPP/+cP/74LdThhYTTp08yYEBPUlJexGI5icVykpSUFxk4MIlTp1ID9tur10AM\nhi+AlGKleURHv8PQoQ9dbdiCMkCZE5QmTZrQuLH33a87duygYcOG1KtXD6PRyMCBA1m1apWKtesN\n2+mUGTfhWXb9bxcrFq2kUuXKxex8i4m3fAyAKUaPKUZPZrovMdG2A951JONZ727risiX+GLp0uXk\n5Y0F9MVK47Fah7B27fJQhRVSFiz4hPz8/hTss9FdfvUnP38A8+fPCdhvvXoNmDDhdUymWzAan0SS\nJhAd3YLOnZvQu7cQlLBALqN06tRJ3rVrl2LdsmXL5EcffbToeOHChfLYsWM97LhyPxYv8RIv8RIv\nP16BEJJlw127duXMmTMe5ZMmTaJnz54+22udr5bDd72BQCAQlDlCIigbN268qvY1a9bkxIkTRccn\nTpygVi2xoUwgEAhCSZnLoRRHbYRxyy23cPjwYVJSUrDZbCxZsoSkpKRSjk4gEAgExSlzgrJixQpq\n167N9u3b6dGjB927dwfg1KlT9OjRAwCDwcCMGTPo1q0bzZo1Y8CAATRt2jSUYQsEAoEgoMxLGWXp\n0qVys2bNZJ1Op5rQl2VZXr9+vXzDDTfIDRs2lCdPnlyKEZYv0tLS5C5dusiNGjWSu3btKl+8eFHR\nrm7dunLLli3l1q1by23atCnlKMs2Wq61J598Um7YsKHcqlUreffu3aUcYfnC1/ncvHmzbDab5dat\nW8utW7eWJ06cGIIoywfDhw+Xr732WrlFixaqNv5em2ElKAcOHJAPHjzodYWY3W6XGzRoIB89elS2\n2WxyYmKivH///lKOtHwwfvx4ecqUKbIsy/LkyZPl559/XtGuXr16clpaWmmGVi7Qcq199dVXcvfu\n3WVZluXt27fLbdu2DUWo5QIt53Pz5s1yz549QxRh+WLr1q3y7t27VQUlkGuzzE15XQ3B38NSsVm9\nejXDhg0DYNiwYaxcuVLVVhYr6jzQcq0VP8dt27bl0qVLnD17NhThlnm0/u+Ka1Eb7du3p0qVKqr1\ngVybYSUoWjh58iS1a9cuOq5VqxYnT54MYURll7Nnz5KQkABAQkKC6sUkSRJdunThlltuYc6cwDe+\nhRtarjUlm9TUwHejhzNazqckSfz8888kJiZy7733sn+/+88MCLQSyLVZ7h5fX1p7WCoKaufzzTff\ndDmWJEn13P3000/UqFGD8+fP07VrV5o0aUL79u1LJN7yRKD7pcQ1qoyW83LTTTdx4sQJoqOjWb9+\nPb169eLQoUOlEF144u+1We4ERexhCS7ezmdCQgJnzpyhevXqnD59mmuvvVbRrkaNGgBUq1aN3r17\ns2PHDiEoaLvW3G1SU1OpWTO4v8cTLmg5n3FxcUXvu3fvzujRo0lPTyc+Pr7U4gwXArk2w3bKS20e\nVexh0U5SUhLz588HYP78+fTq1cvDJjc3l6ysLABycnLYsGEDLVu2LNU4yyparrWkpCQWLFgAwPbt\n26lcuXLRNKPAFS3n8+zZs0X/+zt27ECWZSEmARLQtRmc9QJlg+XLl8u1atWSTSaTnJCQIN9zzz2y\nLMvyyZMn5XvvvbfIbt26dXLjxo3lBg0ayJMmTQpVuGWetLQ0uXPnzh7LhoufzyNHjsiJiYlyYmKi\n3Lx5c3E+3VC61mbNmiXPmjWryGbMmDFygwYN5FatWnld7i7wfT5nzJghN2/eXE5MTJRvu+02edu2\nbaEMt0wzcOBAuUaNGrLRaJRr1aolz50796qvzbD+gS2BQCAQlB5hO+UlEAgEgtJFCIpAIBAIgoIQ\nFIFAIBAEBSEoAoFAIAgKQlAEAoFAEBSEoAgEAoEgKJS7nfICQXlj9uzZXLhwgT///JOhQ4dy7Ngx\nzp07x969e5k6dWqFflKDILwQ+1AEghJkzpw5tG7dmjZt2rBz5066du3KvHnziImJoVu3bqxfv55u\n3bqFOkyBICiIEYpAUIKkpaXRpk0bAI4dO4ZOp6NXr17k5eXx/fffi2eeCcIKkUMRCEqQF154oej9\nli1b6NixIwBRUVEeYnLkyBEeeeSRUo1PIAgmYoQiEJQSmzZtYtSoUYp1M2bMYNeuXaSkpJRuUAJB\nEBEjFIGghHA4HGzcuBGn08mpU6c4ePBg0QgFYOrUqUXvx44dy8MPPxyCKAWC4CEERSAoIT7++GO6\ndevG4cOHWbJkCdHR0UUrutauXcsNN9zgYi/WxwjKO2LKSyAoIdq1a8egQYNYsmQJiYmJzJw5k+ee\ne4569epRr149hg4dGuoQBYKgIgRFICghEhMTWbhwoUvZkCFDQhSNQFDyiCkvgUAgEAQFISgCgUAg\nCApCUASCMsCcOXN455132Lt3Ly+//DKHDh0KdUgCgd+IR68IBAKBICiIEYpAIBAIgoIQFIFAIBAE\nBSEoAoFAIAgKQlAEAoFAEBSEoAgEAoEgKAhBEQgEAkFQEIIiEAgEgqAgBEUgEAgEQUEIikAgEAiC\nwv8DR3Yqo1T5RX4AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x37a9950>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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dyg8AckgIZf2cAQkCz19Hj9LUZHL6SjaTZQ7dvOHfrUAwZWKfIM7i5OnTNGz6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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0xc6020d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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zRfjCjU7IViHTik4c3F4FgFAcyrQIKxbi9dxn6wvxxvQdRgaw8PWF4Hke1/z5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"text": [
"<matplotlib.figure.Figure at 0x3854690>"
]
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the resulting hypothesis looks off we need to remember what the learning algorithm sees: just the data."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"naked_fig = plot_data_set_and_hypothesis(x_subset, y_subset, x_1, x_2, None, title=r'Data, $N={:}$'.format(N))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 0.06 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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xywsAAkVRUZGSk9N09KhPUtQp97ymrl1nav36fCOPwywvAGji/vWvfyk09Nfy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\nYMT/B2fcWDSSFnWSAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x13ebc8d0>"
]
}
],
"prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the metrics below we can see that the quality of the final hypothesis depends on the number of samples we have as predicted by learning theory."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print('Target weights: {:}'.format(w_f))\n",
"print('Target in-sample error: {:.2%}'.format(in_sample_error(z, y, f)))\n",
"print('Target out-of-sample error: {:.2%}'.format(estimate_out_of_sample_error(P_x, phi, P_f, f)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Target weights: [ 0.41537607 -7.94492 8.11922518]\n",
"Target in-sample error: 7.00%\n",
"Target out-of-sample error: 7.85%"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print('Hypothesis (N={:}) weights: {:}'.format(N, w_h))\n",
"print('Hypothesis (N={:}) in-sample error: {:.2%}'.format(N, in_sample_error(z, y, h)))\n",
"print('Hypothesis (N={:}) out-of-sample error: {:.2%}'.format(N, estimate_out_of_sample_error(P_x, phi, P_f, h)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hypothesis (N=100) weights: [ 0.72043721 -5.41271258 5.34073738]\n",
"Hypothesis (N=100) in-sample error: 8.00%\n",
"Hypothesis (N=100) out-of-sample error: 8.77%"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print('Hypothesis (N={:}) weights: {:}'.format(N_subset, w_h_subset))\n",
"print('Hypothesis (N={:}) in-sample error: {:.2%}'.format(N_subset, in_sample_error(z_subset, y_subset, h_subset)))\n",
"print('Hypothesis (N={:}) out-of-sample error: {:.2%}'.format(N_subset, estimate_out_of_sample_error(P_x, phi, P_f, h_subset)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hypothesis (N=10) weights: [ 0.22155369 -3.05283829 1.84902211]\n",
"Hypothesis (N=10) in-sample error: 20.00%\n",
"Hypothesis (N=10) out-of-sample error: 12.71%"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Learning Curve"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we can stochastically estimate the out-of-sample error we can plot approximate learning curves. The learning curve will show us how the in-sample error and out-of-sample error behave as the data resources improve.\n",
"\n",
"Warning: this can take a while to evaluate."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"start_time = time.time()\n",
"\n",
"error_histories = []\n",
"\n",
"for runs in range(10):\n",
" N = 201\n",
" x = np.array([P_x() for i in range(N)])\n",
" z = np.apply_along_axis(phi, 1, x)\n",
" y = P_f(z)\n",
" \n",
" error_history = []\n",
" \n",
" for N_subset in range(1, N+1, 4):\n",
" x_subset = x[:N_subset, :]\n",
" z_subset = z[:N_subset, :]\n",
" y_subset = y[:N_subset]\n",
" \n",
" w_h = gradient_descent(z_subset, y_subset)[-1]\n",
" h = lambda z: logistic(w_h.dot(z.T))\n",
" \n",
" error_history.append([N_subset,\n",
" in_sample_error(z_subset, y_subset, h),\n",
" estimate_out_of_sample_error(P_x, phi, P_f, h)])\n",
" \n",
" error_histories.append(error_history)\n",
"\n",
"error_history = np.mean(np.array(error_histories), axis=0)\n",
"\n",
"print('Error history took {:.2f} seconds.'.format(time.time()-start_time))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Error history took 121.16 seconds.\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"target_error = estimate_out_of_sample_error(P_x, phi, P_f, f, N=100000)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"start_time = time.time()\n",
"\n",
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"ax.set_xlabel(r'Number of Samples ($N$)', fontsize=18)\n",
"ax.set_ylabel(r'Error ($E$)', fontsize=18)\n",
"ax.set_title(r'Learning Curve'.format(N), fontsize=18)\n",
"ax.set_xlim(0, error_history[-1, 0])\n",
"ax.set_ylim(0, 1)\n",
"ax.xaxis.grid(color='gray', linestyle='dashed')\n",
"ax.yaxis.grid(color='gray', linestyle='dashed')\n",
"ax.set_axisbelow(True)\n",
"\n",
"ax.plot(error_history[:, 0], error_history[:, 1], 'r-', label='In-Sample')\n",
"ax.plot(error_history[:, 0], error_history[:, 2], 'b-', label='Out-of-Sample')\n",
"ax.plot(error_history[[0, -1], 0], [target_error]*2, 'm-', label='Target')\n",
"ax.legend()\n",
"\n",
"print('Plot took {:.2f} seconds.'.format(time.time()-start_time))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 0.06 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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CWVmZYGNjI1y+fFnT9ujRo4Kvr29NfhKDqy7+dfm74JY/SS45OVnqLlAtMXZGQqEwzFRH\n6l34AGBtbQ0AyM3NxaFDh2BnZwc7OzsEBwcDEM+wf+2113D48GHcv38fH3zwAV5++WVcuHABALBh\nwwZ07twZjo6OcHR0xD///IOMjAzN/Cte3dXKygoA4OrqqvVcbm7u//88Cnh6empes7GxgZOTE27d\nuqXV/7S0NOTn56NLly6azx0yZAjS09Pr/NsYkiH+75j8SXJMIPLF2BkJQTDMVE969eqFnJwc5OTk\n4OzZs1Vet7S0xGuvvQZHR0ecP38e165dw6uvvoqvv/4a9+7dQ2ZmJjp06FDrEseCIODGjRuax7m5\nubh37x7c3d212rm4uMDKygoJCQnIzMxEZmYmsrKykJ2dXavPrS9M/kREJLnaJOWlS5fijz/+QEFB\nAUpLS7F+/Xrk5uaic+fOyMvLg0KhgIuLC8rKyrB27Vr8888/depjVFQUjhw5guLiYnz44Yfo0aMH\nPDw8tNoolUpMnjwZ06dPR1paGgAgJSUF+/btq9NnGyMmfyIiqhP1cL/KQ/4eNATQ2toaM2fORMuW\nLeHq6opvv/0W27dvh4+PD9q1a4eZM2eiR48eaNGiBf755x88/vjjVT5P389SKBQYO3YsPv74Yzg7\nO+PkyZOIjIzU+d5FixbB398f3bt3R7NmzTBgwABcunRJ799CLhRCbfejGJm6XNeYpBUbG4s+ffpI\n3Q2qBcauYXD5VjcTJ06Ep6cnPv30U6m7UiuV46/+v6vL3wW3/ImIqFHjilNVTP4kOZaIlS/GjuSg\ntlUIjZUh/u+425+IyMhx+Wbaqos/d/sTERGR3pj8iYiITAyTPxERkYlh8iciIjIxTP4kOZaIlS/G\njqjhsbwvNQpMIPLF2JGx+Pbbb+Hm5gZ7e3tkZmZK3Z1q+fj4ICYmpk7zYPInIiKjsG7dOgQHB8PG\nxgYtW7bEa6+9hvv37+v1Xh8fHxw4cKDWn11SUoKZM2ciJiYG2dnZcHR0rNJmwYIFaN26Nezs7ODl\n5YXRo0fX+vPqwlhqDjD5ExFRnSxevBhz5szB4sWLkZ2djWPHjuHatWsYMGAASkpKHvr+utYxuHPn\nDgoLC9G2bVudr69fvx6RkZGIiYlBTk4Ojh8/jv79+9f68xoDJn8iIqq17OxszJs3D8uXL8fAgQNh\nZmYGb29vbN26FcnJyYiMjER4eDg+/PBDzXtiY2Ph5eUFABg/fjyuX7+Op59+GnZ2dvjiiy90fk5R\nURGmT58ODw8PeHh44O2330ZxcTEuXbqkSfoODg46k/rx48cxaNAg+Pr6AgDc3NzwyiuvaF5fu3Yt\n2rVrB3t7e/j5+eG7777T6qunpyf+85//oHnz5nB3d8dPP/2EqKgoBAYGwtnZGQsXLtS0nzdvHkaO\nHInRo0fD3t4eXbp0wZkzZ3R+J0EQsHDhQvj7+8PFxQUvvPBCgx2yYPInIqJaO3r0KAoLCzFixAit\n521sbDB06FD89ttvD9zNvXHjRrRq1Qq//PILcnJyMGvWLJ3tPvvsM8THx+P06dM4ffo04uPjMX/+\nfAQGBuLcuXMAgPv372P//v1V3tu9e3ds2LABX3zxBY4fPw6VSqX1upubG/bs2YPs7GysXbsWb7/9\nNk6ePKl5PTU1FUVFRbh9+zY++eQTvPLKK/jhhx9w8uRJHDp0CJ988gmuXbumab97926MGjUKmZmZ\nGDt2LIYPH17lMwHgq6++wu7du3Hw4EHcvn0bjo6OeP3116v9rQyJyZ8kx/rw8sXYUXp6OlxcXKBU\nVk0nLVu2RHp6ukE+Z9OmTfjoo4/g4uICFxcXzJ07Fxs3bgTw8Av3jBs3DsuWLcOvv/6KPn36wM3N\nDZ9//rnm9aFDh2r2CvTu3RsDBw7EoUOHNK9bWFjggw8+gJmZGV544QXcu3cP06dPh42NDdq1a4d2\n7drh9OnTmvahoaEYMWIEzMzMMGPGDBQWFuLYsWNV+rVy5UrMnz8f7u7usLCwwNy5c7Ft2zaUlZU9\n8PsY4v+OyZ8kxwQiX4ydcVAoDDPVhouLC9LT03UmrFu3bsHFxaXG85w6dSrs7OxgZ2en2aV+69Yt\neHt7a9q0atUKt27dqvLe69eva95rb2+veX7s2LH47bffcP/+faxYsQIffvgh9u3bBwDYu3cvunfv\nDmdnZzg6OiIqKgoZGRma9zo7O2v2XlhZWQEQ9xaoWVlZITc3V/PY09NTc1+hUMDT01NnX5OTk/Hs\ns8/C0dERjo6OaNeuHczNzZGamvrA34fJn4iIIAiGmWqjR48esLS0xPbt27Wez83NRXR0NPr37w8b\nGxvk5+drXrtz545W28qHBVasWIGcnBzk5ORgzpw5AAB3d3etIW7Xr1+Hu7t7lf60atVK897s7Owq\nr5uZmWHkyJHo2LEjzp07h6KiIjz33HOYPXs27t69i8zMTAwdOrROJyDeuHFDc7+srAw3b96stq/R\n0dHIzMzUTPn5+WjZsmWtP1tfTP5ERFRrzZo1w9y5c/HGG2/g119/RUlJCZKTkzFq1Ch4eXlh/Pjx\nCAkJQVRUFDIzM3Hnzh0sWbJEax5ubm64fPnyAz9nzJgxmD9/PtLT05Geno5PPvkE48eP16uP69ev\nR1RUFHJyclBWVoa9e/fi3Llz6NatG4qLi1FcXKw5dLF3717NHoHaOnHiBHbu3InS0lIsWbIETZs2\nRffu3au0mzp1Kt5//31cv34dAJCWlobdu3fX6bP1xeRPRER18s4772DBggWYNWsWmjVrhu7du8Pb\n2xsxMTGwsLDA+PHj0alTJ/j4+GDw4MEYPXq01tb+e++9h/nz58PR0RFffvmlzs/417/+hdDQUHTs\n2BEdO3ZEaGgo/vWvf2lef9BJhfb29liwYAG8vb3h6OiIOXPmYMWKFXjsscdgZ2eHr776CqNGjYKT\nkxM2b96MZ555Ruv9lef9oM9SKBR45plnsGXLFjg5OeGHH37Ajh07YGZmVqXtW2+9hbCwMAwcOBD2\n9vbo0aMH4uPjq523ISmERnKRaF7vmogaKy7f5OPjjz9GUlKS5mREQ6gu/nX5u+CWP0mOJWLli7Ej\n0tYQK2ks70uNAhOIfDF2RNoaonyvIf7vzOveDSIiIgKAuXPnSt0FvXDLn4iIyMQw+RMREZkYJn8i\nIiITw+RPkmOJWPli7IganiH+7zjOn4jIyHH5Zto4zp+IiIjqjMmfiIhqzdbWVnMVPaVSCWtra83j\nzZs3N0gfYmNj4eXl1SCf1VhwnD8REdVaxUvZ+vr6Ys2aNejXr1+N5lFaWgpzc6ajhsQtfyIiMrj4\n+Hj06NEDjo6OcHd3xxtvvIGSkhLN60qlEt988w0CAgLQpk0bAMDnn38Od3d3eHp6YvXq1VAqlbhy\n5QoAoKioCLNmzYK3tzdatGiBiIgIFBYWIi8vD0OGDMGtW7dgZ2cHe3v7KpcMpqqY/ElyLBErX4wd\nVcfc3BxLly5FRkYG/vzzT8TExOCbb77RarNr1y789ddfSEhIQHR0NP773/8iJiYGiYmJiI2N1Wo7\nZ84cJCUl4fTp00hKSkJKSgo++eQT2NjYIDo6Gu7u7sjJyUF2djZatGjRgN+04bG2PzUKTCDyxdhR\ndR555BF07doVSqUS3t7eePXVV/HHH39otXnvvffg4OAAS0tLbN26FS+//DLatm0LKysrfPzxx5p2\ngiBg1apV+PLLL+Hg4ABbW1u89957+PHHHzWvmxLW9iciIsQqYg0ynz5CH4PMBwAuXbqEGTNm4MSJ\nE8jPz0dpaSlCQ0O12lQ8Se/27dvo2rWr5rGnp6fmflpaGvLz89GlSxfNc4IgoKyszGD9NTVM/kRE\nMmfIpG0oERER6NKlC7Zs2QIbGxssWbIE27dv12pT8ep3LVu2xI0bNzSPK953cXGBlZUVEhIS0LJl\nyyqfVd9X0WuMuNufiIgMLjc3F3Z2drC2tsaFCxfw7bffPrD9qFGjsHbtWly4cAH5+fn49NNPNa8p\nlUpMnjwZ06dPR1paGgAgJSUF+/btAwC4ubkhIyMD2dnZ9feFGhkmfyIiMrgvvvgCmzZtgr29PV59\n9VWMHj1aawu98tb64MGD8eabb6Jv374IDAxEjx49AACWlpYAgEWLFsHf3x/du3dHs2bNMGDAAFy6\ndAkAEBQUhDFjxqB169ZwcnLi2f56YHlfklxycjJrxMsUY9cwTHH5dv78eQQHB6O4uBhKpWlvp1aO\nv/r/ri5/F0z+RERGzlSWbzt37sTQoUORn5+PCRMmwNzcHDt27JC6W5JjbX8iImq0vvvuO7i5ucHf\n3x8WFhYPPU+Aao9b/kRERo7LN9PGLX8iIiKqM6NI/tHR0QgKCkJAQAAWLVpU5fX09HQMHjwYISEh\n6NChA9atW9fwnSQiImokJE/+KpUK06ZNQ3R0NBISErB582acP39eq83y5cvRuXNnnDp1CrGxsZg5\ncyZKS0sl6jEZGkvEyhdjR9TwGkVt//j4ePj7+8PHxwcWFhYYPXo0du3apdWmZcuWmuIN2dnZcHZ2\n5uUfGxEmEPli7IgaXqOo7Z+SkqJV39nT0xNxcXFabSZPnox+/fpprtq0detWnfMKDw/X3A8JCUFI\nSAh8fHx0jkNOTk7W+QOyfcO3T05O1lzByxj6w/b6t8/KyqrynJT9aaztHRwcWMLWhDk6OgIAYmNj\nERsbiwsXLtT58LfkZ/tv374d0dHRWLVqFQAgMjIScXFxWLZsmabN/PnzkZ6ejiVLluDy5csYMGAA\nTp8+DTs7O00bng0rX7GxsejTp4/U3aBaYOzki7GTL3XsZH22v4eHR5WLOVS8mhMAHD16FM8//zwA\nwM/PD76+vrh48WKD9pOIiKixkDz5h4aGIjExEcnJySguLsaWLVsQFham1SYoKAj79+8HAKSmpuLi\nxYto3bq1FN0lIiKSPcmP+Zubm2P58uUYNGgQVCoVJk2ahLZt22LlypUAgClTpuD999/HxIkT0alT\nJ5SVleHzzz+Hk5OTxD0nQ2FtePli7OSLsZMvQ8RO8mP+hsJj/kREZEpkfcyfiIiIGhaTPxERkYlh\n8iciIjIxTP5EREQmhsmfJMcSsfLF2MkXYydfjaK2PxEXQvLF2MkXYydfTP5ERERUY0z+REREJobJ\nn4iIyMQw+RMREZkYJn+SHGuMyxdjJ1+MnXyxtn8FrO1PRESmhLX9iYiISG9M/kRERCaGyZ+IiMjE\nMPkTERGZGCZ/khzLjMoXYydfjJ18sbwvNQpcCMkXYydfjJ18MfkTERFRjTH5ExERmRgmfyIiIhPD\n5E9ERGRimPxJcqwxLl+MnXwxdvLF2v4VsLY/ERGZEtb2JyIiIr0x+RMREZkYJn8iIiITw+RPRERk\nYpj8SXIsMypfjJ18MXbyxfK+1ChwISRfjJ18MXbyxeRPRERENcbkT0REZGKY/ImIiEwMkz8REZGJ\nYfInybHGuHwxdvLF2MkXa/tXwNr+RERkSljbn4iIiPTG5E9ERGRimPyJiIhMDJM/ERGRiWHyJ8mx\nzKh8MXbyxdjJF8v7UqPAhZB8MXbyxdjJF5M/ERER1RiTPxERkYlh8iciIjIxTP5EREQmhsmfJMca\n4/LF2MkXYydfrO1fAWv7ExGRKWFtfyIiItIbkz8REZGJYfInIiIyMUz+REREJobJnyTHMqPyxdjJ\nF2MnXyzvS40CF0LyxdjJF2MnX0z+REREVGNM/kRERCaGyZ+IiMjEMPkTERGZGKNI/tHR0QgKCkJA\nQAAWLVqks01sbCw6d+6MDh06oE+fPg3bQapXrDEuX4ydfDF28iVZbf+LFy8iISEBd+/ehUKhgKur\nKzp06ICAgIAad0ClUqFNmzbYv38/PDw88Oijj2Lz5s1o27atpk1WVhZ69uyJX3/9FZ6enkhPT4eL\ni4v2F2FtfyIiMiF1yXvm+jZMSEjAihUrsG3bNty5c0dnmxYtWuD555/HlClT0K5dO73mGx8fD39/\nf82azOjRo7Fr1y6t5L9p0yY899xz8PT0BIAqiZ+IiIj099Dkn5SUhHfffRc7d+6EtbU1evXqhSlT\npsDPzw/Ozs4QBAH37t1DUlISjh07htWrV2PZsmUYMWIEFi1aBD8/vwfOPyUlBV5eXprHnp6eiIuL\n02qTmJjO6iN8AAAgAElEQVSIkpIS9O3bFzk5OXjrrbcwfvz4KvMKDw/X3A8JCUFISAh8fHx07iJJ\nTk7WOVaS7dme7dme7dneGNvHxsYiNjYWWVlZyMrKqtK+Jh6629/S0hLBwcF466238Oyzz8LW1vaB\nM8zNzcX27duxdOlSJCQkoLCw8IHtt2/fjujoaKxatQoAEBkZibi4OCxbtkzTZtq0afj7778RExOD\n/Px89OjRA3v27NE6zMDd/kREZErqdbf/1q1b8cwzz+g9Q1tbW0yYMAETJkzATz/99ND2Hh4euHHj\nhubxjRs3NLv31by8vODi4gIrKytYWVmhd+/eOH36dK3OMSAiIjJ1Dz3bX534J06ciA8++ACrVq3C\n0aNH9Zr58OHDH9omNDQUiYmJSE5ORnFxMbZs2YKwsLAqfTh8+DBUKhXy8/MRFxen9zkFZPx07e4i\neWDs5Iuxky9DxE7voX4bNmyAp6cn+vbtC2dnZ63Xli9fjk2bNqGkpKTGHTA3N8fy5csxaNAgtGvX\nDi+88ALatm2LlStXYuXKlQCAoKAgDB48GB07dkS3bt0wefJkJv9GhAsh+WLs5Iuxky9DxE7voX7d\nu3fHsWPHqn09Pj4eX3zxBQICAjB16lStk/gaAo/5y1dsbCxrN8gUYydfjJ18qWNXl7yn95Z/xTMO\n09PTq7zetWtXbN68GXfv3n3oGf5EREQkHb2Tv4WFheb+8ePHMWzYMIwaNQrffvstLl68CAAwMzPD\n0qVLYWVlZfieEhERkUHUqrzv4MGD8cMPP+DAgQNwdXXFuXPnNK9ZW1sjNDTUYB0kIiIiw9K7wl/l\nk/kcHBzQr18/jBw5skrb5s2b171nZDJ0Fb0geWDs5Iuxky9DxE7vLf+dO3fiueeew3fffac509DG\nxkZnW3NzvdcpiLgQkjHGTr4YO/kyROz0ztJmZmaIi4vDzp07AQD+/v4wMzPD1q1b0bt3b7Ro0aLO\nnSEiIqL6p3fyf+qpp7B161ZcuHABBw4cwIEDBxAbG4vRo0cDEFcGnnjiCfTq1Qu3bt2qtw4TERFR\n3eg9zv+PP/7AE088ofWcIAg4c+aMZmXg4MGDyMnJgUKhgEqlqpcOV4fj/ImIyJTUJe/pnfz1oVKp\n8Ndff2HcuHG4fPmyoWarFyZ/IiIyJQ1S5EcfZmZm6N69O4f6UY2wzKh8MXbyxdjJV4PW9q+J9957\nrz5mS40UF0LyxdjJF2MnX0ab/ENCQupjtkRERGQAD03+MTExtZ75/v37a/1eIiIiqh8PTf6DBg1C\n37598fPPP+t1Bn9xcTF27NiB3r17Y8iQIQbpJBERERnOQ8f5nzp1CjNmzMAzzzwDV1dX9O/fH127\ndoWfnx+cnJwgCALu3buHxMRE/Pnnn4iJiUFWVhYGDRqE06dPN8R3ICIiohrQe6jfn3/+iW+++QY/\n/fQT8vLydLaxt7fHiBEjEBERgUcffdSgHX0YDvWTr+TkZJYalSnGTr4YO/lSx65Bx/mXlpbixIkT\nSEhIQFpaGhQKBVxdXREcHIyQkBCYmZnVqiN1xeRPRESmxGiK/EiJyZ+IiEyJ0RT5ISIiIuPH5E9E\nRGRimPyJiIhMDJM/SY5lRuWLsZMvxk6+jLa8L1FNcCEkX4ydfDF28tXgyb+goADr169HXFxcnT+Y\niIiIpFGj5N+kSRNMnjwZJ0+erK/+1NmJE8B330ndCyIiIuNVo+RvZmYGLy8vZGdn11d/6uzuXWDn\nTql7QUREZLxqfMw/PDwcGzduRGFhYX30p85cXID0dKl7QUREZLweemGfyh577DHs2LEDnTt3RkRE\nBAIDA2FtbV2lXe/evQ3SwZpycQHS0iT5aKol1heXL8ZOvhg7+TJE7Gpc3lepfPjOAoVCodflfw1J\nXeYwJwdo2RLIzW3QjyciImpQdSnvW+Mt/++//75WH9RQbG2BkhKgoACwspK6N0RERManUV7Yx8MD\niIsDPD0l7hQREVE94YV9KuFJf0RERNWrVfLPzc3FRx99hODgYNja2sLW1hYdO3bE3LlzkZeXZ+g+\n1hiTPxERUfVqnPzv3buHrl27Yv78+bh79y5CQkIQEhKCO3fu4NNPP8Wjjz6Ke/fu1Udf9cbkLy8s\nMypfjJ18MXbyJUlt/48++ggXL17E8uXLcevWLRw+fBiHDx/GrVu38PXXX+PSpUuYO3dunTtWF66u\nTP5ywoWQfDF28sXYyZckyX/37t2YNGkSXnvtNZiZmWmeNzc3R0REBF5++WXs2rWrzh2rC275ExER\nVa/GyT81NRWPPPJIta937twZd+7cqVOn6orJn4iIqHo1Tv7NmzfH33//Xe3rp06dgpubW506VVes\n8kdERFS9Gif/sLAwrFmzBitWrEBZWZnmeZVKhZUrV2LNmjUICwszaCdrilv+RERE1atxkZ/09HQ8\n9thjSEpKQvPmzdGmTRsAwIULF5CWloaAgAAcOXIELi4u9dLh6lQsdnDqFDBhAnD6dIN2gWopOTmZ\ndcZlirGTL8ZOvtSxq0uRn1pV+Lt//z4+//xz7Ny5E1evXgUAtG7dGs8++yxmz54Ne3v7WnWmLir+\nCDdvAt26ASkpDd4NIiKiBtHgyd8YVfwRCgoABwegsBBQKCTuGBERUT1osPK+BQUFWL9+PeLi4mr1\nYQ3FygqwsOCV/YiIiHSpUfJv0qQJJk+ejJMnT9ZXfwyGJ/0RERHpVqPkb2ZmBi8vL2RnZ9dXfwyG\nyZ+IiEi3Gg/1Cw8Px8aNG1FYWFgf/TEYlviVD5YZlS/GTr4YO/kyROzMa/qGxx57DDt27EDnzp0R\nERGBwMBAWFtbV2nXu3fvOneuLrjlLx8cciRfjJ18MXbyZYjY1Tj5DxgwQHN/+vTpOtsoFAqoVKra\n98oAmPyJiIh0q3Hy//777+s0vKChsMQvERGRbjVK/gUFBVAoFGjTpg26d+9eX30yCBcX4No1qXtB\nRERkfGo11O/UqVP11R+D4W5/IiIi3TjUjyTHk47ki7GTL8ZOvgwRu0Y71I/JXz64EJIvxk6+GDv5\nMkTsONSPiIjIxNT4wj5K5cN3Fkgx1K/yCISSEsDaGigqAvToMhERkazUZeRdrYb6yYGFBWBnB2Rl\nAU5OUveGiIjIeDTKS/qqBQYCv/wi3hIRETUmDXZJX33k5eXhypUrhp5trfC4vzywxrh8MXbyxdjJ\nlyFip1fyt7CwwI8//qh5nJOTg7CwMJw9e7ZK2507dyIgIKBGnYiOjkZQUBACAgKwaNGiatv99ddf\nMDc3x44dO/SaL6v8yQMXQvLF2MkXYydfDZb8VSoVysrKNI+Liorwyy+/IK2azFqT3RAqlQrTpk1D\ndHQ0EhISsHnzZpw/f15nu3fffReDBw/We/7c8iciIqpK8vPg4+Pj4e/vDx8fH1hYWGD06NHYtWtX\nlXbLli3DyJEj4erqqve8mfyJiIiqqvHZ/oaWkpICLy8vzWNPT0/ExcVVabNr1y4cOHAAf/31FxQK\nhc55hYeHa+6HhITg/v2nkZXlAqBZlbbJyck6d534+PjoLKDA9vXXPjk5GbGxsUbTH7bXv31WVlaV\n56TsD9uzfWNuHxsbi9jYWFy4cAHr1q2r0r5GBD0oFArhhx9+0DxOS0sTFAqFEBMTU6Xtxo0bBYVC\noc9sBUEQhG3btgmvvPKK1vunTZum1WbkyJHCsWPHBEEQhAkTJgjbtm2rMh9dX2XNGkEID9e7KySR\n33//XeouUC0xdvLF2MmXOnZ6pnCdJN/y9/DwwI0bNzSPb9y4AU9PT602J06cwOjRowEA6enp2Lt3\nLywsLBAWFvbAeXO3vzzoWhMmeWDs5Iuxky9DxE7v5B8VFYU7d+4AEIfzAcD//ve/Klf4O3HiRLW7\n5XUJDQ1FYmIikpOT4e7uji1btmDz5s1abSoOHZw4cSKefvrphyZ+gMlfLrgQki/GTr4YO/lq0OS/\nadMmbNq0Seu5lStX1r0D5uZYvnw5Bg0aBJVKhUmTJqFt27aaeU+ZMqXW83Z1ZfInIiKqTK8Kf+qT\nsfSeqUKBJ554orZ9qhVdlY4yM4HWrcVbIiKixqQuFf4adXnfsjLA0hLIzxdr/RMRETUWRlXe15go\nleJFfTIypO4JERGR8WjUyR/gSX9yoGt8K8kDYydfjJ18GSJ2TP4kOS6E5Iuxky/GTr6Y/PXA5E9E\nRKSNyZ+IiMjEMPkTERGZGCZ/IiIiE9Pokz+r/Bk/lhmVL8ZOvhg7+TJE7Bp98ueWv/HjQki+GDv5\nYuzki8lfD0z+RERE2kwi+aelSd0LIiIi42ESyZ9b/kREROUaffK3sQFUKvHiPkRERGQCyV+hELf+\neXEf48Uyo/LF2MkXYydfLO+rJ+76N25cCMkXYydfjJ18MfnricmfiIioHJM/ERGRiWHyJyIiMjEm\nkfxZ4peIiKicSSR/bvkbN5YZlS/GTr4YO/lieV89scqfceNCSL4YO/li7OSLyV9P3PInIiIqx+RP\nRERkYpj8iYiITIxCEARB6k4YgkKhQHVfpbAQsLcHiorEcr9ERERy96C89zAmseXftClgaQnk5Ejd\nE9KFZUbli7GTL8ZOvljetwa46994cSEkX4ydfDF28sXkXwNM/kRERCKTSf6s8kdERCQymeTPLX8i\nIiKRSSV/VvkjIiIyseTPLX/jxDKj8sXYyRdjJ18s71sDTP7Giwsh+WLs5Iuxky8m/xpg8iciIhIx\n+RMREZkYJn8iIiITw+RPRERkYkwm+Ts5AZmZgEoldU+oMpYZlS/GTr4YO/lied8aMDcHmjUDsrKk\n7glVxoWQfDF28sXYyReTfw1x1z8REZEJJn9W+SMiIlNncsmfW/5ERGTqmPyJiIhMDJM/SY5lRuWL\nsZMvxk6+WN63hpj8jRMXQvLF2MkXYydfTP41xORPRETE5E9ERGRymPyJiIhMDJM/ERGRiTGp5O/q\nyuRvjFhmVL4YO/li7OSL5X1rqFkzIC8PKC6WuidUERdC8sXYyRdjJ19M/jWkUADOzkBGhtQ9ISIi\nko5JJX+Ax/2JiIiY/ImIiEwMkz8REZGJYfInybHMqHwxdvLF2MkXy/vWApO/8eFCSL4YO/li7OSr\n0ST/6OhoBAUFISAgAIsWLary+g8//IBOnTqhY8eO6NmzJ86cOVPrz2LyJyIiUyd58lepVJg2bRqi\no6ORkJCAzZs34/z581ptWrdujYMHD+LMmTP48MMP8eqrr9b685j8iYjI1Eme/OPj4+Hv7w8fHx9Y\nWFhg9OjR2LVrl1abHj16oFmzZgCAbt264ebNm7X+PFb5IyIiU2cudQdSUlLg5eWleezp6Ym4uLhq\n269ZswZDhw7V+Vp4eLjmfkhICEJCQuDj46N1fMTFBUhLEysk6aqSVLm9GtuzPduzPduzvZTtY2Nj\nERsbi6ysLGRlZVVpXxMKQRCEOs2hjrZv347o6GisWrUKABAZGYm4uDgsW7asStvff/8dr7/+Oo4c\nOQJHR0et1xQKBfT5KteuAb16AdevG6b/VHfJyck6/yHI+DF28sXYyZc6dvrmPV0k3+3v4eGBGzdu\naB7fuHEDnp6eVdqdOXMGkydPxu7du6sk/prgMX/jo2uNl+SBsZMvxk6+DBE7yZN/aGgoEhMTkZyc\njOLiYmzZsgVhYWFaba5fv44RI0YgMjIS/v7+dfo8a2tAEID8/DrNhoiISLYkP+Zvbm6O5cuXY9Cg\nQVCpVJg0aRLatm2LlStXAgCmTJmCTz75BJmZmYiIiAAAWFhYID4+vlafp1CUb/23amWwr0FERCQb\nkid/ABgyZAiGDBmi9dyUKVM091evXo3Vq1cb7POY/ImIyJRJvttfCjzuT0REpozJnyTHM47li7GT\nL8ZOvgwROyZ/khwXQvLF2MkXYydfTP615OoKpKZK3QsiIiJpmGTyHzgQWL0auHRJ6p4QERE1PJNM\n/t27A599Bjz9NJCZKXVviIiIGpbk5X0NpTZlDt9+Gzh7Fti7F7CwqKeOERER1QNZl/eV0n/+AzRp\nAkyfLnVPTBvLjMoXYydfjJ18NYryvlIyNwc2bwZiY4Gvv5a6N6aLCyH5Yuzki7GTL0PEzigq/Emp\nWTPg55+Bnj2BwEBgwACpe0RERFS/THrLX611a2DLFuDFF4GLF6XuDRERUf1i8v9/vXsDCxaIIwDu\n3ZO6N0RERPWHyb+CSZOAsDDg+eeBkhKpe0NERFQ/mPwrWbQIsLIC3ngDaByDII0fy4zKF2MnX4yd\nfBkidiY9zr862dnAY48BTzwBfPop4ORkkNkSEREZDMf5G5i9vTj8r6wMCAoCvvqKhwGIiKjx4Jb/\nQ5w9C8ycCVy/DnzxBTBsGKBQGPxjiIiIaqQueY/JXw+CAERFiSsBXl7Al18CwcH18lFERER64W7/\neqZQiFv8Z8+KowGefBKYOhW4e1fqnhEREdUck38NWFiIowAuXBBHBLRrB0yeDGzbxqsD1gXLjMoX\nYydfjJ18sba/RJycgP/+F/jrL6B9e+D77wFvb/FSwXPnAkeOAKWlUvdSPrgQki/GTr4YO/li8peY\nr694RcCoKCAtTawQWFgITJsGuLgAzz4LrFjBioFERGRcmPwNxNIS6NdPLBJ08qR4jYCRI4GDBwF/\nf+D114FLl6TuJREREZN/vXFzA8aNAzZtAs6dEw8VPP64eMJgbCyrBxIRkXSY/BtAy5ZipcDkZHHU\nQEQE0KULsHEjUFwsde+IiMjUMPk3IGtrYMoUcU/A/PnAhg3ieQMLFgBJSVL3TjqsMS5fjJ18MXby\nxdr+FdRnkZ/6dOYM8PXXwO7dQLNm4p6Bp54SDxFYWEjdOyIiMlas8Af5Jn+1sjLxRMFffgH27AES\nE4EBA8QVgSFDAFdXqXtIRETGhMkf8k/+ld25Iw4h3LMH2L8fCAwE2rQR6wn4+IiTtzfQqhXQtKnU\nvSUioobG5I/Gl/wrKioSCwpduSKeNHjtWvntjRviSAIfH8DDQ6w8aGkJNGki3laemjYFbG3Fycam\n+vtKng1CRGTUmPzRuJP/g6hU4l6C5GTg1i2xyFBRUfVTQQGQlydOubnltxXvl5aKKxN+flUnX19x\nJUItL0/8fF2Tubk45FHXZGtbt6sjFheL11ZITRWLKFlZiedMODiIt7a2hl+BKS0F8vPF+SoU4q2u\n+7zqIxE1BCZ/mG7yrw/5+eJehsuXq07Xr4vJ29JSTPClpeJQxhYttCc3N/G11FTdkyCIbeztAXPz\nQjg6NoW1NTSTjY1427SpeN2Eyu/PyRHPg3BzA5ydxZWarCzg/n1xys8H7OzKVwjs7cUVhMpT06bl\n983MxM9ST/fuad/PzxfbCYJ4job6tuJ9QRBXAtR7XireVrzftKn4/aysyr+z+r761tERaN5cnFxd\nxdu6rDQJgvg75eRoT/n54sml6j1DTZuW31ffKpXi75qVJf4e6tvLlzOgVDojM1Oct/p7VZwqfkcz\nM/HzHjSVlIjt1CtUlSczM/E3rPw5lSdBEOelnoqLq95XLzIqLjoq3lcoxL8vdRzc3MS/TSlW8NR/\na+bmhplfcnKybM/4V6mAjIzyDYC7d8Xn1IdE3d0b995LdeyY/MHk31BKS8UVgJISMenb2dVuQZiX\nV57EDx36G0FBj2gW/nl55YmgoEBM4OoVCvXk5PTgf+7SUiA7u3xl4P59cV6FheKteqr4WKUSVxSc\nnMTE6+hYft/JSfyu+ixQSkvF5FJcLO5tqXirvq/+XPV3rHyblycm17Q0ccGmnlSq8pUBV1cxEZaW\nilNJSdX7JSXi3pycHPHWwkL8HhUna2uxrXqvUWGh9v2iIvFzmzUTfwsHh/LfJy/vJjp08ISDg5jk\nK36vipP6udLS8hW76iZz8/JEV3lSqcSpuPjhKxEKhfh9LSzElQVd9yvGs+Lfsfq+SiWu+KmTTGqq\n+Lx6RaB5c3HlwMysfK9Pxb0/6vtmZtormrpWPgWharwrThkZYhs7O7F8eHWTUin+7T9oatIEAO6h\ndWsnrXiq4+vgIMY9K6v66f59MZ4VV3wr3xeE8u+oXhFUT+rHlpbasa14Xz0VFpb/Nqmp4v+Gg4N2\nHJRK8VDo1atizLy8xD2V6hUCX19x5Vn9/1Dd1LSpuGyrPLm7i7HWtQwQhPL/G/WkVIp/Y+bm5X9v\n6sdmZg9fjjxIbGws+vTpw+QPMPnLmfoPmR4uL698IZiWJi50zM3LJ/XCpeJ9Gxtxz4etreGHj5pi\n7NQrrhWTskqlnfAq7lEQhPIEVt2KZ0GB2F69h0HX5OIiJo2sLCA9XfeUliYmz2bNxJjrmuzsxJWn\ngwdPw8urk9aeHPWUlSUmQfWKgK7J3r58BUq9klP5PlB1RbfilJ8vrmSo9+iop8qPLS219744Oz94\nD0hhYfm5UVevlk95eVVXfitOtrbie2/dAm7frjrl5Iifb2amneiLisQ+qlfo1Cs06hVw9aR+DJSv\niFa3d1C9kqreU1VxAyI3twiAJTIyap/3DLQDiYgago2NOMl0b22jYGMDtG4tTlJwchKnwMC6zaeg\nIBONdb2taVNxdFSbNoadb1GReLhTvUdDPTVpUrPDDCpVeVKvOFXeQ1hSUr4iUHHF4PjxE+jT57E6\nDQFvdFv+sYpYqbtCRERU7/qiL3f7c7e/fJniruPGgrGTL8ZOvgxxzJ+7/Ulycj3jmBg7OWPsDKTi\n0IOKJ+QUFFTdr68eZlJcLJ4A4Oyse6iU+mzeygQBKC5GawcH4ObNOnWbW/5ERGQ4KhWQkiKebXf9\nunj2YE6OOMxA1211Y0QrDguxsHhwAZPKk/qgeeXH6rGSFc+Mre6MWfVkZlb1cU5OeZK/d6986EHF\nszNtbMrP2qt44F79WKkU33vnjngGqbpAirp4ibOzOBUVlQ+ByssT3/f/J/8oUlK425/Jn4gkIQhi\nIrt3r7w4hPq+eiooEBOEs3P5GXvq+87O4hg7Cwtxa1DXWEn1gl8QtBNj5dvqxqHpGj9X3bi6ys9V\nNw6vpERM8leviolefWr9zZti8vP1FeuPOzqKp9KrhxpUvlWPEa3uO+fni8lbV7lSXWVM1VPlMqfq\nhKseD1t5Up+Sr1JVfa3icyUlYr/Vif5hQw9qo7RUXLHIyBD7rj7TV70i9P841A9M/kT0/9TJrvL4\nqor31QtyhUJ7667yLSBuid26JSY69VTxcWqqmMDUSb1icQj1ZGUlbgFnZIgrA+pb9f3MTDExqVQP\nLoKgUFRNjOqSnQUFYqIwM6uavNXFBipPlcfUVfd8xcfq++bm4uB39WB69a23t3YZUKo3TP5g8icy\nKnl54lbg5ctiuUh1ycj8fHFrUNdka6s9j/v3ywdrV5yuXRMTaeXEXnGqWOGncqUV9X0zs/JB+BW3\n7ireCoK4defhISY6D4+q91u0UFfNqT31ykqTJnUv4ahSVU3mrDndKDH5g8mfqF6UlADnzwMXLoiJ\nu+LFIyrfv3+/PNFnZZVfIEI9KN7PT9x6vXlTTODXr2tPTZuKW42AmORLSsrLs1W8lKW3t7g1rat8\nmq7SfUSNFJM/mPzlrEqNcXWd08REMZGUlFRf6F29hefpKe52dHLiVk5tFRQAZ84AJ08Cf/8t3p47\nJybbdu3ELfNKx1ozCwrg2KKF+NjevjzR17S4uiCIu7+vXRPv+/iIx1IZy3oj59r+ps4Qtf051I+k\nk50NnD+Pgt27xS24xMTySaEQS5j5+YnJprpi72Vl4slAN26IKwqCICYfX19xUt93dxd3RauvTlOx\n6L/6cWFh+YlI6vqolW/VJynZ2oq3TZs2bIISBHH3+ZEjQFyc+N3VJwOpr8dccbKyEttUPD5c+TYz\nU0z6V66IJdEeeQTo3BkIDwc6dqy6O76C04YaK65QlBenpwbB5C9fhogdkz/VjCCIibawUEysNTnL\nNScHOHwY+P13cTp/HggMhLODA9CzJzB4MPDGG0BAQO22+gRBTGTqQt5Xrohbrr/8IhbmtrXVvu6v\nevL2Fm+bNi0fgpSdLW6JXr1afoUg9fMVrwJSWqpdGNzOTtz7UHnsbsXJ3l7/71ZcLG6BHzlSPpmZ\nAY8/DvToIe5GV5/wlZMjDhWqeL1m9Ulg6jPCK54d7uIiHmu3twdmzQLat+eJWkQmgsmfHiwvDzh+\nXNzKPHZMnMrKxARy65a4AtCmDRAUJE7q+w4O4pbl0aPAgQNisj97FggNBfr2BRYvBrp1AywtkRAb\ni+aG2npUn13dpUvd56ePipfNU08ZGeXjdtVb6eoxvHfuiO9xcKj+urfqaxlfuiT+9n5+4srRiBHi\n7+btzd3hRFQnTP6NQUkJsH+/OKkv0F7dpFJpD0GqOKnHHefklCf6S5eA4GCge3dg1Cjgyy/Lk09B\nAZCUJJ4MdvEi8NtvwLJl4n31FmmnTmKynz8feOwxMck1JhYW5ddC1Zf68EPl691Wvj9ihLh136xZ\n/fWfiEwSk79cCYKYnH/4Adi6Vdw6DAsTt7wfNk5YVxGS9HQx0d+7J251du8uHvMNCal+V7CVlbhi\nEBxctW+3bolJ6wHHi02Wevc7EZFEmPzlJiEB2LRJnCwtgXHjxJWAmlxfVD2cqr4oFOL4Zz3xpCP5\nYuzki7GTL0PEjkP9jFl+fvnJa2fPAlu2iEPgxowRk35ICI/9EhGZKI7zh8yTf1ycmNzViV59pnp2\ntriV7usrngH/7LNA7966r/ZEREQmhckfMk3+t2+LQ9v+/ht44gnt8em+vuKwMFYqIyIiHVjkR27K\nyoBVq4B//QuYOhWIjBRPsiMiImoATP4NLSEBePVVcQXg99+BDh2k7hEREZkY7lNuKIWFwNy54u79\nsWPFSndM/ADEUpUkT4ydfDF28mWI2DH5N4SDB8Uz88+cAU6dAl57jcfyK+BCSL4YO/li7OSr0ST/\n6OhoBAUFISAgAIsWLdLZ5s0330RAQAA6deqEkydPNnAPa6CkRKx4t2sXsGgR8Pzz4pb+v/8N7NxZ\no4DFyI8AABM4SURBVPHvpuLUqVNSd4FqibGTL8ZOvgwRO8mP+atUKkybNg379++Hh4cHHn30UYSF\nhaFt27aaNlFRUUhKSkJiYiLi4uIQERGBY8eOSdhriMfsT54Ut+TV5W0vXhQvSerpWV7nfuBAYPVq\nlmh9AC6E5Iuxky/GTr4aRfKPj4+Hv7+/pmLR6NGjsWvXLq3kv3v3bkyYMAEA0K1bN2RlZSE1NRVu\nbm4N29msLGDfPiAqCti7V6yD362bmOTDw8WE7+fHK6MREZFRkzz5p6SkwMvLS/PY09MTcXFxD21z\n8+bN+k/+ggD884+Y7KOixC39Xr2AoUPFk/d8fev384mIiOqB5MlfoWd52sqFDHS9T9951Yl6RYAM\nav369VJ3gWqJsZMvxk6+6ho7yZO/h4cHbty4oXl848YNeHp6PrDNzZs34VHpxDnZVfcjIiKSiORn\n+4eGhiIxMRHJyckoLi7Gli1bEBYWptUmLCwMGzZsAAAcO3YMDg4ODX+8n4iIqJGQfMvf3Nwcy5cv\nx6BBg6BSqTBp0iS0bdsWK1euBABMmTIFQ4cORVRUFPz9/WFjY4O1a9dK3GsiIiIZExqBvXv3Cm3a\ntBH8/f2FhQsXSt0deghvb28hODhYCAkJER599FFBEAQhIyND6N+/vxAQECAMGDBAyMzMlLiXJAiC\nMHHiRKF58+ZChw4dNM89KFYLFiwQ/P39hTZt2gi//vqrFF2m/6crdnPnzhU8PDyEkJAQISQkRIiK\nitK8xtgZj+vXrwt9+vQR2rVrJ7Rv315YunSpIAiG/d+TffIvLS0V/Pz8hKtXrwrFxcVCp06dhISE\nBKm7RQ/g4+MjZGRkaD33zjvvCIsWLRIEQRAWLlwovPvuu1J0jSo5ePCg8Pfff2slkOpide7cOaFT\np05CcXGxcPXqVcHPz09QqVSS9Jt0x27evHnC4sWLq7Rl7IzL7du3hZMnTwqCIAg5OTlCYGCgkJCQ\nYND/PcmP+ddVxToBFhYWmjoBZNyESidoVqzlMGHCBPz0009SdIsq6dWrFxwdHbWeqy5Wu3btwpgx\nY2BhYQEfHx/4+/sjPj6+wftMIl2xA3SfHM3YGZcWLVogJCQEAGBra4u2bdsiJSXFoP97sk/+umoA\npKSkSNgjehiFQoH+/fsjNDQUq1atAgCtok1ubm5ITU2Vsov0ANXF6tatW1ojdfi/aJyWLVuGTp06\nYdKkScjKygLA2Bmz5ORknDx5Et26dTPo/57sk3+DjO0ngzpy5AhOnjyJvXv34uuvv8ahQ4e0Xlco\nFIyrTDwsVoyjcYmIiMDVq1dx6tQptGzZEjNnzqy2LWMnvdzcXDz33HNYunQp7OzstF6r6/+e7JO/\nPnUCyLi0bNkSAODq6opnn30W8fHxcHNzw507dwAAt2/fRvPmzaXsIj1AdbHSpx4HSat58+aapPHK\nK69odg0zdsanpKQEzz33HMaPH4/hw4cDMOz/nuyTvz51Ash45OfnIycnBwCQl5eHffv2ITg4GGFh\nYZqKVevXr9f8sZPxqS5WYWFh+PHHH1FcXIyrV68iMTERXbt2lbKrVMnt27c193fu3Ing4GAAjJ2x\nEQQBkyZNQrt27TB9+nTN8wb936vHExYbTFRUlBAYGCj4+fkJCxYskLo79ABXrlwROnXqJHTq1Elo\n3769Jl4ZGRnCk08+yaF+Rmb06NFCy5YtBQsLC8HT01P4/vvvHxirzz77TPDz8xPatGkjREdHS9hz\nqhy7NWvWCOPHjxeCg4OFjh07Cs8884xw584dTXvGzngcOnRIUCgUQqdOnTTDMvfu3WvQ/z2FILAu\nLhERkSmR/W5/IiIiqhkmfyIiIhPD5E9ERGRimPyJiIhMDJM/ERGRiWHyJyIiMjFM/kQGsm7dOiiV\nShw8eFDqrtTK1atXMXz4cLi6ukKpVGLixIlSd6lBxMbGQqlUaoqnSOGff/6Bubk5YmJiDDK/Xbt2\nwdLSEklJSQaZHzU+TP5k9NQLZ6VSidWrV+tso1Qq8fTTTzdwzxqX8PBwHDx4EO+99x4iIyMxderU\nB7a/cuUKXn31VQQFBcHGxgZOTk5o164dwsPDERsb2zCdNiApa9nPmDEDvXr1wpNPPmmQ+T3zzDMI\nDg7Gu+++a5D5UePD5E+yMm/ePBQWFup8jRciqb2ioiIcPnwYL730EmbMmIGxY8eiW7du1bY/fvw4\ngoODsW3bNgwePBhLlizBvHnz0K9fPxw9ehQ7duxowN7L259//on9+/djxowZOl//66+/MHr0aLRo\n0ULnnqU///wTvXr1glKpRFBQkCbhv/XWW9i5cycSEhLq/TuQ/JhL3QEifYWGhuL48eNYsmQJ5syZ\nI3V3JKVSqVBcXAwrKyuDzC81NRWCIOi8/rsuH3/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"text": [
"<matplotlib.figure.Figure at 0x14200ad0>"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Visualizing the Error Surface"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For curiosity sake, let's try and visualize the error surface. But before visualizing the surface let's look at how the error measure changes as the gradient descent proceeds."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_gradient_descent(w_h_i, cross_entropy_error):\n",
" start_time = time.time()\n",
" \n",
" fig = plt.figure(figsize=(8, 6))\n",
" ax = fig.add_subplot(1, 1, 1)\n",
" ax.set_xlabel(r'Iteration', fontsize=18)\n",
" ax.set_ylabel(r'In-Sample Error ($E_{in}$)', fontsize=18)\n",
" ax.set_title(r'Gradient Descent Evolution'.format(N), fontsize=18)\n",
" ax.set_xlim(0, w_h_i.shape[0]-1)\n",
" ax.set_ylim(0, 1)\n",
" ax.xaxis.grid(color='gray', linestyle='dashed')\n",
" ax.yaxis.grid(color='gray', linestyle='dashed')\n",
" ax.set_axisbelow(True)\n",
" \n",
" ax.plot(range(w_h_i.shape[0]), np.apply_along_axis(cross_entropy_error, 1, w_h_i), 'r-')\n",
" \n",
" print('Plot took {:.2f} seconds.'.format(time.time()-start_time))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_gradient_descent(w_h_i, cross_entropy_error)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 0.05 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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gr7+AWrUsHQ4REZFZVbg3/q5du8r94Tt37iz3eyvMy0vKXflERERFlVrse/bs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\nx/snk3LCdCcAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1e9cead0>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The in-sample error is parameterized by our model parameters ${\\bf w}$. Unfortunately our parameter is of dimension $d_{\\bf w}=3$ which makes visualization a bit more difficult (a four dimensional visualization problem: three parameters and an error value). Instead of tackling that directly (volumetrics and other fun stuff) we'll just visualize the top, front, and left slices of the error surface centered on the final hypothesis parameters. Along with these slices the iterations we've taken on the error surface using gradient descent which will be colored by iteration number backwards through a rainbow color map. Using the history of the weight vector through the gradient descent iterations we can determine the extents of our visualization."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def visualize_error_surface_slices(w_h_i, cross_entropy_error, s=150, figsize=(6, 6)):\n",
" d_z = w_h_i.shape[1]\n",
" \n",
" w_h_i_mean = np.mean(w_h_i, axis=0)\n",
" w_h_i_std = np.std(w_h_i, axis=0)\n",
" w_h_i_min_extent = w_h_i_mean - 4 * np.max(w_h_i_std)\n",
" w_h_i_max_extent = w_h_i_mean + 4 * np.max(w_h_i_std)\n",
" w_h_i_colors = cm.ScalarMappable(norm=matplotlib.colors.Normalize(0, w_h_i.shape[0]-1),\n",
" cmap=cm.gist_rainbow_r).to_rgba(range(w_h_i.shape[0]-1))\n",
" \n",
" for i_x, i_y in itertools.combinations(list(range(1, d_z)) + [0], 2):\n",
" \n",
" start_time = time.time()\n",
" \n",
" components = list(range(d_z))\n",
" components.remove(i_x)\n",
" components.remove(i_y)\n",
" \n",
" w_zs = [w_h[i] * np.ones((s*s, 1)) for i in components]\n",
" w_x, w_y = np.array(np.meshgrid(np.linspace(w_h_i_min_extent[i_x], w_h_i_max_extent[i_x], s),\n",
" np.linspace(w_h_i_min_extent[i_y], w_h_i_max_extent[i_y], s)))\n",
" \n",
" restack = [None] * (d_z)\n",
" restack[i_x] = np.reshape(w_x, (s*s, 1))\n",
" restack[i_y] = np.reshape(w_y, (s*s, 1))\n",
" for i_z, w_z in zip(components, w_zs):\n",
" restack[i_z] = w_z\n",
" w_grid = np.hstack(restack)\n",
" \n",
" error_grid = np.reshape(np.apply_along_axis(cross_entropy_error, 1, w_grid), (s, s))\n",
" \n",
" fig = plt.figure(figsize=figsize)\n",
" ax = fig.add_subplot(1, 1, 1)\n",
" ax.set_aspect(1)\n",
" ax.set_xlabel(r'$w_{:}$'.format(i_x), fontsize=18)\n",
" ax.set_ylabel(r'$w_{:}$'.format(i_y), fontsize=18)\n",
" if d_z == 3:\n",
" ax.set_title(r'Error Surface ({:} view)'.format({0: '\"top-to-bottom\"',\n",
" 1: '\"right-to-left\"',\n",
" 2: '\"back-to-front\"'}[components[0]]),\n",
" fontsize=18)\n",
" else:\n",
" ax.set_title(r'Error Surface', fontsize=18)\n",
" ax.set_xlim(w_h_i_min_extent[i_x], w_h_i_max_extent[i_x])\n",
" ax.set_ylim(w_h_i_min_extent[i_y], w_h_i_max_extent[i_y])\n",
" ax.autoscale(False)\n",
" \n",
" ax.pcolor(w_x, w_y, error_grid, cmap=cm.gist_heat, vmin=np.min(error_grid), vmax=np.max(error_grid))\n",
" \n",
" ax.xaxis.grid(color='gray', linestyle='dashed')\n",
" ax.yaxis.grid(color='gray', linestyle='dashed')\n",
" \n",
" for i in range(w_h_i.shape[0]-1):\n",
" ax.plot(w_h_i[i:i+2, i_x], w_h_i[i:i+2, i_y], '-', c=w_h_i_colors[i])\n",
" \n",
" print('Plot took {:.2f} seconds.'.format(time.time()-start_time))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"visualize_error_surface_slices(w_h_i, cross_entropy_error, s=150)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 2.43 seconds.\n",
"Plot took 2.50 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.37 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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levh0a2jYvZnq83M188WJsCitUBKXTufOnVFVVYVt27ahoqIC27ZtQ79+/Uqh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RAAAG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\n",
"text": [
"<matplotlib.figure.Figure at 0x13ea82d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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BBo1OIFzkouHnyUvD8wnLraST4mrigpJtTPNWv1WlpqZyPanG9LYl0RhWaA1S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\naeQbazqP6ZxRPcsmQXMJJhZM1BvUTLyGqDammcwTdmNaUOs/n6zsXlR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"text": [
"<matplotlib.figure.Figure at 0x251a9390>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Q5DFxC6muRckjXtfx0bl6kkxNVY1RShoTN1Dc1NQ4faL6Ufqb8LHhm9RYcWEq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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x25184910>"
]
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Nonlinear Transformation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Like with the other linear models (perceptron, linear regression) we can transform the input data from the original input space ($\\mathcal{X}$) into a higher dimension space ($\\mathcal{Z}$) and fit our model there.\n",
"\n",
"In this example we'll use a second-order polynomial transformation:\n",
"\n",
"$$\n",
"\\phi({\\bf x}) = \\begin{bmatrix} 1 & x_0 & x_1 & x_0 x_1 & x_0^2 & x_1^2 \\end{bmatrix}\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d_x = 2\n",
"\n",
"phi = lambda x: np.array([1, x[1], x[2], x[1]*x[2], x[1]**2, x[2]**2])\n",
"d_z = len( phi( np.ones((d_x+1,)) ) ) - 1\n",
"\n",
"N = 30"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w_f, f, P_f = generate_target(d_z, w_f=np.array([-3, 2, 3, 6, 9, 10]))\n",
"x, z, y, cross_entropy_error = generate_data_samples(N, P_x, phi, P_f)\n",
"x_1, x_2, x_grid, z_grid = generate_fill_data(300, phi)\n",
"f_grid = apply_to_fill(z_grid, f)\n",
"target_fig = plot_data_set_and_hypothesis(x, y, x_1, x_2, f_grid, title=r'Target, $N={:}$'.format(N))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 5.23 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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BoEGDIIoiJk2ahK5du+KFF14AAEyePBlvv/02nnvuOfA8D6/Xi4ULF9ZTb7NT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\nbBbqSgyFuL0cOI7REBPt2L922/r1y0k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P8unHFEo6IQSoLIs+noVNw+jSskVL3Dv9Xlw7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\nTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x13e23850>"
]
}
],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w_h_i = gradient_descent(z, y, eta=4.0)\n",
"w_h = w_h_i[-1]\n",
"print('Number of iterations: {:}'.format(w_h_i.shape[0]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of iterations: 143\n"
]
}
],
"prompt_number": 39
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = lambda z: logistic(w_h.dot(z.T))\n",
"h_grid = apply_to_fill(z_grid, h)\n",
"hypothesis_fig = plot_data_set_and_hypothesis(x, y, x_1, x_2, h_grid, title=r'Hypothesis, $N={:}$'.format(N))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 5.35 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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MkL1r6eL4FTkWXJYLXJYLAKSLEK8/cq+LFV+Jt8uqrdLeWlnzvhL3TakP0FcA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OMe7vy7Iyq3BEQ+xpmoqd2Ksy84C8+99Bzee+1djBt9WAEIg6ePtligIRWdyBIEWcp4Mj7bHs0P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\n+wU/FpsQHQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x142006d0>"
]
}
],
"prompt_number": 40
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print('Target weights: {:}'.format(w_f))\n",
"print('Hypothesis weights: {:}'.format(w_h))\n",
"print('Hypothesis in-sample error: {:.2%}'.format(in_sample_error(z, y, h)))\n",
"print('Hypothesis out-of-sample error: {:.2%}'.format(estimate_out_of_sample_error(P_x, phi, P_f, h)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Target weights: [-3 2 3 6 9 10]\n",
"Hypothesis weights: [-2.03435116 1.43625398 1.42565611 6.32051478 4.462231 8.56118427]\n",
"Hypothesis in-sample error: 10.00%\n",
"Hypothesis out-of-sample error: 14.87%"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For fun we'll try visualizing the error surface again. However, since we're operating in the $\\mathcal{Z}$ space with dimension $d_\\mathcal{Z}=6$ our two-dimensional visualizations are even more woefully inadequate. Regardless, below is the gradient descent evolution and all 15 combinations of two axes and their two-dimensional error \"surface\" slice centered on the hypothesis weight vector."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_gradient_descent(w_h_i, cross_entropy_error)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 0.05 seconds.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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nbOOSPUmLvk1MuKyEuctH1rwB5i4ri/XeN0ZKSgrCw8NNvVmDqVQqiF69gE2b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\nWPSJiIjSBIs+ERFRmvgBOc2qf26AnD0AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x3faf7d0>"
]
}
],
"prompt_number": 42
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"visualize_error_surface_slices(w_h_i, cross_entropy_error, s=150)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot took 2.31 seconds.\n",
"Plot took 2.48 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.35 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.31 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.44 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.30 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.43 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.31 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.29 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.45 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.29 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.29 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.29 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.48 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Plot took 2.30 seconds."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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rgaaL2m0uO6ZJcYYeY+qZRtpeyE07wEGGi6bPWQq5jPl92WsMJrSRaaSlB4tw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\noWnZSjntCwMDmL9yJUvTtAObldIk7YZmu4yktvz84sc6LMv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0E42pryousuiMuweUjxac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"text": [
"<matplotlib.figure.Figure at 0x2845b950>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Zsv0MDAaDwdAl5u3LQA3vah5aWSvEi+ubHIeYJfkOWrif1B/XnraBQuvK/dxE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\nBkIIIZBiIIQQAikGQgghkGIghBAC+B+iHjn+F3oINQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x204e8b10>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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HIN7/SyDSSuUsJEmCS2p/p8Lvt96bf9sVylRFrz1GVSHbtBQNV83sqqouWs3s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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x6511f90>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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gUnyOml1drAZutvfZX6yCuwc2sLnPWbKFssojOIRmaHO+lCmw0apNbVzWD0dj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\n1UbJqLepfPRz+muA+v5FpY/qbTbpo2r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