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Stanford Online/ DeepLearning.AI. Supervised Machine Learning: Feature scaling and Learning Rate (Multi-variable).
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Optional Lab: Feature scaling and Learning Rate (Multi-variable)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Goals\n",
"In this lab you will:\n",
"- Utilize the multiple variables routines developed in the previous lab\n",
"- run Gradient Descent on a data set with multiple features\n",
"- explore the impact of the *learning rate alpha* on gradient descent\n",
"- improve performance of gradient descent by *feature scaling* using z-score normalization"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Tools\n",
"You will utilize the functions developed in the last lab as well as matplotlib and NumPy. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np # Get numpy library as 'np' constructor\n",
"import matplotlib.pyplot as plt # Get matplotlib, pyplot library as 'plt' constructor\n",
"\n",
"# 'lab_utils_multi.py' file is loaded to use some functions, when you load data set, run Gradient Descent and plot graphs.\n",
"from lab_utils_multi import load_house_data, run_gradient_descent \n",
"from lab_utils_multi import norm_plot, plt_equal_scale, plot_cost_i_w\n",
"from lab_utils_common import dlc\n",
"\n",
"np.set_printoptions(precision=2) # reduced display precision on numpy arrays\n",
" # These options determine the way floating point numbers, arrays \n",
" # and other NumPy objects are displayed. (Precision = integer or None \n",
" # defining the number of digits of precision for floating point output. \n",
" # default 8)\n",
" \n",
"plt.style.use('./deeplearning.mplstyle') # Use or import 'available style sheets', using its 'name',\n",
" # on a common set of example plots: scatter plot, image, \n",
" # bar graph, patches, line plot and histogram."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Notation\n",
"\n",
"|General <br /> Notation | Description| Python (if applicable) |\n",
"|: ------------|: ------------------------------------------------------------||\n",
"| $a$ | scalar, non bold ||\n",
"| $\\mathbf{a}$ | vector, bold ||\n",
"| $\\mathbf{A}$ | matrix, bold capital ||\n",
"| **Regression** | | | |\n",
"| $\\mathbf{X}$ | training example maxtrix | `X_train` | \n",
"| $\\mathbf{y}$ | training example targets | `y_train` \n",
"| $\\mathbf{x}^{(i)}$, $y^{(i)}$ | $i_{th}$Training Example | `X[i]`, `y[i]`|\n",
"| m | number of training examples | `m`|\n",
"| n | number of features in each example | `n`|\n",
"| $\\mathbf{w}$ | parameter: weight, | `w` |\n",
"| $b$ | parameter: bias | `b` | \n",
"| $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ | The result of the model evaluation at $\\mathbf{x}^{(i)}$ parameterized by $\\mathbf{w},b$: $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) = \\mathbf{w} \\cdot \\mathbf{x}^{(i)}+b$ | `f_wb` | \n",
"|$\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j}$| the gradient or partial derivative of cost with respect to a parameter $w_j$ |`dj_dw[j]`| \n",
"|$\\frac{\\partial J(\\mathbf{w},b)}{\\partial b}$| the gradient or partial derivative of cost with respect to a parameter $b$| `dj_db`|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem Statement\n",
"\n",
"As in the previous labs, you will use the motivating example of housing price prediction. The training data set contains many examples with 4 features (size, bedrooms, floors and age) shown in the table below. Note, in this lab, the Size feature is in sqft while earlier labs utilized 1000 sqft. This data set is larger than the previous lab.\n",
"\n",
"We would like to build a linear regression model using these values so we can then predict the price for other houses - say, a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old. \n",
"\n",
"## Dataset: \n",
"| Size (sqft) | Number of Bedrooms | Number of floors | Age of Home | Price (1000s dollars) | \n",
"| ----------------| ------------------- |----------------- |--------------|----------------------- | \n",
"| 952 | 2 | 1 | 65 | 271.5 | \n",
"| 1244 | 3 | 2 | 64 | 232 | \n",
"| 1947 | 3 | 2 | 17 | 509.8 | \n",
"| ... | ... | ... | ... | ... |\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"X_train matrix Size (rows, cols) = (99, 4) \n",
" [[1.24e+03 3.00e+00 1.00e+00 6.40e+01]\n",
" [1.95e+03 3.00e+00 2.00e+00 1.70e+01]\n",
" [1.72e+03 3.00e+00 2.00e+00 4.20e+01]\n",
" [1.96e+03 3.00e+00 2.00e+00 1.50e+01]\n",
" [1.31e+03 2.00e+00 1.00e+00 1.40e+01]\n",
" [8.64e+02 2.00e+00 1.00e+00 6.60e+01]\n",
" [1.84e+03 3.00e+00 1.00e+00 1.70e+01]\n",
" [1.03e+03 3.00e+00 1.00e+00 4.30e+01]\n",
" [3.19e+03 4.00e+00 2.00e+00 8.70e+01]\n",
" [7.88e+02 2.00e+00 1.00e+00 8.00e+01]\n",
" [1.20e+03 2.00e+00 2.00e+00 1.70e+01]\n",
" [1.56e+03 2.00e+00 1.00e+00 1.80e+01]\n",
" [1.43e+03 3.00e+00 1.00e+00 2.00e+01]\n",
" [1.22e+03 2.00e+00 1.00e+00 1.50e+01]\n",
" [1.09e+03 2.00e+00 1.00e+00 6.40e+01]\n",
" [8.48e+02 1.00e+00 1.00e+00 1.70e+01]\n",
" [1.68e+03 3.00e+00 2.00e+00 2.30e+01]\n",
" [1.77e+03 3.00e+00 2.00e+00 1.80e+01]\n",
" [1.04e+03 3.00e+00 1.00e+00 4.40e+01]\n",
" [1.65e+03 2.00e+00 1.00e+00 2.10e+01]\n",
" [1.09e+03 2.00e+00 1.00e+00 3.50e+01]\n",
" [1.32e+03 3.00e+00 1.00e+00 1.40e+01]\n",
" [1.59e+03 0.00e+00 1.00e+00 2.00e+01]\n",
" [9.72e+02 2.00e+00 1.00e+00 7.30e+01]\n",
" [1.10e+03 3.00e+00 1.00e+00 3.70e+01]\n",
" [1.00e+03 2.00e+00 1.00e+00 5.10e+01]\n",
" [9.04e+02 3.00e+00 1.00e+00 5.50e+01]\n",
" [1.69e+03 3.00e+00 1.00e+00 1.30e+01]\n",
" [1.07e+03 2.00e+00 1.00e+00 1.00e+02]\n",
" [1.42e+03 3.00e+00 2.00e+00 1.90e+01]\n",
" [1.16e+03 3.00e+00 1.00e+00 5.20e+01]\n",
" [1.94e+03 3.00e+00 2.00e+00 1.20e+01]\n",
" [1.22e+03 2.00e+00 2.00e+00 7.40e+01]\n",
" [2.48e+03 4.00e+00 2.00e+00 1.60e+01]\n",
" [1.20e+03 2.00e+00 1.00e+00 1.80e+01]\n",
" [1.84e+03 3.00e+00 2.00e+00 2.00e+01]\n",
" [1.85e+03 3.00e+00 2.00e+00 5.70e+01]\n",
" [1.66e+03 3.00e+00 2.00e+00 1.90e+01]\n",
" [1.10e+03 2.00e+00 2.00e+00 9.70e+01]\n",
" [1.78e+03 3.00e+00 2.00e+00 2.80e+01]\n",
" [2.03e+03 4.00e+00 2.00e+00 4.50e+01]\n",
" [1.78e+03 4.00e+00 2.00e+00 1.07e+02]\n",
" [1.07e+03 2.00e+00 1.00e+00 1.00e+02]\n",
" [1.55e+03 3.00e+00 1.00e+00 1.60e+01]\n",
" [1.95e+03 3.00e+00 2.00e+00 1.60e+01]\n",
" [1.22e+03 2.00e+00 2.00e+00 1.20e+01]\n",
" [1.62e+03 3.00e+00 1.00e+00 1.60e+01]\n",
" [8.16e+02 2.00e+00 1.00e+00 5.80e+01]\n",
" [1.35e+03 3.00e+00 1.00e+00 2.10e+01]\n",
" [1.57e+03 3.00e+00 1.00e+00 1.40e+01]\n",
" [1.49e+03 3.00e+00 1.00e+00 5.70e+01]\n",
" [1.51e+03 2.00e+00 1.00e+00 1.60e+01]\n",
" [1.10e+03 3.00e+00 1.00e+00 2.70e+01]\n",
" [1.76e+03 3.00e+00 2.00e+00 2.40e+01]\n",
" [1.21e+03 2.00e+00 1.00e+00 1.40e+01]\n",
" [1.47e+03 3.00e+00 2.00e+00 2.40e+01]\n",
" [1.77e+03 3.00e+00 2.00e+00 8.40e+01]\n",
" [1.65e+03 3.00e+00 1.00e+00 1.90e+01]\n",
" [1.03e+03 3.00e+00 1.00e+00 6.00e+01]\n",
" [1.12e+03 2.00e+00 2.00e+00 1.60e+01]\n",
" [1.15e+03 3.00e+00 1.00e+00 6.20e+01]\n",
" [8.16e+02 2.00e+00 1.00e+00 3.90e+01]\n",
" [1.04e+03 3.00e+00 1.00e+00 2.50e+01]\n",
" [1.39e+03 3.00e+00 1.00e+00 6.40e+01]\n",
" [1.60e+03 3.00e+00 2.00e+00 2.90e+01]\n",
" [1.22e+03 3.00e+00 1.00e+00 6.30e+01]\n",
" [1.07e+03 2.00e+00 1.00e+00 1.00e+02]\n",
" [2.60e+03 4.00e+00 2.00e+00 2.20e+01]\n",
" [1.43e+03 3.00e+00 1.00e+00 5.90e+01]\n",
" [2.09e+03 3.00e+00 2.00e+00 2.60e+01]\n",
" [1.79e+03 4.00e+00 2.00e+00 4.90e+01]\n",
" [1.48e+03 3.00e+00 2.00e+00 1.60e+01]\n",
" [1.04e+03 3.00e+00 1.00e+00 2.50e+01]\n",
" [1.43e+03 3.00e+00 1.00e+00 2.20e+01]\n",
" [1.16e+03 3.00e+00 1.00e+00 5.30e+01]\n",
" [1.55e+03 3.00e+00 2.00e+00 1.20e+01]\n",
" [1.98e+03 3.00e+00 2.00e+00 2.20e+01]\n",
" [1.06e+03 3.00e+00 1.00e+00 5.30e+01]\n",
" [1.18e+03 2.00e+00 1.00e+00 9.90e+01]\n",
" [1.36e+03 2.00e+00 1.00e+00 1.70e+01]\n",
" [9.60e+02 3.00e+00 1.00e+00 5.10e+01]\n",
" [1.46e+03 3.00e+00 2.00e+00 1.60e+01]\n",
" [1.45e+03 3.00e+00 2.00e+00 2.50e+01]\n",
" [1.21e+03 2.00e+00 1.00e+00 1.50e+01]\n",
" [1.55e+03 3.00e+00 2.00e+00 1.60e+01]\n",
" [8.82e+02 3.00e+00 1.00e+00 4.90e+01]\n",
" [2.03e+03 4.00e+00 2.00e+00 4.50e+01]\n",
" [1.04e+03 3.00e+00 1.00e+00 6.20e+01]\n",
" [1.62e+03 3.00e+00 1.00e+00 1.60e+01]\n",
" [8.03e+02 2.00e+00 1.00e+00 8.00e+01]\n",
" [1.43e+03 3.00e+00 2.00e+00 2.10e+01]\n",
" [1.66e+03 3.00e+00 1.00e+00 6.10e+01]\n",
" [1.54e+03 3.00e+00 1.00e+00 1.60e+01]\n",
" [9.48e+02 3.00e+00 1.00e+00 5.30e+01]\n",
" [1.22e+03 2.00e+00 2.00e+00 1.20e+01]\n",
" [1.43e+03 2.00e+00 1.00e+00 4.30e+01]\n",
" [1.66e+03 3.00e+00 2.00e+00 1.90e+01]\n",
" [1.21e+03 3.00e+00 1.00e+00 2.00e+01]\n",
" [1.05e+03 2.00e+00 1.00e+00 6.50e+01]] \n",
"y_train vector Size (rows, cols) = (99,) \n",
" [300. 509.8 394. 540. 415. 230. 560. 294. 718.2 200.\n",
" 302. 468. 374.2 388. 282. 311.8 401. 449.8 301. 502.\n",
" 340. 400.28 572. 264. 304. 298. 219.8 490.7 216.96 368.2\n",
" 280. 526.87 237. 562.43 369.8 460. 374. 390. 158. 426.\n",
" 390. 277.77 216.96 425.8 504. 329. 464. 220. 358. 478.\n",
" 334. 426.98 290. 463. 390.8 354. 350. 460. 237. 288.3\n",
" 282. 249. 304. 332. 351.8 310. 216.96 666.34 330. 480.\n",
" 330.3 348. 304. 384. 316. 430.4 450. 284. 275. 414.\n",
" 258. 378. 350. 412. 373. 225. 390. 267.4 464. 174.\n",
" 340. 430. 440. 216. 329. 388. 390. 356. 257.8 ]\n",
"List of input features names [X0, X1, X2, X3] = ['size(sqft)', 'bedrooms', 'floors', 'age']\n"
]
}
],
"source": [
"# load the training set or dataset, using 'load_house_data()' function\n",
"X_train, y_train = load_house_data()\n",
"\n",
"# Print X_train matrix and y_train vector as shape (rows, cols), and full training set\n",
"print('X_train matrix Size (rows, cols) = ', X_train.shape,'\\n', X_train, \n",
" '\\ny_train vector Size (rows, cols) = ', y_train.shape,'\\n', y_train) \n",
"\n",
"# Create the list of input features 'strings'/'names'\n",
"X_features = ['size(sqft)','bedrooms','floors','age']\n",
"\n",
"# Prin the list of Input Features names\n",
"print('List of input features names [X0, X1, X2, X3] = ', X_features)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's view the dataset and its features by plotting each feature versus price."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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hmDRpEl577TWPVTCQyaUNMjHdhrKXnzMhCth4r/yqaCItcJQ6yxvmHwCqbZaCVwupvF8L79VDK7Sycx95h9bOQ3JTnKoF0DYSSIi0rn9rg+/HJ1IvhwF248aNMXfuXLz66qv4+eefcebMGQDSRjM333wzIiMjPV7JQCG38n7dEODWFUBxZd3nO3MbKiHKfhDO1f6kZvZSZ3kLpzy4Ris795H32U1ZphJK/b2ZHvj+XusyR+MTz6+BzemNZgwGAzIyMjxZl4Bmb+X9oFbS7SpbDb0NxdX+pAWOviR6mtIgGeTVWmgHp4iQJa2dZ5SmpeVclN6LbZ2VxietvW9yP4dzsAHg6tWr+M9//oMJEyZgyJAhuOeeezBhwgR89NFHuHr1qqfrGBDsrbyfnSbddrLkjttQXO1P5NgvJa6VBzpOESFLWjvPzE6T5ljbKq92rc5ae9/kfg4D7Pz8fKSkpGDChAk4ePAgwsLCoNfrcejQITz++OPo1KkT8vPzvVFXv3ZE4WR9uuL6bagRHYCMFtJ/3fEtmLe+SQssV/SPXO9cBh13Kr8mX16hUB7oOEWELGntPJMQBXS6Qf7Y6QrnxyOtvW9yP4dTRCZPnoykpCTs3r27Tjq+S5cu4ZFHHsFTTz2Fr7/+2mOV9HcFpUDOBfljWwqBhI+BJbdb34YydfKGzO1SQ4YGInvUcJs1JhQokQkOo0O98/u1JipEvjxSoZz8mxbPM4lG+Y1wNhcCSZ9YL3q2HY9M864PXJR/bTW/b3IvhwH2pk2bsHXrVtlc19HR0Xj99dfRt29fj1QuUNjbKeqakNIEpa8CBrQEFvSXym2Djs2FQLdYoOSa8wG3GjI0ENlj7zart+Zlj+wAvPo/+XKq65zCFTqlcvJvE1KAzw5bB6WNdVK5Will8LLNJgRIz7ntv8DmodJj23OzJZ5fA4vDAFuv11vtt26rtLQUer3erZUKNPZ2irK04ZTUeTvF1O3Ax8ulfybOXOVTQ4YGInvUcJv1b9nK5bN7eq8eWrHrvGvl5N/m7JVPczlnr3rTXFqeG7PygSs19p9/6jKQvhLoFicfXMeHAQNb8fwaaBzOwR46dCjGjh2LDRs2QIjrvUQIgQ0bNmD8+PEYNmyYRyvp75Ruock5Ugpsk7l1Jfc8ZxZTmFZAf3+v9F92flITNdxevlrrWnmgu6bwd1EqJ/+2vUi+fIdCuVqYzo2hTqYLOlGh/F5TYnh+DUQOA+y3334bnTp1wqBBgxAWFoZWrVqhVatWCAsLwx133IHU1FS8/fbb3qir35LLEmKPs4vxLa/y+XqhGFF9eCqDDnlOsMJZRamcSM1iXFhrcfGKfDnnXQcmh1NEDAYDVq5ciby8PGzduhWFhYUApI1m+vTpgw4dOBGxoWynagQB2FgoP98LADrHAudPKR83MXVqNSwUI6oPNUxjigwCymRuEUcyEbas25pL09nkyinwJEbKb5TWTiN71C25HRiw2vH5FpDWTNniBYHA5fRGMx06dGAw7QUCQHwE8NEA4Llt0hxUyz6bGAVEBDnu7JadWg0LxYjqy9cbzUSEAGUyAUIEs2LIWtAf6LkcOGuxRUJc6PUF2hRYTiisl1AqV5t+LaTz8fiNQIVCMgI5nHdNTgfYSq5du4bCwkK0adPGHfUJSEpXmDfdJ/2/7dW7sT/Iv058mDTXy/YqnxoWihFpFfNguy4sGMBVm8cUkMoU+olSv1KbglLgpZ2uBdfA9XnXFLgaHGAfOHAA3bt3R02Ng2W2pMjRFWbbTqq08GtgK/kOrYaFYkRapXSziGv25GXutM5oBEiPeccsMGk9j7zc+dkZPL8Sl52ogL0rzHKLE11d+MWFYkT1l2R0rTzQ8Y4ZWVpyOxBkszI/SCeVq43c+dZRGt3WEUAbg3WZv5xfmRyhYRxewU5KSrJ7vKqK+982REEpcFghzXhQI+XFiR9kAKO/By5dla4EfJChPM9LDQvFiOrLtDNaQ3YtbYjYMNfKAx13ciRLrQ3ADSHWc/JvCJHK1URpqmaqwrbplnOsAcfnV1+PY65icoSGcxhgHzt2DA899BDatWsne7ywsBALFixwe8UCgakBn1T4hrzvHFBsk/bnSCnwzFYg94K0wyMAXKqS5mXba/i+XihGVB9qGOSzz7pWHujOySwItVdO/u2ZrdbBNSA9fmYrsGqwb+okR2mqZrzCF+m5fYCHLPI+2Du/qmEccxWTIzScwwA7NTUVvXv3xsSJE2WP7927lwF2PTma23Xxqnz5jiKgyOZkxYZP/kgNg/x5hX6oVB7odit88VAqJ/+mlY1mlKaCKLXb53dYB9j2qGEccxWnejWcwwD7d7/7HbKzFfYKBhASEsIMIjYsbwUZgwGhA0qr6t4WcjS3K6gRcE1m7ajSois2fPI3HOS1R2nxJxeFkpopJQOoUmi45124I6PFcYzJERrOYYD9/vvv280Q0rFjRxQUFLi1UlohN6cKqHsryJLlbSFHW6T3jQcKyq1fKzEK6BQDrDpW9/ls+ORvbBdHmTRydjtTN4gLBYplrlbHaSQLgrdFNgYuyCzNiWxwzirSol5N5c9Xtzb1fl3smZ0mnZ9tz91KF7Qqa6QYwJkpHloMVuX+Hv6yeNNbHA55oaE8i8hRmlPVKcb+tA/L20JKHRqQVibPz5D+33bxBADkXGTDJ/+Xc961ck/44i4gfZV8OdWl9OXHm1+KSD3e7gv875z1xjKtI6RyNbFMBrD+ZN1pmLaqhfNTPLQYrDI5QsPZDbArKysRFub8UnlXn69lSnOqlJLqWzLdFrJswEdKgTOXgWZ6IDHauiHLdWA2fAoEcldC7ZV7Qr8WwI/3WmftWXK7VE51lSiMgUrl5N8SooAf79PG+cqUDCBjleMAG3B+iodWg1UmR2gYu3mwExMT8c477+DSpUt2X2T79u0YNmwY3nrrLad+aV5eHvR6PUaOHGku27BhA5KTkxEeHo6MjAwcO3b9npIQAtOnT0dsbCxiY2Mxbdo0COFgr3APU5pT5cxFGsvbQqYGvG0YUDAS2Ha/9Niy48nlojT93Pf31n0+kb9QGqB8lcDft6OONqjtMyP10Er/cTR908R2ioe9vNE8Zwceu1ewV69ejT/96U+YMWMG+vXrh7S0NLRs2RJ6vR4XLlxAbm4uNm3ahOLiYjz33HN49tlnnfqlTz75JG655Rbz43PnzmHYsGFYuHAhhgwZgszMTAwfPhzbt28HAMyfPx8rV67E3r17odPpMGjQILRr1w6TJk1qwFtvGKUO2DkWOH9Kun0kx9XbQnJTUVYVAKkxQPtobXwLJqqv21pIt2vlyr1l02lgwOrrfbqkSnq84R5exZbToymw9Yx8OQWeglKg/yrr3T03FwIb71XvuWtCCvBJnv0vBLbncm+m4tNaTu1AZTfA7tGjBzZt2oRdu3Zh6dKl+Oqrr1BQUIDKykrExcWhe/fumDp1KkaMGAGDwbms8cuWLUN0dDR69+6Nw4cPAwBWrFiB1NRUPPDAAwCAV155BU2aNMHBgweRnJyMJUuWYOrUqWjVqhUAYOrUqViwYIFPA+zZadIgYTlotDEAEUHywbVlUnpXOsKEH+pORSmvBnaclf7VpwNvOi3d7r54VdrGlre7Sa3mpwO9Vljfro0Pk8q95ZH1dft0tZDKT47yXj200m+bKCzbUSon//bMVuvzJCA9VlsebEvzD8gH1411QI8mQEQIcOgS0O2L631x/gHvpOKTC+Q3nACCgoDya+oeGwKNU+u6e/TogR49ejT4l5WWluLll1/Ghg0bsGjRInN5bm4uunbtan4cERGBxMRE5ObmIjk5uc7xrl27Ijc3t8H1aSjbWSpnLwPHFHYrS4mROpnpFpIz3zw3nQbWn7ZfB1c7MK/GkdbU1tp/7GlK8yy9mWJLS/32zGX58iKFcvJva2UyiADAOoVyNTisMCu2QxTwZm/5vpgaLf8z7h4n5NZ/nbHYkE7NY0Og8eq0uMzMTIwbNw6tW7e2Ki8vL4fRaLQqMxqNKCsrkz1uNBpRXl7u03nYmTutV0UDQGWtlN1DTouI67fKluYBG09L/+2/ynqelqXR3ztXF1c68Ojv5a/GOfu7iLzp8Y3yu8A9vtF7dVAaZbw5+mip3xaUyZfnK5STf7ui0FEqVTwhu+iKfHleqfIdrRyFoNzdqfgc7Z9hqo8ax4ZA47UAOzs7G+vXr8eUKVPqHDMYDCgttY4yS0tLERkZKXu8tLQUBoMBOp3v8j4pNfJqARhs7guY5mrZu1UmR2knR1uudGCl17zEXelIhbbIzOUF5Of4eorSIBnkvSpoqt8q1dXZ8YzI15opJEOrFkCxwp2YGpkvDJ5IxefsAkw1jg2Bxmup/zdu3IijR4+ad30sLy9HTU0NDhw4gEmTJmHJkiXm51ZUVODIkSNITU0FIG3XvnfvXqSlSS1179695mO+Yq+Rd4qRUu3ZpuNR2jJ2a6F8eUyodLvHHlc7sNJrRnN+JKmQ0nSQGi9OEwkNkjaVsBXixQhbS/1WaYG3Ujn5tyCdfPCptImUGiQage3F8seUt92z1jbSMwscZ6cBWfnAFQcVUePYEGi8dgV7woQJOHLkCLKzs5GdnY1Jkybh7rvvxnfffYehQ4ciJycHWVlZuHLlCmbNmoUuXbogOTkZADBq1Ci89dZbOHXqFE6fPo05c+ZgzJgx3qq6rNlpda9UmyRGu5aO51KVNMfSNr3PktulRRWWGuuAgS2AjBbAiA7WHdheiiATpddccrtz75vIm+LDXSv3hLYKX6bbOreu2y201G+DFc4qSuXk357v5lq5Gtg7v9c6+UUxIdIzmT0SooA7Wtt/Tn3GBmfiB3KN165gh4eHIzz8+lnRYDBAr9cjLi4OAJCVlYXJkydj5MiR6NmzJ5YtW2Z+7sSJE5Gfn4/OnTsDAMaPH4+JEyd6q+qyEqKABf2BRzdYX5mxd0W5fRRQLJO8vkYAd38tZQcxMWUH2XCPcxtcOJsiqF8L51+TyNeWDgRuX2V91Sjot3JvsZ0Dbi5XmKfpCVrqtz3igJ9k7tb1iPN+Xcj3tincuVUqV4OEKODru+uel13hyW3Q5/YBci9Yn+8b64CwICA2zPWxwZspBgOJTri4UnDfvn3Iy8vD4MGDER4ejqtXryI4OBiNGvn+8kRJSYn5/20XTbqbXIM0NJY6pVIAnPqptBDSWSM6OJ8dZOR6adFkQ16DvNuGfPk7taKgFOizAii0+GLaPAzYOsx7A3+j9+UXNOoA1P4/79TBGWppu4NWyWc/GtgCWHevV6pFKhI6D6iSOe+FNAKuTvTd+OfM7y0oBTouA646Oy/kN4lRng9OTbmw3bEzJOOH+nHUhpy+gn3hwgUMGzYMmzZtgk6nQ15eHtq1a4cnn3wSUVFRTu/i6C/kUuWUV0u5MOUC7MydrgXXgGvZQZQWXXozlRiRu2XutA6uAemxu3PL2qOGLCJask8hk9J+hXLyb9cUzntK5WqSEAUYQ+TvPMuJDgHuvtE7G7+4cxtzxg+e4fRl52effRZBQUE4evSo1VSP+++/H999951HKqdmSg3yiEWqHss5TetkdqMzsZ1baeLKLSalRZeevE1F5GlqGPiV1mL5/p4dkfppfU7+rfHOPzc6VJu7KjJ+8Aynr2CvXbsWq1atMmcBMUlKSsLx48fdXjG1U2qQORevLw6wnUKi5JY44NRl6xR+rmYHmZ0mzZmy/H2eSBFE5E1qGPg7RgEHZPpxssZOot6SGCl/xa9dpPfrQr7Xr5n8lKF+zbxfl/qY2wfIPlc3xa6co2VA+kqgWxxQWqWdbcwZP3iGS1NEYmJi6pSXlZWpYv61t81OA1YV1F0AUV4t3b4GnAuuAWBbMdA6ArinLVBWBUSGADoBjP1BuYOa5l9Z7gi5boj75mQRqYEaBv7z11wrD3THFe4uKJWTf8u8BVi/Sr5cCxKigI33Xp8Wuu88cNnOwscTFdab0K0quL42S+68rYZzdEKUeuMHtf7NnOF0gN29e3d8++23eOKJJ6zKlyxZgp49e7q9YmqXEAV0ukE+V+bpCuX5mUGQz6N5okLqgHP7OF7Na2/FLxckkD9Rw8B/VmH+pVJ5oCtX+OJRwS8kAen5n08EFxIAACAASURBVJTLt97v3bo0lD4IGNhKSqt7ycEeFSbl1VI2kq/vli6aqTVThzvndLuL1rObOB1gz5w5E/fddx9OnjyJmpoafPTRR8jNzcWqVavw/feBuSenUjJ6e7ev7S1GPnJJfvHkkVLrRV3OPIfIX/h64Fdai6WBNVo+oaVNccjztp2VL9+uUK42ShnDXFFeLaXYPFpmXc7ztn1aj3WcntsxaNAgfPnll9i2bRsaNWqEN998E2fOnMF3332HPn36eLKOPqeUgH12mnS72pLp9rXcMb2Dnd/OXHFuUZcaFn4ReQs3QNAWLW2KQ56ndDdXK19QlTKGuRpkK21dbnne5lhnTeuxjktN5Pbbb8fttwfWKOnoFoW929e2x85cBjacUv5dMSHOLepSw8IvIm/Q+i3CQNTaAEQHA+csrmJHB0vlRFqjFOR1igGaRgDfHQeuWnxb0EH+S0V0qPy0EtN529djnRrnOms91nH6CvbPP/+MHTt21CnfsWMHdu3a5dZKqYm9WxTA9dvXctuim44typAeZ5+z/7vySoAJKcpXxU3kro4bGks/S+RPHPU/b4hRmNqgVO4pWrm6NWWLdXANSI+nbPFNfci3muhdK1cbpSAvMRqIDLYOrgEpuLa9g5MYJd3BsXdu98RY5+yYYQrul+YBG09L/+3yGdArq+7PeXMcsjdLQAucvoL91FNPYcqUKXUWNJ44cQJz5szBtm3b3F45NXB0i2LTaWlu1cWr0gnXdotSuW+lSkwb1Tha1JUQBXyQYb2Na3m1tICCV/bIn6jhFmGNwsIJpXJP8PXVLVf8IJOSDZBO3BR4WkcA567Il6uN3PncXiajsT/Iv06PptJzbM/h9s7t7h7rXBkzlKbBbC/+7d9vPwd4dxxSwyL3hnA6wM7NzUWPHj3qlHfv3h0HDhxwa6XUxN4tik2ngQGrgerf7geVVEmPN9xzPciWa7j2nK5wblHX/AN1UwRqafI/kTOUBigHyxncqlwhkFYq9wQtLfaxHZdMyuykNiP/pRQ4KpX7ir3zuVKQp3h1W+Ecbu/c7u7pEK6MGY4+C8sr6d4eh3y9yL0hnJ4i0qhRI5SW1o0UL168iNparSxXcJ29WxSjv7/eGU2qhVRu4uog4mxnUsOVPSJP+6XEtXJP0Cms0lIq9wQt9Xelk0rg7ZZAgHI6O2fT3HmLvfO50lRQd05hcPd0CFfGDKXg3vbntDQOqYHTY17v3r0xZ86cOuVz5sxBr1693FopNTHdohjRAchoIf33gwzpG9sJhZ2dLFcLO9NwTVzpTFqf/E/kDDXkVG6m0KeUyj1BS/09Pty1cvJvQuGLqFK5r1xUyPKhlP0DkI8P6jtdwp2vBSiPGVHBdedQywX3tlpEaGscUgOnp4i8+uqrSE9PR7du3TBgwADodDqsX78eeXl52Lhxower6D71XSVreYvCmTnVlvle5eZvWTI0llYjJ0a7NrdIDTvckf/z9cpyNeRU/nsv4OH18uXeoqX+roa/F6lHfDhwUuYKp9q+cDkaa5TGQndOYXDna8mNGa0jgD3nrbd9N82hNk2DOXIJyLloPdXLcqzRyjikBk4H2DfffDN27NiBN954A2vWrDGXffTRR+jUqZPHKugu7lok5GhOdZBNvlfbSfpRwYDQSVuiN2TCvtYn/5P6qWFh3ZLbredFAt7PqfzVMeXyhzp4pw5a6u+fHlYu99bfi9Rj6UDg9tVAjUUfDtJJ5Wpib6xRw1joKrkxo+wasPqo9fMs51BbXki0HWsAqSxOL32WzfSuXxgMNDoh1Hajpv5KSq5PzDQajVbHRq6XUs/YGtFB/huj5WpiQzDQ0QhUAzhwESi2s0Vy8zBg6zA2OK2y14b86Xc6w9U+4ymmvnjpqnQ1yTZTj6f1ypLfsfXWeGDbMO/VwxG1tN0mHwDnZW6rx4YC58Z6pVqkMvb6sK/GP7nfq1TPhsQPctnFnOGJu4cZq+Sz+WS0kOaX26uL7ReMxCh1f8HwBkdt18W9iLTLlcn5cquJnV2sWFgJPLMVWDW4fvUkUgu1LGhpbQD6NLt+ovH2hiWHFe5YHfbiQkstkbvNbq+c/J+v+7Cz+rUACkbWLW9o/GCbXcwRV66YuxKI13cOtVJGkttXA9/fE9hBtj12A+yQkBCcOnUKcXFxCA4Ohk6nU3xuVZW6R09nG1ZBKXDXV3VXE7ti7QnpddjoSMvUsKCloBRIXwmcsDiRbToN/Hif9/qXXA5fe+WBTmnsbMiYStqlxekVtqJC5MsjZcrtZSORC97lOJtiz9VAvLwK0AcBVyxSjDozh1rpC8bRMun3a+mz9Ca7AfaCBQsQFSX91RYuXOiVCnmKM4uETI210on8traN1NKVGnXmpyVyhRoW1k3ZYh1cA9LjKVuAlf/nvXoQUf1oKYe7EldSddYnG4ktZ66YF/x2BflomfVznA3E9UHAHa2BuX0cB8f2sqFp7bP0JrsB9ujRowEA1dXViIuLQ8+ePREbG+uVirmbM4uEXNkUJryxcoANMC8kaZ8aFtZtk5n7DMjPiSYi9VHLVLOGOHNZvrxUJl2oUjaSyhppLrczY6iju4emgNk2uDax/dvKxTZXaqSt3p0Zzx1lQ9PSZ+lNTs3Bbty4MYYNG4aDBw9qNsAGHKfAcWVTmEoHu5IxLyT5A1/volWtsIeVUrknNAIg9+u4cQqRY8Zg+fIohXK1KSgFci/KH5M7z8tlIwGAqzXSQklnpsc4unvo6GKgbb0a+iXHdLFF7oq53O8jidPniJSUFBw9etSDVfE9VzaFqayRUvjIYV5IIvcIU7gEoPfi8myjwvxLpfJAF6JwVlEqJ/8mFM6TSuVqk7nTOie0iaGx/Hm+XwtpQWPbSCBY5j1abjuuxNGmM/YuBsrFH0qxTUGZ9AXCEdNCymZhQHiQ9bHWEYx3lDg95L311luYPn06fvrpJ9UvaKyv2WlSp3FWtZCC7I5GqTPdGtfw3ZdcUVBad0cmIn/SVO9auSfUKMy/rPXyoj2t9HelIVQjFyzJzUoVwoUyjYQRSsFsp1jl87wpG0mf5vLHnblyrLQ9O6AcMLeNlI8/lHZqNC1StDeWmKajLM2TpuZdtpkaayf3hV9oyLjrdDg5aNAg1NbW4rbbbgMABAVZf43xh6A7IQr4+m7g7q/lv7HKqRZAXqlrKXjcwR9WZhM5clFhWFEq94QqhekoV704TUVL/f2KwhePSmYRCUiuZOBQI6Vg1tHW4vZ+tqFTKpSmkCiNBwlRwAcZ8lNXHC1SdDQd5Xi5thY5upLWsKHjrtMB9oIFC+ym6fMX/VoA+4YDt66wv6GMpWohBeX7hnvvZOcPK7OJHDEqjFDRXpwiooZ54Frq70pX9r19xZ/UwZUMHGrUkGxKnsrEVJ8F6PMPKKfKtHdF3Zm1aVpZ5OhqwNzQcdfp09TDDz+M6upqRET4/2z2hCigV1NglcIWyXLKq717svOHldlEjpQo3Em65OQdJncIagRUy2QMauzFOcXs76RVJTKZNgD5DBxq1JBsSp7MxOTqAnR7gbK9K+rOrE3TyiJHVwPmho67DgPsCxcuYPTo0fj2229RW1uLW2+9FUuXLkXbtm2d+w0aYXnbwBgM/HzW9dfw5slODZuAEHlaszD5VevNwr1Xh5tvAH6SGQ+63+C9Omipv0cEARUyX0giguqWkf/TUttV0pBsSr7OxGSi9DkoLdY0mZACfHZY+eq3oyvyntjyvb5cDZgb2nYdXoN58cUXsWPHDvz5z3/G3/72NxQVFWHSpEnOvbpGmHaLW5oHbDwtXbk+LZP30hgMDGwBBCnMlPHmgCG3aIHZS8jfNFUIpJuGea8OTRT6tVK5J2ipvyvNrdXKnFtyLy21XX82IaVuEgdDY2ndWX2mluiDpHE41c6FBssFkhtPS/91tKjSk1wNmBvadh1ewV6zZg0WLVqEIUOGAADuuusudOnSBdeuXUNwsH+sC5fbLU5OVS0wPwM4UV53IaS3Bww1bAJC5GmXFRYzKpV7QrHCJhPOrtFwBy319wqFW/+XNTIlgNxLS23XXxWUAmN/sI5ZTMG1o+QMSld9r9QAVyqB1UeB3Avy85jVtnbE1TnxDW27DgPsU6dO4eabbzY/TklJQUhICAoLC9GmTRvnfovKKe0WZ6vSYgv0fcN9P2Co5dYTkafsU9jgYb9CuSecUQiklXZ38xSt9He56SEAUG5n51vyb1ppu/5KLtAtr5auTjsKsJ2Zg60UNKtt7Uh9AuaGtF2HAXZNTU2dK9VBQUGoqdHWaOmueUCmhsEBgygwxOsV5oF7MRe3lnDnSyL3amj80pBA19E26fZeS43z770ZuzmVReSBBx5ASMj1CXRXrlzBqFGjEBZ2fSLk2rVr3V87N3GUmuXWeOk2hzO0tDCDSOu6xALrT9Yt7xzrvTq0jwZ2yCxyTIz2Xh20pIle/qp/E34hIXKZO3LgNyTQtb3qW1Dm/HbpnkpTqBUOA+zRo0fXKRs5cqRHKuMpjuYBze0DZJ+TEqabNA8DgoOsywKpYRCpgVLmCW9mpAj0k4SrOsXIB9idYrxfFyKtc8c85oaOYZZXfeUCfqXXCvT59w4D7MWLF3ujHh7l6PZIQhSw8d7rjSAyREqCf+Yy0EgnpQQzNSDbhqGmFDRE/kYNOXRNu6CN/h64dBWIDpUes5/LU0pRrq1JheROPE/WnzvmMdcn0FX6zFx9LVNwbnq9sT8EThvw4n5ovuPM7RHLRmD77SxIB3wyUD641sr2xURapIZtlk0r8E23RS9VSY/Zz+Wp4TMj9eB5smHcNY/ZlbnHjj4zV+cxB2obCIh1J3K5DPVBQHlV3XyM9m7H2HLluUTkOjVss8x+7ho1fGakHuw/DeOLPOLOfGYFpcDI9UDGKum/9nJbB2obCIgr2KZbGs9sBdae+C1/Y420ocyGU9a5IF25HaO2FDRE/qZIIUVe0RXv1YH93DVq+MxIPdh/GqYh85jrOzXH0Wfm6hXpQG0DARFgm+w7LwXWlsqrpU1j9g2XGoYrt2PUmIKGyJ+oIQe1UWE/rSj/2GfL7U6UK5TLZB4g/8fzZMPVJ7VcfaZlmALyAwr7DJg+M1cXXgZqGwiIKSKmhiaXWgaQguzbV0vPk7sdowPwaR5gWAAsy7tezi1giTzLqHAJINqLlwaEzrXyQFehsMrxstLqR/JrPE/6hqvTPO77Bui/StrOXG6XWsvPzNUr0mpsA8t+i+ka/7tubOcuAXEFW66h2TpaBqQsA+5oLWUImH8A2FMMHCgBBKR/FdXAw+ul5z/UgSloiDztlMKV6pNevIKthq3StaRMYRv7Ui9ub0/qwfOkbygFwUcuSUH1kRIg54L19uly4sOAga2sPzNXr0irrQ0sy7seywF1Yzt3CYgAW6mh2bpSI204k3tBagydP5N/3viN1z8E7uhI5DkXrrpW7gmc8uAapXR8TNMXuHie9D6lIDjnIrBdZuMsJSkxdT+7+uTVVlMbGL9RudydAXZATBFRamhKTLdRbOdrmyiVE5F7yW25ba/cEzgOEJHWyE3LMDR2fMXaltxVadMV6REdgIwW0n+1lHLPW2N6QFzBlvu21VgHVNtJG3W6QkrlJzefUO/FXeSIAllYEFApM+iFebEPBilchmgcEJcniEiL5KZlHCkBthc7/xr2rkqr6Yq0q7wV23ntFHH16lWMGzcON954IyIjI9GtWzesWbPGfHzDhg1ITk5GeHg4MjIycOzYMfMxIQSmT5+O2NhYxMbGYtq0aRDCuaSqplWxTUKBtpHArfHSt60N99T9dmepRQSwsL/8MaVyInKvDzJcK/eEW+Ply3sqlAe6m5u4Vk5EnmEKgr+/V/pvotH+81tHAPe09c1VaVfyajeUt2I7r13Brq6uRuvWrfHjjz+iTZs2+Oabb/Dggw9i//79MBgMGDZsGBYuXIghQ4YgMzMTw4cPx/bt2wEA8+fPx8qVK7F3717odDoMGjQI7dq1w6RJk+z+Tke7Mq4bAkzZAqw9aX2VzHZb9PEbpVsH+iDpA3DnHB0iUtYzHmgSApyzWCDXJMS7we3cPkD2OeC4xVzsNgapnOp6q4+UjcDyEojut3Ii8h25u/mGxkCnGCAx2ncLD72906MphvN0bKcTzl4K9oAuXbpg5syZOH/+PD788EP89NNPAICKigo0adIEe/bsQXJyMnr37o0xY8ZgwoQJAIBFixZhwYIF5gDcpKSkxPz/RqMRI9dLKWdsjehgfWvDdJVbDatbybds25C//k6tcLYPe5oWxgi1tF21fGakDb4a/wJ13FXjWKbVMcNRG/LZHOyioiL8+uuvSE1Nxfvvv4+uXbuaj0VERCAxMRG5ublITk5Gbm6u1fGuXbsiNzfX4e9wNlejlucSEfkztewAxjHCeWr5zIioLjWOZf46Zvhkmc61a9cwYsQIjB49GsnJySgvL68T/RuNRpSVSXmwbI8bjUaUl5c7nIcdqLsHEfkL9mHt4WdGRK7w1zHD6wF2bW0tHn30UYSEhODdd98FABgMBpSWWs9oLy0tRWRkpOzx0tJSGAwG6HT2t1JT4+5BROQ89mHt4WdGRK7w1zHDqwG2EALjxo1DUVERsrKyEBwcDABITU3F3r17zc+rqKjAkSNHkJqaKnt879695mP2aD1XI1GgYx/WHn5mROQKfx0zvBpg/7//9//wyy+/4Msvv0RYWJi5fOjQocjJyUFWVhauXLmCWbNmoUuXLkhOTgYAjBo1Cm+99RZOnTqF06dPY86cORgzZoxTvzPht29BLSKkeT6ZOz2b/oWIPMNnq7Gp3viZEZEr/GnM8Noix2PHjmHevHkIDQ1Fs2bNzOXz5s3DiBEjkJWVhcmTJ2PkyJHo2bMnli1bZn7OxIkTkZ+fj86dOwMAxo8fj4kTJzr1e72d/oWI3If9V3v4mRGRK/x1zPBpmj53Y8ooaii1pDojCfuv89TSdvmZkSuYpo+0OmY4akN+v9mvv6Z/IQoE7L/aw8+MiFzhr2OGz/Jge4s70r+YErOfqpBeTw2J2YkCgb+mb/Jn/MzIFs+hZI83xgxftEG/D7DltgZ1Jf2Lv84NItKCCSnAZ4eBaouJbI11UjmpU0PHXPIvPIeSI54eM3zVBv1+ikhD079k7rT+UADpceZO99eViKzNP2AdXAPS4/kHfFMfcsxfU25R/fAcSo54eszwVRv0+yvYQMO2BvXXuUFEWsD+p01q3I6ZfIN9mJzhyTHDV23Q769gNxTnExL5DvsfkbaxD5Ov+aoNMsB2wF+38CTSAvY/Im1jHyZf81UbDIgpIg1hmhuUuVO6ndCCK6CJvIb9j0jb2IfJ13zVBv1+oxkiV6hlsw4iV7HtkhZxoxnSqoDfaIaIiIiIyJv8doqI5TcLIq1guyWtYtslrWLbJU/gFWwiIiIiIjdigE1ERERE5EZ+tciRiIiIiMjXeAWbiIiIiMiNGGATEREREbkRA2wiIiIiIjfy+wD73XffRY8ePRAaGooxY8ZYHduwYQOSk5MRHh6OjIwMHDt2zHxMCIHp06cjNjYWsbGxmDZtGiynqx89ehQZGRkIDw9HcnIy1q9f7623BAC4evUqxo0bhxtvvBGRkZHo1q0b1qxZ4xfvDQBGjhyJ5s2bIyoqCklJSVi4cKH5mNbfm7MuXLiAoUOHIiIiAjfeeCM++eQTX1fJ6xy180CUl5cHvV6PkSNH+rQe9sZWW2+//TaaNWsGo9GIsWPH4urVq96ppJc4+7f48MMPERQUBIPBYP63ceNGr9XTk1ztq/7eJnylf//+0Ov15vZ10003mY/ZO3f6G0/Ffi4Rfi4rK0v897//FZMmTRKjR482l589e1ZERUWJzz//XFRWVopnn31W9OzZ03z83//+t0hKShInTpwQJ0+eFB07dhTvv/+++fitt94qpkyZIi5fviyWL18ujEajKC4u9tr7Ki8vFzNnzhQFBQWipqZGfPnll8JgMIiCggLNvzchhMjJyRFXrlwRQgjxyy+/iPj4eLFr1y6/eG/Oeuihh8SDDz4oysrKxObNm0VUVJTIycnxdbW8yl47D1SDBg0Sffv2FSNGjPBpPZTGVlvffvutaNq0qcjJyREXLlwQ6enpYvr06d6rqBc4+7dYvHix6NOnj/cq5kWu9NVAaBO+kp6eLhYsWFCn3NG50994KvZzhd8H2CYvvvii1R953rx5olevXubH5eXlQq/Xi19++UUIIUSvXr3EvHnzzMcXLlxo/hAOHTokQkJCRGlpqfl437596/0huEvnzp3F8uXL/e69HTx4UDRr1kx89tlnfvfelJSXl4vg4GBx6NAhc9nIkSN5EhLX23kg+vTTT8UDDzwgZs6c6fMA28R2bLX18MMPi+eff978eP369SI+Pt4LNfM+R38Lfw6w5Sj11UBqE96mFGA7Onf6K3fGfq7y+ykiSnJzc9G1a1fz44iICCQmJiI3N1f2eNeuXa2OtWvXDpGRkbLHfaGoqAi//vorUlNT/ea9PfHEE+apHM2bN8f//d//+c17c+TXX39FUFAQkpKSzGVqras3WbbzQFNaWoqXX34Zc+bM8XVVXCLXJ4uKinD+/Hkf1sp39uzZgyZNmiApKQmzZ89GdXW1r6vkEfb6KtuEZz3//PNo0qQJ+vTpY56C5OjcGSgaEkO4KmAD7PLychiNRqsyo9GIsrIy2eNGoxHl5eUQQjj8WW+7du0aRowYgdGjRyM5Odlv3tt7772HsrIybN68GcOGDUNoaKjfvDdHtFRXb7Ft54EmMzMT48aNQ+vWrX1dFZfI9UkAAdmW+/Xrh5ycHBQXFyMrKwuffvop/va3v/m6Wm7nqK+yTXjOm2++ifz8fJw6dQoTJkzAkCFDcOTIEZ5TftOQGMJVARtgGwwGlJaWWpWVlpaar27aHi8tLYXBYIBOp3P4s95UW1uLRx99FCEhIXj33XcB+M97A4CgoCD07dsXJ0+exPvvv+9X780eLdXVG+TaeSDJzs7G+vXrMWXKFF9XxWVyfRJAQLbldu3aISEhAY0aNULnzp3x8ssvY/ny5b6ulls501fZJjynZ8+eiIyMRGhoKEaPHo0+ffrgm2++4TnlNw2JIVwVsAF2amoq9u7da35cUVGBI0eOmG9n2R7fu3ev1bH8/Hyrb36Wx71FCIFx48ahqKgIWVlZCA4Olq27Ft+brerqavN78Lf3JicpKQnV1dXIy8szl6m1rp6m1M4DycaNG3H06FG0adMGzZo1w9///ndkZWWhe/fuvq6aQ3J9Mj4+HrGxsT6slTrodLr6ZyhQIWf7KtuE95jamKNzZ6BoSAzhsnrN3NaQa9euicrKSjFjxgwxcuRIUVlZKa5duyaKi4tFVFSUWL58uaisrBTTpk2zmsj+/vvvi+TkZHHy5Elx6tQpkZKSYrUYrmfPnmLq1KmisrJSrFixwifZKCZOnCh69uwpysrKrMq1/t6KiorEp59+KsrKykR1dbX49ttvRXh4uFi5cqXm35srhg8fLh566CFRXl4utmzZEpBZRIRQbueBpKKiQhQWFpr/TZ06VfzhD3/wadtVGlttrVmzRsTHx4vc3Fxx4cIFkZGR4XeLdZ39W3zzzTfizJkzQggpO1Jqaqp45ZVXvF1dj3G2rwZCm/CFixcvim+//dbc/j7++GMRHh4uDh486PDc6W88Ffu5wu8D7JkzZwoAVv9mzpwphBBi3bp14qabbhJ6vV6kp6dbpROqra0Vzz33nIiJiRExMTHiueeeE7W1tebjBQUFIj09Xej1epGUlCTWrVvn1fd19OhRAUCEhoaKiIgI87+PP/5Y8++tuLhY9OvXTxiNRhEZGSk6deok5s+fbz6u5ffmivPnz4t7771XhIeHi9atW4ulS5f6ukpe56idByo1ZBFRGluPHTsmIiIixLFjx8zPnTNnjmjatKmIjIwUY8aMMafg9BfO/i2mTp0qmjZtKsLDw0VCQoLIzMwUVVVVPq69e9jrq4HYJnyhuLhY9OjRQxgMBmE0GkXPnj3F2rVrzcftnTv9jadiP1fohPCj+1NERERERD4WsHOwiYiIiIg8gQE2EREREZEbMcAmIiIiInIjBthERERERG7EAJuIiIiIyI0YYBMRERERuREDbJXR6XT4+OOP3fqatbW16Natm9u35N2/fz/S0tKg1+vRtm1bxedNnDgRzz77rFt/N3lP//79MX78eLe/7pgxYzBw4EC3vy6Ru7zwwguIj4+HTqdD27Zt0b59e19XiYg0ggG2yhQWFuL+++9362suXrwYQgj84Q9/cOvrTps2DVFRUTh48CB+/vlnfPzxx9DpdHWe9/LLL+P9999Hfn6+W38/EZGn7NixA3/5y18wf/58FBYWYvjw4b6uEhFpCANslWnWrBn0er1bX/Ptt9/GhAkTZIPfhsjLy0N6ejratm2LuLg4xee1bNkSAwYMwHvvvefW30/+raqqytdVoACWl5eHRo0a4d5770WzZs0QFhbmld/Ldk/kHxhg+8CWLVvQp08fREZGIjIyEl27dsV3330HwHqKyCuvvAKdTlfn35gxY8yvtW7dOvTp0wdhYWFo2bIlHnvsMZw/f958PDs7G7m5ubjvvvus6rBw4UJ07NgRer0esbGx6NevH06ePGk+/vnnn6N9+/bQ6/Xo3bs3Vq9eDZ1Ohy1btuDo0aPQ6XQ4cuQIXn75Zeh0OvTv3x+PPvqo+T3Y1nPo0KFun/pC3lNbW4sZM2agSZMmiIqKwvjx41FZWWk+/s9//hPJycnQ6/Xo0KEDXnvtNVRXV5uPX7x4EcOHD0dERATi4+Px0ksvwXYT2f79+2PcuHHIzMxE8+bN0bJlSwDA9u3b0a9fP4SFhSEmJgaPPPIIiouLrX52yZIlSElJQWhoKFq1aoWXXnrJ6vebXvull15C06ZNER0djRdffBG1tbWYNWsW4uPjERcXnhoXjAAADbNJREFUhxdffNHqdVetWoVu3bohPDwc0dHRSEtLw549e9z2dyV1GjNmDB599FHU1taaxzM5jtrdtWvXMGPGDLRs2RIhISFISUnBJ598YvUaOp0O77zzDh555BEYjUaMGDECAPD666+jXbt2CA0NRVxcHO68806rPkdUH+vWrUP//v1xww03wGg0Ij09HTt37jQfLygowB133AG9Xo82bdrgX//6V51pgtXV1XjllVeQkJAAvV6P1NRUzJs3zxdvR90auN07uai6ulrExMSIKVOmiF9//VX8+uuvYsWKFWLTpk1CCCEAiI8++kgIIURZWZkoLCw0/1u9erVo3LixWLx4sRBCiA0bNoiwsDDxzjvviF9//VXs3LlT9O/fX9x2222itrZWCCHE3LlzRcuWLa3qsGvXLhEUFCSWLFkijh49Kvbt2ycWLFggTpw4IYQQ4n//+5/Q6XRixowZ4uDBgyIrK0u0bdtWABCbN28W1dXVorCwULRq1UpMnz5dFBYWipKSEvHuu+8KAOb6Xrp0yfw7c3NzBQBx4MABT/+Jyc3S09NFZGSkGD9+vDhw4IBYvXq1iIuLE0899ZQQQoiZM2eKNm3aiBUrVoj8/Hzx9ddfi9atW4uXXnrJ/Br33XefSExMFBs2bBA5OTlixIgRIjIyUgwYMMDq9xgMBjFx4kSRm5sr9u3bJwoLC0VkZKR4+OGHxb59+8TmzZtF586dRd++fc0/99VXX4lGjRqJ119/XRw6dEgsW7ZMREdHW/3+9PR0ERUVJaZNmyYOHTokFi1aJACIwYMHi+eee04cOnRIfPjhhwKA+Oabb4QQQhQWForg4GDx5ptvivz8fHHgwAGxdOlSsW/fPk//ycnHLl26JObOnSuCgoLM49nMmTNFYmKi+TnOtLtnn31W3HDDDeLzzz8Xhw4dEq+99prQ6XRi/fr15ucAEDfccIN45513xOHDh8WhQ4dEVlaWiIyMFKtXrxbHjh0Te/bsEW+//ba4fPmyV/8O5H9WrFhhbo85OTli3LhxIiYmRpw7d07U1taKrl27irS0NLFjxw6xZ88eMXjwYBEVFSXGjRtnfo3Ro0eLzp07i++++07k5+eLZcuWCaPRKBYuXOjDd6Y+DLC97MKFCwKA+OGHH2SPWwbYlo4fPy6aNWsmnnvuOXNZenq6mD59utXzjh07JgCIPXv2CCGEePrpp0VaWprVc1asWCGioqJESUmJbB1GjBghevXqZVX2z3/+0xxgm9x4441i9uzZ5scfffSRUPrOVlJSIgCIr776SvY4qVd6erq48cYbRXV1tbls3rx5IiQkRJSXl4uwsDCxZs0aq59ZsmSJMBqNQggh8vLyBACxdu1a8/GrV6+KFi1a1AmwO3ToIGpqasxlL730kmjZsqW4evWquSw7O1sAED/++KMQQoi+ffuKBx54wOr3z507V+j1evPPpaeni65du1o9JyUlRXTq1MmqrEuXLmLq1KlCCOmLJgBRUFDg3B+K/MrixYtFUFCQ+bFtgO2o3VVUVIiQkBDxr3/9y+o59913n8jIyDA/BiDGjh1r9Zy33npLdOjQQVRVVbnzLRHVUVNTI6Kjo8XHH38s1q5dKwCIvLw88/Hz58+LsLAwc4Cdn58vdDqd+OWXX6xe589//nOdMTbQcYqIl8XExGD8+PG48847MXjwYLzxxhs4dOiQ3Z8pLy/HkCFD0KtXL7zxxhvm8p9//hlz586FwWAw/0tJSQEgzR8EgMrKyjpzugcNGoR27dohISEBDz30EObPn49z586Zjx84cAB9+vSx+pm+ffs26H2b6sBbnNqUlpaGoKAg8+M+ffqgqqoKu3btQmVlJf7whz9YtcOJEyeipKQEZ8+exYEDBwAAvXv3Nv98SEgIbrnlljq/5+abb0ajRteHpdzcXNx6660ICQkxl3Xt2hVGoxG5ubnm5/Tr18/qddLT03HlyhUcOXLE6ucsNWvWDF26dKlTZpp+0qVLF9x5553o1KkThg4din/84x84ceKEc38w8nuO2t3hw4dRVVUl+xxT2zVJS0uzevzggw/i2rVruPHGGzFmzBh89NFHKCsr88wboYBSUFCARx99FO3bt0dUVBSioqJQUlKCY8eO4cCBA2jSpIlVtpwbbrgBN910k/nxrl27IIRAjx49rMb8119/3Rx3kIQBtg8sWLAAu3fvxqBBg/Djjz+iU6dOivOXamtr8cgjjyA4OBgff/yxVfBRW1uL6dOnIzs72+pfXl4eBg8eDACIi4vDhQsXrF7TYDBg165d+O9//4ukpCT8+9//Rvv27bF7924AgBDC7QsiTXWwtxiStEPYzJ/+4osvrNrg/v37kZeXhxtuuKHOc+2JiIioU6bUFi3LbZ9j+p2W5cHBwXV+Xq6strYWABAUFIQ1a9bg+++/xy233IKsrCwkJSXhq6++cvr9kH9zpt3JPce2zLbdt2zZEgcPHsQHH3yApk2bYvbs2bjpppv4BY8a7Pe//z2OHz+Of/3rX9i+fTuys7PRtGlT8+JaR+d+0/j4008/WY35OTk52Ldvn8frryUMsH2kU6dO+NOf/oQ1a9Zg3LhxmD9/vuzznn32WWRnZ+PLL79EeHi41bEePXogNzcX7du3r/PPYDAAALp37468vLw6K9ODgoLQr18/zJo1C7t370bz5s3Ni29SU1OxdetWq+fbPpZjuspYU1NT59j+/fsRFBSEbt26OXwdUp+ff/7Z6nPdtm0bQkJC8Lvf/Q56vR75+fmy7TAoKAipqakApAHZpKqqCj///LPD35uamopt27ZZtd+9e/eipKTE/Lqpqan48ccfrX5u06ZNCAsLQ7t27Rr0vnU6HdLS0vDCCy9g06ZNSE9Px+LFixv0muQfHLW79u3bIzQ0VPY5prZrT2hoKO666y789a9/xf79+3H58mWsXLnSre+BAsv58+dx4MABzJgxA3feeSdSUlKg1+vNd+1SUlJw9uxZHD582PwzFy9exK+//mp+fPPNNwMAjh8/Xme8T0xM9O4bUrnGvq5AoDl8+DAWLFiAIUOGoHXr1jh9+jQ2b96M7t2713nuhx9+iPfeew+rV68GAJw5cwYAEBYWBqPRiFmzZuGOO+7AlClTMHr0aERGRiIvLw9ffPEF3n33XYSFhSEjIwM6nQ47duzAbbfdBkDKjJCfn49+/fohLi4Ou3fvxokTJ8zTS6ZMmYJbbrkFL774IkaPHo3c3FzMmTPH4XtLSEgAAKxevRp9+/ZFWFiYOdDfuHEj+vbti6ioqIb/Ecnrzp8/jyeffBJPP/008vPzkZmZiccffxxGoxEvvPACXnjhBQDS9KPq6mrs378fe/bswZtvvon27dvjnnvuwZNPPol58+YhPj4eb7zxhlO3vCdPnox//OMfGDNmDF544QVcunQJTzzxBPr27Wtuz88//zyGDBmCN954A8OGDUN2djZeeeUVTJ061Wpqiat++uknbNiwAXfccQeaN2+OvLw87Nu3D+PGjav3a5L/cNTuQkJC8Mc//hGZmZmIi4vD7373O3zxxRdYtWoV1q1bZ/e1Fy1ahNraWqSlpSE6OhobNmxAWVmZeYwmqo+YmBjExcVhwYIFSExMxPnz5zFt2jRzCsqBAweia9euGDVqFP7xj38gJCQEL774Iho3bmy+st2+fXuMHTsWjz/+OP7617+iV69eqKiowO7du3H27FlMnz7dl29RXXw4/zsgnT59WgwdOlS0bNlShISEiObNm4vx48ebM27AYpHj6NGjBYA6/0aPHm1+vU2bNokBAwYIg8EgwsPDRXJysnj66afFtWvXzM8ZM2aMePzxx82Pf/zxR5GRkSGaNGkiQkNDRfv27cVf/vIXc+YRIYT49NNPRbt27URISIhIS0sTK1eudLjIUQhpUWXTpk2FTqcz17O2tla0bdtWfPLJJ277O5L3pKeni8cee8ycEcFgMIjHHntMVFRUmJ+zcOFC0bVrVxEaGiqio6NFWlqaeO+998zHz507Jx544AERHh4umjRpImbMmCFGjRpVZ5Gj5Up1k23btonbbrtN6PV6YTQaxcMPPyyKioqsnvPhhx+K5ORkERwcLFq0aCFeeOEFqz4g99oDBgyw6ktCCHHnnXeKESNGCCGEyMnJEYMHDxbx8fEiJCREtGnTRjz77LNWCy7Jfzla5CiE43ZXVVUlpk+fLlq0aCGCg4NFx44dxdKlS61eAzIL27OyskSvXr1EdHS0CAsLE6mpqczQQG6xceNG0aVLFxEaGiqSkpLE8uXLRWJiopg5c6YQQlrEOHDgQBEaGipatWol3n33XXHLLbeIyZMnm1+jurpavPnmm+Kmm24SwcHBIjY2VvTr1098/vnnPnpX6qQTwoUJkqRJR44cMU8nadGiRb1e4+jRo0hISMDmzZtdXvD4+eefY/bs2cjOzrZaKEdERETqVVZWhlatWuHVV1/FU0895evqaAqniASAxMREzJs3DwUFBfUOsBvi6tWrWLx4MYNrIiIiFVu9ejUaN26Mjh07ori4GH/+85+h0+nw4IMP+rpqmsMAO0D4snOYdngkIiIi9bp8+TJmzZqFo0ePIiIiAjfffDO2bNmC+Ph4X1dNczhFhIiIiIjIjZimj4iIiIjIjRhgExERERG5EQNsIiIiIiI3YoBNRERERORGDLCJiIiIiNzo/wMESA5DJFqhgQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 864x216 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create 'figure' object including 4 'ax' subplots/objects\n",
"# Figure has 1 row, 4 cols}\n",
"# total size of figure is (col = 12 inches, rows = 3 inches)\n",
"# sharey = True, means that ALL 4 subplots, have the same y-axis scale of the first subplot\n",
"fig,ax = plt.subplots(1, 4, figsize=(12, 3), sharey=True)\n",
"\n",
"for i in range(len(ax)): # Iterate through each of 4 'ax' subplots/objects, so i = 0,1,2,3\n",
" \n",
" # Select at 'X_train' Matrix, ALL the vectors/rows, per each i-th feature/col value, at x-axis\n",
" # Select each y_train vector value at y-axis\n",
" # Plot one scatter per each i-th feature, at each i-th 'ax' subplot. \n",
" ax[i].scatter(X_train[:,i],y_train)\n",
" \n",
" # Select the name of each 'Xi' feature from list of names, and put at x-axis, each i-th 'ax' subplot\n",
" ax[i].set_xlabel(X_features[i])\n",
"\n",
"# Out of for loop, as all subplots share the same y-axis values and name, \n",
"# then we set the y-axis label just once at the first 'ax' subplot. \n",
"ax[0].set_ylabel(\"Price (1000's)\")\n",
"\n",
"# Display figure\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting each feature vs. the target, price, provides some indication of which features have the strongest influence on price. Above, increasing size also increases price. Bedrooms and floors don't seem to have a strong impact on price. Newer houses have higher prices than older houses."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a name=\"toc_15456_5\"></a>\n",
"## Gradient Descent With Multiple Variables\n",
"Here are the equations you developed in the last lab on gradient descent for multiple variables.:\n",
"\n",
"$$\\begin{align*} \\text{repeat}&\\text{ until convergence:} \\; \\lbrace \\newline\\;\n",
"& w_j := w_j - \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j} \\tag{1} \\; & \\text{for j = 0..n-1}\\newline\n",
"&b\\ \\ := b - \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial b} \\newline \\rbrace\n",
"\\end{align*}$$\n",
"\n",
"where, n is the number of features, parameters $w_j$, $b$, are updated simultaneously and where \n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j} &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})x_{j}^{(i)} \\tag{2} \\\\\n",
"\\frac{\\partial J(\\mathbf{w},b)}{\\partial b} &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)}) \\tag{3}\n",
"\\end{align}\n",
"$$\n",
"* m is the number of training examples in the data set\n",
"\n",
" \n",
"* $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ is the model's prediction, while $y^{(i)}$ is the target value\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Learning Rate\n",
"<figure>\n",
" <img src=\"./images/C1_W2_Lab06_learningrate.PNG\" style=\"width:1200px;\" >\n",
"</figure>\n",
"The lectures discussed some of the issues related to setting the learning rate $\\alpha$. The learning rate controls the size of the update to the parameters. See equation (1) above. It is shared by all the parameters. \n",
"\n",
"Let's run gradient descent and try a few settings of $\\alpha$ on our data set"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $\\alpha$ = 9.9e-7"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration Cost w0 w1 w2 w3 b djdw0 djdw1 djdw2 djdw3 djdb \n",
"---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
" 0 9.55884e+04 5.5e-01 1.0e-03 5.1e-04 1.2e-02 3.6e-04 -5.5e+05 -1.0e+03 -5.2e+02 -1.2e+04 -3.6e+02\n",
" 1 1.28213e+05 -8.8e-02 -1.7e-04 -1.0e-04 -3.4e-03 -4.8e-05 6.4e+05 1.2e+03 6.2e+02 1.6e+04 4.1e+02\n",
" 2 1.72159e+05 6.5e-01 1.2e-03 5.9e-04 1.3e-02 4.3e-04 -7.4e+05 -1.4e+03 -7.0e+02 -1.7e+04 -4.9e+02\n",
" 3 2.31358e+05 -2.1e-01 -4.0e-04 -2.3e-04 -7.5e-03 -1.2e-04 8.6e+05 1.6e+03 8.3e+02 2.1e+04 5.6e+02\n",
" 4 3.11100e+05 7.9e-01 1.4e-03 7.1e-04 1.5e-02 5.3e-04 -1.0e+06 -1.8e+03 -9.5e+02 -2.3e+04 -6.6e+02\n",
" 5 4.18517e+05 -3.7e-01 -7.1e-04 -4.0e-04 -1.3e-02 -2.1e-04 1.2e+06 2.1e+03 1.1e+03 2.8e+04 7.5e+02\n",
" 6 5.63212e+05 9.7e-01 1.7e-03 8.7e-04 1.8e-02 6.6e-04 -1.3e+06 -2.5e+03 -1.3e+03 -3.1e+04 -8.8e+02\n",
" 7 7.58122e+05 -5.8e-01 -1.1e-03 -6.2e-04 -1.9e-02 -3.4e-04 1.6e+06 2.9e+03 1.5e+03 3.8e+04 1.0e+03\n",
" 8 1.02068e+06 1.2e+00 2.2e-03 1.1e-03 2.3e-02 8.3e-04 -1.8e+06 -3.3e+03 -1.7e+03 -4.2e+04 -1.2e+03\n",
" 9 1.37435e+06 -8.7e-01 -1.7e-03 -9.1e-04 -2.7e-02 -5.2e-04 2.1e+06 3.9e+03 2.0e+03 5.1e+04 1.4e+03\n",
"w,b found by gradient descent: w: [-0.87 -0. -0. -0.03], b: -0.00\n"
]
}
],
"source": [
"# Input learning rate alpha = 9.9e-7\n",
"# Input 'X_train' matrix\n",
"# Input 'y_train' vector\n",
"# Input total iterations/steps of GD for loop\n",
"# Outputs COST J history of values per iteration\n",
"_, _, hist = run_gradient_descent(X_train, y_train, 10, alpha = 9.9e-7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It appears the learning rate is too high. The solution does not converge. Cost is *increasing* rather than decreasing. Let's plot the result:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Input ‘X_train’ matrix \n",
"# Input ‘y_train’ vector \n",
"# Input COST J history of values, per iteration \n",
"# Plot COST J(w,b) vs iterations \n",
"# Plot COST J(w,b) vs first weights parameter w0 \n",
"plot_cost_i_w(X_train, y_train, hist)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot on the right shows the value of one of the parameters, $w_0$. At each iteration, it is overshooting the optimal value and as a result, cost ends up *increasing* rather than approaching the minimum. Note that this is not a completely accurate picture as there are 4 parameters being modified each pass rather than just one. This plot is only showing $w_0$ with the other parameters fixed at benign values. In this and later plots you may notice the blue and orange lines being slightly off."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### $\\alpha$ = 9e-7\n",
"Let's try a bit smaller value and see what happens."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration Cost w0 w1 w2 w3 b djdw0 djdw1 djdw2 djdw3 djdb \n",
"---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
" 0 6.64616e+04 5.0e-01 9.1e-04 4.7e-04 1.1e-02 3.3e-04 -5.5e+05 -1.0e+03 -5.2e+02 -1.2e+04 -3.6e+02\n",
" 1 6.18990e+04 1.8e-02 2.1e-05 2.0e-06 -7.9e-04 1.9e-05 5.3e+05 9.8e+02 5.2e+02 1.3e+04 3.4e+02\n",
" 2 5.76572e+04 4.8e-01 8.6e-04 4.4e-04 9.5e-03 3.2e-04 -5.1e+05 -9.3e+02 -4.8e+02 -1.1e+04 -3.4e+02\n",
" 3 5.37137e+04 3.4e-02 3.9e-05 2.8e-06 -1.6e-03 3.8e-05 4.9e+05 9.1e+02 4.8e+02 1.2e+04 3.2e+02\n",
" 4 5.00474e+04 4.6e-01 8.2e-04 4.1e-04 8.0e-03 3.2e-04 -4.8e+05 -8.7e+02 -4.5e+02 -1.1e+04 -3.1e+02\n",
" 5 4.66388e+04 5.0e-02 5.6e-05 2.5e-06 -2.4e-03 5.6e-05 4.6e+05 8.5e+02 4.5e+02 1.2e+04 2.9e+02\n",
" 6 4.34700e+04 4.5e-01 7.8e-04 3.8e-04 6.4e-03 3.2e-04 -4.4e+05 -8.1e+02 -4.2e+02 -9.8e+03 -2.9e+02\n",
" 7 4.05239e+04 6.4e-02 7.0e-05 1.2e-06 -3.3e-03 7.3e-05 4.3e+05 7.9e+02 4.2e+02 1.1e+04 2.7e+02\n",
" 8 3.77849e+04 4.4e-01 7.5e-04 3.5e-04 4.9e-03 3.2e-04 -4.1e+05 -7.5e+02 -3.9e+02 -9.1e+03 -2.7e+02\n",
" 9 3.52385e+04 7.7e-02 8.3e-05 -1.1e-06 -4.2e-03 8.9e-05 4.0e+05 7.4e+02 3.9e+02 1.0e+04 2.5e+02\n",
"w,b found by gradient descent: w: [ 7.74e-02 8.27e-05 -1.06e-06 -4.20e-03], b: 0.00\n"
]
}
],
"source": [
"# Input learning rate alpha = 9e-7\n",
"# Input 'X_train' matrix\n",
"# Input 'y_train' vector\n",
"# Input total iterations/steps of GD for loop\n",
"# Outputs COST J history of values per iteration\n",
"_,_,hist = run_gradient_descent(X_train, y_train, 10, alpha = 9e-7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cost is decreasing throughout the run showing that alpha is not too large. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x216 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Input ‘X_train’ matrix \n",
"# Input ‘y_train’ vector \n",
"# Input COST J history of values, per iteration \n",
"# Plot COST J(w,b) vs iterations \n",
"# Plot COST J(w,b) vs first weights parameter w0\n",
"plot_cost_i_w(X_train, y_train, hist)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the left, you see that cost is decreasing as it should. On the right, you can see that $w_0$ is still oscillating around the minimum, but the cost is decreasing with every iteration rather than increasing. Note above that `dj_dw[0]` changes sign with each iteration as `w[0]` jumps over the optimal value.\n",
"This alpha value will converge. You can vary the number of iterations to see how it behaves."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### $\\alpha$ = 1e-7\n",
"Let's try a bit smaller value for $\\alpha$ and see what happens."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration Cost w0 w1 w2 w3 b djdw0 djdw1 djdw2 djdw3 djdb \n",
"---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
" 0 4.42313e+04 5.5e-02 1.0e-04 5.2e-05 1.2e-03 3.6e-05 -5.5e+05 -1.0e+03 -5.2e+02 -1.2e+04 -3.6e+02\n",
" 1 2.76461e+04 9.8e-02 1.8e-04 9.2e-05 2.2e-03 6.5e-05 -4.3e+05 -7.9e+02 -4.0e+02 -9.5e+03 -2.8e+02\n",
" 2 1.75102e+04 1.3e-01 2.4e-04 1.2e-04 2.9e-03 8.7e-05 -3.4e+05 -6.1e+02 -3.1e+02 -7.3e+03 -2.2e+02\n",
" 3 1.13157e+04 1.6e-01 2.9e-04 1.5e-04 3.5e-03 1.0e-04 -2.6e+05 -4.8e+02 -2.4e+02 -5.6e+03 -1.8e+02\n",
" 4 7.53002e+03 1.8e-01 3.3e-04 1.7e-04 3.9e-03 1.2e-04 -2.1e+05 -3.7e+02 -1.9e+02 -4.2e+03 -1.4e+02\n",
" 5 5.21639e+03 2.0e-01 3.5e-04 1.8e-04 4.2e-03 1.3e-04 -1.6e+05 -2.9e+02 -1.5e+02 -3.1e+03 -1.1e+02\n",
" 6 3.80242e+03 2.1e-01 3.8e-04 1.9e-04 4.5e-03 1.4e-04 -1.3e+05 -2.2e+02 -1.1e+02 -2.3e+03 -8.6e+01\n",
" 7 2.93826e+03 2.2e-01 3.9e-04 2.0e-04 4.6e-03 1.4e-04 -9.8e+04 -1.7e+02 -8.6e+01 -1.7e+03 -6.8e+01\n",
" 8 2.41013e+03 2.3e-01 4.1e-04 2.1e-04 4.7e-03 1.5e-04 -7.7e+04 -1.3e+02 -6.5e+01 -1.2e+03 -5.4e+01\n",
" 9 2.08734e+03 2.3e-01 4.2e-04 2.1e-04 4.8e-03 1.5e-04 -6.0e+04 -1.0e+02 -4.9e+01 -7.5e+02 -4.3e+01\n",
"w,b found by gradient descent: w: [2.31e-01 4.18e-04 2.12e-04 4.81e-03], b: 0.00\n"
]
}
],
"source": [
"# Input learning rate alpha = 1e-7 \n",
"# Input 'X_train' matrix \n",
"# Input 'y_train' vector \n",
"# Input total iterations/steps of GD for loop \n",
"# Outputs COST J history of values, per iteration\n",
"_,_,hist = run_gradient_descent(X_train, y_train, 10, alpha = 1e-7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cost is decreasing throughout the run showing that $\\alpha$ is not too large. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Input ‘X_train’ matrix \n",
"# Input ‘y_train’ vector \n",
"# Input COST J history of values, per iteration \n",
"# Plot COST J(w,b) vs iterations \n",
"# Plot COST J(w,b) vs first weights parameter w0\n",
"plot_cost_i_w(X_train,y_train,hist)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the left, you see that cost is decreasing as it should. On the right, you can see that $w_0$ is approaching the minimum without oscillations. `dj_w0` is negative throughout the run. This solution will also converge."
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"## Feature Scaling \n",
"<figure>\n",
" <img src=\"./images/C1_W2_Lab06_featurescalingheader.PNG\" style=\"width:1200px;\" >\n",
"</figure>\n",
"The lectures described the importance of rescaling the dataset so the features have a similar range.\n",
"If you are interested in the details of why this is the case, click on the 'details' header below. If not, the section below will walk through an implementation of how to do feature scaling."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details>\n",
"<summary>\n",
" <font size='3', color='darkgreen'><b>Details</b></font>\n",
"</summary>\n",
"\n",
"Let's look again at the situation with $\\alpha$ = 9e-7. This is pretty close to the maximum value we can set $\\alpha$ to without diverging. This is a short run showing the first few iterations:\n",
"\n",
"<figure>\n",
" <img src=\"./images/C1_W2_Lab06_ShortRun.PNG\" style=\"width:1200px;\" >\n",
"</figure>\n",
"\n",
"Above, while cost is being decreased, its clear that $w_0$ is making more rapid progress than the other parameters due to its much larger gradient.\n",
"\n",
"The graphic below shows the result of a very long run with $\\alpha$ = 9e-7. This takes several hours.\n",
"\n",
"<figure>\n",
" <img src=\"./images/C1_W2_Lab06_LongRun.PNG\" style=\"width:1200px;\" >\n",
"</figure>\n",
" \n",
"Above, you can see cost decreased slowly after its initial reduction. Notice the difference between `w0` and `w1`,`w2`,`w3` as well as `dj_dw0` and `dj_dw1-3`. `w0` reaches its near final value very quickly and `dj_dw0` has quickly decreased to a small value showing that `w0` is near the final value. The other parameters were reduced much more slowly.\n",
"\n",
"Why is this? Is there something we can improve? See below:\n",
"<figure>\n",
" <center> <img src=\"./images/C1_W2_Lab06_scale.PNG\" ></center>\n",
"</figure> \n",
"\n",
"The figure above shows why $w$'s are updated unevenly. \n",
"- $\\alpha$ is shared by all parameter updates ($w$'s and $b$).\n",
"- the common error term is multiplied by the features for the $w$'s. (not $b$).\n",
"- the features vary significantly in magnitude making some features update much faster than others. In this case, $w_0$ is multiplied by 'size(sqft)', which is generally > 1000, while $w_1$ is multiplied by 'number of bedrooms', which is generally 2-4. \n",
" \n",
"The solution is Feature Scaling."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The lectures discussed three different techniques: \n",
"- Feature scaling, essentially dividing each positive feature by its maximum value, or more generally, rescale each feature by both its minimum and maximum values using (x-min)/(max-min). Both ways normalizes features to the range of -1 and 1, where the former method works for positive features which is simple and serves well for the lecture's example, and the latter method works for any features.\n",
"- Mean normalization: $x_i := \\dfrac{x_i - \\mu_i}{max - min} $ \n",
"- Z-score normalization which we will explore below. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### z-score normalization \n",
"After z-score normalization, all features will have a mean of 0 and a standard deviation of 1.\n",
"\n",
"To implement z-score normalization, adjust your input values as shown in this formula:\n",
"$$x^{(i)}_j = \\dfrac{x^{(i)}_j - \\mu_j}{\\sigma_j} \\tag{4}$$ \n",
"where $j$ selects a feature or a column in the $\\mathbf{X}$ matrix. $µ_j$ is the mean of all the values for feature (j) and $\\sigma_j$ is the standard deviation of feature (j).\n",
"$$\n",
"\\begin{align}\n",
"\\mu_j &= \\frac{1}{m} \\sum_{i=0}^{m-1} x^{(i)}_j \\tag{5}\\\\\n",
"\\sigma^2_j &= \\frac{1}{m} \\sum_{i=0}^{m-1} (x^{(i)}_j - \\mu_j)^2 \\tag{6}\n",
"\\end{align}\n",
"$$\n",
"\n",
">**Implementation Note:** When normalizing the features, it is important\n",
"to store the values used for normalization - the mean value and the standard deviation used for the computations. After learning the parameters\n",
"from the model, we often want to predict the prices of houses we have not\n",
"seen before. Given a new x value (living room area and number of bed-\n",
"rooms), we must first normalize x using the mean and standard deviation\n",
"that we had previously computed from the training set.\n",
"\n",
"**Implementation**"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def zscore_normalize_features(X): # Input ‘X_train’ (matrix/2D array) \n",
" \n",
" \"\"\" \n",
" computes X, z-score normalized by column\n",
" \n",
" Input arguments: \n",
" X (ndarray (m,n)) : input data, m examples, n features \n",
"\n",
" Output returns: \n",
" X_norm (ndarray (m,n)): input normalized by column \n",
" mu (ndarray (n,)) : mean of each feature \n",
" sigma (ndarray (n,)) : standard deviation of each feature \n",
" \"\"\"\n",
" # Find the mean = mu for each column/feature at ‘X_train’ matrix. \n",
" # Direction of selected values for finding mean is cols -> ‘axis=0’\n",
" mu = np.mean(X, axis=0) # mu will have vector shape (n,). An array with one mean per j feature column\n",
"\n",
" # Find the standard deviation = sigma for each column/feature at ‘X_train’ matrix. \n",
" # Direction of selected values for finding sigma is cols -> ‘axis=0’ \n",
" Sigma = np.std(X, axis=0) # sigma will have vector shape (n,). An array with one sigma per j feature column\n",
" \n",
" # Element-wise, subtract the computed mean = mu, from each example/row at ‘X_train’, \n",
" # then divide element-wise the resulting element/col each row, with sigma = std \n",
" X_norm = (X - mu) / sigma # Get matrix nomalized ‘X_train_normalized’ \n",
"\n",
" return (X_norm, mu, sigma) # return ‘X_train_normalized’ (matrix/2D array), \n",
" # mean of each feature (vector/1D array), \n",
" # sigma of each feature (vector/1D array) \n",
"\n",
"#check our work\n",
"#from sklearn.preprocessing import scale\n",
"#scale(X_orig, axis=0, with_mean=True, with_std=True, copy=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at the steps involved in Z-score normalization. The plot below shows the transformation step by step."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 3 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Find the mean = mu for each column/feature at ‘X_train’ matrix. \n",
"# Direction of selected values for finding mean is cols -> ‘axis=0’\n",
"mu = np.mean(X_train,axis=0) # mu will have vector shape (n,). An array with one mean per j feature column\n",
"\n",
"# Find the standard deviation = sigma for each column/feature at ‘X_train’ matrix. \n",
"# Direction of selected values for finding sigma is cols -> ‘axis=0’\n",
"sigma = np.std(X_train,axis=0) # sigma will have vector shape (n,). An array with one sigma per j feature column\n",
" \n",
"# Element-wise, subtract the computed mean = mu, from each example/row at ‘X_train’\n",
"X_mean = (X_train - mu) # Get matrix with the feature values error, respect to the mean 'mu' of each feature\n",
" # How much each feature row value, takes apart from the mean Xj ^(i) - mu\n",
"\n",
"# Element-wise, subtract the computed mean = mu, from each example/row at ‘X_train’, \n",
"# then divide element-wise the resulting element/col each row, with sigma = std\n",
"X_norm = (X_train - mu)/sigma # Get matrix nomalized ‘X_train_normalized’ \n",
"\n",
"# Create 'figure' object including 3 'ax' subplots/objects\n",
"# Figure has 1 row, 3 cols\n",
"# total size of figure is (col = 12 inches, rows = 3 inches) \n",
"fig, ax=plt.subplots(1, 3, figsize=(12, 3))\n",
"\n",
"# Select at 'X_train' Matrix, ALL the vectors/rows, X0 = size feature/col 0 as x-axis\n",
"# Select at 'X_train' Matrix, ALL the vectors/rows, X3 = age feature/col 3 as y-axis\n",
"# Plot a scatter of X3 = age vs X0 = size, at 'ax0' subplot.\n",
"ax[0].scatter(X_train[:,0], X_train[:,3])\n",
"\n",
"# Set X0 = size feature 'name' as x-axis label and X3 = age feature 'name' as y-axis label of subplot 0. \n",
"ax[0].set_xlabel(X_features[0]); ax[0].set_ylabel(X_features[3]);\n",
"\n",
"ax[0].set_title(\"unnormalized\") # Set subplot 0, X3 = age vs X0 = size features, the title = 'unnormalized' \n",
"ax[0].axis('equal') # Use the same/'equal' scale, at x and y axes \n",
"\n",
"# Select at 'X_mean' Matrix, ALL the vectors/rows, X0_mean = size feature/col 0 as x-axis\n",
"# Select at 'X_mean' Matrix, ALL the vectors/rows, X3_mean = age feature/col 3 as y-axis\n",
"# Plot a scatter of X3_mean = age vs X0_mean = size, at 'ax1' subplot.\n",
"ax[1].scatter(X_mean[:,0], X_mean[:,3])\n",
"\n",
"# Set X0_mean = size feature 'name' as x-axis label and X3_mean = age feature 'name' as y-axis label \n",
"ax[1].set_xlabel(X_features[0]); ax[0].set_ylabel(X_features[3]);\n",
"\n",
"ax[1].set_title(r\"X - $\\mu$\") # Set subplot 1, X3_mean = age vs X0_mean = size features, the title = 'X - mu'\n",
"ax[1].axis('equal') # Use the same/'equal' scale, at x and y axes\n",
"\n",
"# Select at 'X_norm' Matrix, ALL the vectors/rows, X0_norm = size feature/col 0 as x-axis\n",
"# Select at 'X_norm' Matrix, ALL the vectors/rows, X3_norm = age feature/col 3 as y-axis\n",
"# Plot a scatter of X3_norm = age vs X0_norm = size, at 'ax2' subplot.\n",
"ax[2].scatter(X_norm[:,0], X_norm[:,3])\n",
"\n",
"# Set X0_norm = size feature 'name' as x-axis label and X3_norm = age feature 'name' as y-axis label\n",
"ax[2].set_xlabel(X_features[0]); ax[0].set_ylabel(X_features[3]);\n",
"\n",
"ax[2].set_title(r\"Z-score normalized\") # Set subplot 2, X3_norm = age vs X0_norm = size features, the title = 'X - mu'\n",
"ax[2].axis('equal') # Use the same/'equal' scale, at x and y axes\n",
"\n",
"plt.tight_layout(rect=[0, 0.03, 1, 0.95]) # This parameter is rectangle in the normalized figure coordinate,\n",
" # that the whole subplots area will fit into.\n",
" \n",
"fig.suptitle(\"distribution of features before, during, after normalization\") # Set 'supertitle' name of figure 'fig'\n",
"plt.show() # Display whole figure 'fig'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot above shows the relationship between two of the training set parameters, \"age\" and \"size(sqft)\". *These are plotted with equal scale*. \n",
"- Left: Unnormalized: The range of values or the variance of the 'size(sqft)' feature is much larger than that of age\n",
"- Middle: The first step removes the mean or average value from each feature. This leaves features that are centered around zero. It's difficult to see the difference for the 'age' feature, but 'size(sqft)' is clearly around zero.\n",
"- Right: The second step divides by the standard deviation. This leaves both features centered at zero with a similar scale."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's normalize the data and compare it to the original data."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"vector mu = [1.42e+03 2.72e+00 1.38e+00 3.84e+01], \n",
"vector sigma = [411.62 0.65 0.49 25.78]\n",
"Peak to Peak range by column in Raw X:[2.41e+03 4.00e+00 1.00e+00 9.50e+01]\n",
"Peak to Peak range by column in Normalized X:[5.85 6.14 2.06 3.69]\n"
]
}
],
"source": [
"# Normalize the original matrix X_train with input features, \n",
"# calling the function 'zscore_normalize_features()' \n",
"# that returns the normalized 2D matrix X_train_norm = (X_train - mu) / sigma, \n",
"# the mu 1D vector and the sigma 1D vector.\n",
"X_norm, X_mu, X_sigma = zscore_normalize_features(X_train)\n",
"print(f\"vector mu = {X_mu}, \\nvector sigma = {X_sigma}\")\n",
"\n",
"# The 'numpy.ptp()' method computes the range of values (maximum - minimum) in an array \n",
"# along the specified (axis=0 -> cols/features). Here, ptp stands for peak to peak.\n",
"print(f\"Peak to Peak range by column in Raw X:{np.ptp(X_train,axis=0)}\") \n",
"print(f\"Peak to Peak range by column in Normalized X:{np.ptp(X_norm,axis=0)}\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The peak to peak range of each column is reduced from a factor of thousands to a factor of 2-3 by normalization."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x216 with 8 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x216 with 8 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create 'figure' object including 4 'ax' subplots/objects\n",
"# Figure has 1 row, 4 cols\n",
"# total size of figure is (col = 12 inches, rows = 3 inches)\n",
"fig,ax=plt.subplots(1, 4, figsize=(12, 3))\n",
"\n",
"for i in range(len(ax)): # Iterate through each of 4 'ax' subplots/objects, so i = 0,1,2,3\n",
" norm_plot(ax[i], X_train[:,i]) # Input each ax[i] object subplot and all rows for each X_train feature/col, and\n",
" # return a gaussian/normal distribution plot, and histogram plot,\n",
" # for each of 4 features, before normalization.\n",
" ax[i].set_xlabel(X_features[i]) # Set the x_label at each subplot, selecting its name from 'X_feature[i]' list, i-th element\n",
"\n",
"ax[0].set_ylabel(\"count\"); # Set the y_label -> 'count' once, just at the first subplot \n",
"fig.suptitle(\"distribution of features before normalization\") # Set 'fig' object super title\n",
"plt.show() # Display figure with 4 distribution subplots (one per feature)\n",
"\n",
"# Create 'figure' object including 4 'ax' subplots/objects\n",
"# Figure has 1 row, 4 cols\n",
"# total size of figure is (col = 12 inches, rows = 3 inches)\n",
"fig,ax=plt.subplots(1,4,figsize=(12,3))\n",
"\n",
"for i in range(len(ax)): # Iterate through each of 4 'ax' subplots/objects, so i = 0,1,2,3\n",
" norm_plot(ax[i], X_norm[:,i]) # Input each ax[i] object subplot and all rows for each X_normalized feature/col, and\n",
" ax[i].set_xlabel(X_features[i]) # return a gaussian/normal distribution plot, and histogram plot,\n",
" # for each of 4 features, after normalization. \n",
" \n",
"ax[0].set_ylabel(\"count\"); # Set the y_label -> 'count' once, just at the first subplot\n",
"fig.suptitle(\"distribution of features after normalization\") # Set 'fig' object super title\n",
"plt.show() # Display figure with 4 distribution subplots (one per feature)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice, above, the range of the normalized data (x-axis) is centered around zero and roughly +/- 2. Most importantly, the range is similar for each feature."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's re-run our gradient descent algorithm with normalized data.\n",
"Note the **vastly larger value of alpha**. This will speed up gradient descent."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration Cost w0 w1 w2 w3 b djdw0 djdw1 djdw2 djdw3 djdb \n",
"---------------------|--------|--------|--------|--------|--------|--------|--------|--------|--------|--------|\n",
" 0 5.76170e+04 8.9e+00 3.0e+00 3.3e+00 -6.0e+00 3.6e+01 -8.9e+01 -3.0e+01 -3.3e+01 6.0e+01 -3.6e+02\n",
" 100 2.21086e+02 1.1e+02 -2.0e+01 -3.1e+01 -3.8e+01 3.6e+02 -9.2e-01 4.5e-01 5.3e-01 -1.7e-01 -9.6e-03\n",
" 200 2.19209e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -3.0e-02 1.5e-02 1.7e-02 -6.0e-03 -2.6e-07\n",
" 300 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -1.0e-03 5.1e-04 5.7e-04 -2.0e-04 -6.9e-12\n",
" 400 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -3.4e-05 1.7e-05 1.9e-05 -6.6e-06 -2.7e-13\n",
" 500 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -1.1e-06 5.6e-07 6.2e-07 -2.2e-07 -2.6e-13\n",
" 600 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -3.7e-08 1.9e-08 2.1e-08 -7.3e-09 -2.6e-13\n",
" 700 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -1.2e-09 6.2e-10 6.9e-10 -2.4e-10 -2.6e-13\n",
" 800 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -4.1e-11 2.1e-11 2.3e-11 -8.1e-12 -2.7e-13\n",
" 900 2.19207e+02 1.1e+02 -2.1e+01 -3.3e+01 -3.8e+01 3.6e+02 -1.4e-12 7.0e-13 7.6e-13 -2.7e-13 -2.6e-13\n",
"w,b found by gradient descent: w: [110.56 -21.27 -32.71 -37.97], b: 363.16\n"
]
}
],
"source": [
"# Input learning rate alpha = 1e-1 = 0.1 \n",
"# Input 'X_train' matrix \n",
"# Input 'y_train' vector \n",
"# Input total iterations/steps of GD for loop \n",
"# Output 1D vector w, with weights parameters, computed at GD, when use 'X_normalized' as input training set\n",
"# Output scalar b, bias parameter, computed at GD, when use 'X_normalized' as input training set\n",
"# Output COST J history of values, per iteration\n",
"w_norm, b_norm, hist = run_gradient_descent(X_norm, y_train, 1000, 1.0e-1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The scaled features get very accurate results **much, much faster!**. Notice the gradient of each parameter is tiny by the end of this fairly short run. A learning rate of 0.1 is a good start for regression with normalized features.\n",
"Let's plot our predictions versus the target values. Note, the prediction is made using the normalized feature while the target plot is shown using the original feature values."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'dlblue': '#0096ff', 'dlorange': '#FF9300', 'dldarkred': '#C00000', 'dlmagenta': '#FF40FF', 'dlpurple': '#7030A0'} \n",
" y^= [295.18 485.98 389.52 492.15 420.25 222.78 523.42 267.55 685.2 181.75\n",
" 317.95 479.63 409.95 393.53 286.97 323.28 405.96 436.43 269.84 500.72\n",
" 328.61 388.16 551.59 241.48 295.46 282.48 217.11 491.17 228.84 341.21\n",
" 291.36 490.12 238.29 598.53 383.73 452.82 401.27 405.94 172.18 423.58\n",
" 434.41 277.01 228.84 448.61 489.06 331.76 465.8 221.67 386.72 456.66\n",
" 370.49 468.87 310.19 426.51 391.78 347.54 339.21 471.59 243.32 297.94\n",
" 272.87 249.66 297.83 334.93 375.9 288.86 228.84 621.12 352.77 511.13\n",
" 364.05 363.09 297.83 407.27 288.55 385.9 488.28 260.88 259.05 427.65\n",
" 238.04 355.57 339.63 390.3 381.62 220.04 434.41 243.33 465.8 185.78\n",
" 341.22 410.26 445.65 231.87 331.76 409.23 405.94 351.39 274.21]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x216 with 4 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Predict (y^) the target (y), using normalized features 'X_norm'\n",
"m = X_norm.shape[0] # Get the total number of rows/samples m = 99 at 'X_norm'\n",
"yp = np.zeros(m) # Create an ALL zeros vector, with the same size of rows (m = 99)\n",
" # yp = y^ = [0, 0, 0,...,0], to be filled with each repeated predicted price y^[0-98]\n",
" # y^ = [y^[0],y^[1],y^[2],...,y^[98]] linear model prediction, to be plotted vs each X[i] input feature\n",
"\n",
"for i in range(m): # Iterate through each input feature (m=99), so range(m) -> i = 0, 1, 2,...,98\n",
" yp[i] = np.dot(X_norm[i], w_norm) + b_norm # Compute each model prediction y^[i] = X_norm[i].w + b \n",
" # using dot product of vectors X_norm.w and overwrite y^ (all zeros vector)\n",
"\n",
"# Plot predictions y^ = [y^[0],y^[1],y^[2],...,y^[98]] previously computed with normalized features 'X_norm'\n",
"# and compare with targets y = [y[0],y[1],y[2],...,y[98]] using original features 'X_train'. \n",
"# The plot uses 'X_train' values at x-axis for each subplot.\n",
"# Create 'figure' object including 4 'ax' subplots/objects\n",
"# Figure has 1 row, 4 cols\n",
"# total size of figure is (col = 12 inches, rows = 3 inches)\n",
"# sharey = True, means that ALL 4 subplots, have the same y-axis scale of the first subplot\n",
"fig,ax=plt.subplots(1,4,figsize=(12, 3),sharey=True)\n",
"\n",
"for i in range(len(ax)): # Iterate through each of 4 'ax' subplots/objects, so i = 0,1,2,3\n",
" \n",
" # Select at 'X_train' Matrix, ALL the vectors/rows, per each i-th feature/col value, at x-axis\n",
" # Select each y_train vector value at y-axis\n",
" # Plot one scatter per each i-th feature, at each i-th 'ax' subplot.\n",
" ax[i].scatter(X_train[:,i],y_train, label = 'target') # Assign the label of 'target' for blue points\n",
" ax[i].set_xlabel(X_features[i]) # Set the x_label at each subplot, \n",
" # selecting its name from 'X_feature[i]' list, i-th element\n",
" \n",
" # Select at 'X_train' Matrix, ALL the vectors/rows, per each i-th feature/col value, at x-axis\n",
" # Select each yp = y^ vector value at y-axis\n",
" # Plot one scatter per each i-th feature, at each i-th 'ax' subplot.\n",
" # Assign orange color of predicted points, as color = dlc[\"dlorange\"] = '#FF9300'. \n",
" ax[i].scatter(X_train[:,i],yp,color=dlc[\"dlorange\"], label = 'predict') # Assign the label of 'predict' for orange points\n",
"\n",
"print(dlc,'\\n y^=',yp) # dlc is a dictionary dlc={'color_name_0':'value_0', 'color_name_1':'value_1',... }\n",
"ax[0].set_ylabel(\"Price\"); ax[0].legend(); # Set y_label -> 'price', just at the first subplot due its shared by other subplots\n",
" # Display the legend at first subplot with 'ax[0].legend()'\n",
" \n",
"fig.suptitle(\"target y and prediction y^ comparison, using z-score normalized model\") # Set 'fig' object super title \n",
"plt.show() # Display figure with 4 subplots (one per input feature)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The results look good. A few points to note:\n",
"- with multiple features, we can no longer have a single plot showing results versus features.\n",
"- when generating the plot, the normalized features were used. Any predictions using the parameters learned from a normalized training set must also be normalized."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Prediction**\n",
"The point of generating our model is to use it to predict housing prices that are not in the data set. Let's predict the price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old. Recall, that you must normalize the data with the mean and standard deviation derived when the training data was normalized. "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-0.53 0.43 -0.79 0.06]\n",
" predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = $318709\n"
]
}
],
"source": [
"# First, normalize out example.\n",
"x_house = np.array([1200, 3, 1, 40]) # X_test = [X0, X1, X2, X3] = [1200 sqft, 3 bedrooms, 1 floor, 40 years old]\n",
"\n",
"# In[12]: When we normalized the original matrix 'X_train' input features, we called the function 'zscore_normalize_features()' \n",
"# and obtained the normalized 2D matrix 'X_norm' = (X_train - mu) / sigma, \n",
"# the mu 1D vector 'X_mu' = [mu0, mu1, mu2, mu3] and the sigma 1D vector 'X_sigma' = [sigma0, sigma1, sigma2, sigma3] . \n",
"x_house_norm = (x_house - X_mu) / X_sigma # Test set house price is normalized, using previously obtained 'X_mu' and 'X_sigma' \n",
"print(x_house_norm) # Print out X_test_norm = [-0.53 sqft, 0.43 bedrooms, -0.79 floors, 0.06 years old] \n",
"\n",
"x_house_predict = np.dot(x_house_norm, w_norm) + b_norm # Compute predicted price ($1000s) y^ = X_test_norm.w_norm + b_norm\n",
"\n",
"# As predicted price = y^ = $319 (in $1000s), we multiply by *1000 to get $319.000 \n",
"# and display all the number with 0 decimals using :0.0f \n",
"print(f\" predicted price of a house with 1200 sqft, 3 bedrooms, 1 floor, 40 years old = ${x_house_predict*1000:0.0f}\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Cost Contours** \n",
"<img align=\"left\" src=\"./images/C1_W2_Lab06_contours.PNG\" style=\"width:240px;\" >Another way to view feature scaling is in terms of the cost contours. When feature scales do not match, the plot of cost versus parameters in a contour plot is asymmetric. \n",
"\n",
"In the plot below, the scale of the parameters is matched. The left plot is the cost contour plot of w[0], the square feet versus w[1], the number of bedrooms before normalizing the features. The plot is so asymmetric, the curves completing the contours are not visible. In contrast, when the features are normalized, the cost contour is much more symmetric. The result is that updates to parameters during gradient descent can make equal progress for each parameter. \n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x360 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Graph of Contour Plots of COST J, considering W1 (# bedrooms) vs W0 (size in square feet)\n",
"# with non-normalized (left) input features 'X0', 'X1' and normalized (right) input features 'X0_norm', 'X1_norm'\n",
"# Input normal 'X_train' at training set\n",
"# Input normalized 'X_norm' as normalized training set\n",
"# Input normal 'y_train' target at training set\n",
"plt_equal_scale(X_train, X_norm, y_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## Congratulations!\n",
"In this lab you:\n",
"- utilized the routines for linear regression with multiple features you developed in previous labs\n",
"- explored the impact of the learning rate $\\alpha$ on convergence \n",
"- discovered the value of feature scaling using z-score normalization in speeding convergence"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Acknowledgments\n",
"The housing data was derived from the [Ames Housing dataset](http://jse.amstat.org/v19n3/decock.pdf) compiled by Dean De Cock for use in data science education."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.6"
},
"toc-autonumbering": false
},
"nbformat": 4,
"nbformat_minor": 5
}
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