kjordahl/bootstrap.ipynb

## bootstrap.ipynb
{
 "metadata": {
  "name": "Bootstrap density plots"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy import ndimage\nfrom sklearn.gaussian_process import GaussianProcess",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def pdense(x, y, sigma, M=1000):\n    \"\"\" Plot probability density of y with known stddev sigma\n    \"\"\"\n    assert len(x) == len(y) and len(x) == len(sigma)\n    N = len(x)\n    # TODO: better y ranging\n    ymin, ymax = min(y - 2 * sigma), max(y + 2 * sigma)\n    yy = np.linspace(ymin, ymax, M)\n    a = [np.exp(-((Y - yy) / s) ** 2) / s for Y, s in zip(y, sigma)]\n    A = np.array(a)\n    A = A.reshape(N, M)\n    plt.imshow(-A.T, cmap='gray', aspect='auto',\n               origin='lower', extent=(min(x)[0], max(x)[0], ymin, ymax))\n    plt.title('Density plot')",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def gpr(seed=0, N=20, M=1000, sigma=1.0):\n    \"\"\" from scikits.learn demo\n    \"\"\"\n    np.random.seed(seed)\n\n    def f(x):\n        \"\"\"The function to predict.\"\"\"\n        return x * np.sin(x)\n    \n    X = np.linspace(0.1, 9.9, 20)\n    X = np.atleast_2d(X).T\n    y = f(X).ravel()\n    y = np.random.normal(y, sigma)\n    x = np.atleast_2d(np.linspace(0, 10, M)).T\n    nugget = (sigma / y) ** 2\n    gp = GaussianProcess(corr='squared_exponential', theta0=1e-1,\n                         thetaL=1e-1, thetaU=1.0,\n                         nugget=nugget,\n                         random_start=100)\n    gp.fit(X, y)\n    y2, MSE = gp.predict(x, eval_MSE=True)\n    s2 = np.sqrt(MSE)\n    return X, y, x, y2, s2\n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "X, y, x, y2, s2 = gpr(seed=0)\nplt.figure(1)\npdense(x, y2, s2, M=1000)\nplt.plot(X, y, 'r.')\nplt.plot(x, y2, 'b:')\na = plt.gca()\na.set_ylim(-10, 15)\nplt.xlabel('$x$')\nplt.ylabel('$f(x)$')\nplt.show()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "1.0\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "/Users/kjordahl/dev/github/scikit-learn/sklearn/utils/__init__.py:80: DeprecationWarning: Function theta is deprecated; ``theta`` is deprecated and will be removed in 0.14, please use ``theta_`` instead.\n  warnings.warn(msg, category=DeprecationWarning)\n"
      },
      {
       "output_type": "display_data",
       "png": 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ciqqqKlRVVaGyshLaE0/EDfffj7t27cIt06bhsjvuQGlpacqgwVAoBJ/PB5fLhd7eXnR1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\nj0iD5Mceuw3l5a8jHI6I7qqBEebGEa0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cvJCwcSTvvHMKKiu7MGvWFvGOMZNoSCdmItEg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\nSBIWBxERSfIfelFdIzAT6TcAAAAASUVORK5CYII=\n",
       "text": "<matplotlib.figure.Figure at 0x10c67af90>"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Run the experiment many times\nN = 200\nY = np.nan * np.ones((N, len(x)))\ns = np.nan * np.ones((N, len(x)))\nprint 'Running trial',\nfor i in xrange(N):\n    X, y, x, y2, s2 = gpr(seed=i)\n    Y[i,:] = y2\n    s[i,:] = s2\n    print i,\nprint '\\nDone!'\nplt.plot(x, Y.T, 'b', alpha=0.15)\na = plt.gca()\na.set_ylim(-10, 15)\nplt.title('Bootstrap spaghetti plot')\nplt.xlabel('$x$')\nplt.ylabel('$f(x)$')\nplt.show()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Running trial "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "0 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "1 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "2 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "3 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "4 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "5 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "6 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "7 "
      },
      {
       "output_type": "stream",
       "stream": "stdout",
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KCgqLE8kkkc9H5PeDNMxmosxMIYl4nGhigigcJjKZiLKziXJy8P9iwPRF9fe+9720fj8v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\nIOji/wG6DbpsDhewYwAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x109f1e190>"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "ymin, ymax = -10, 15\nbin_width = 0.15\ny_bins = np.arange(ymin, ymax, bin_width)\nH = np.zeros((len(y_bins)-1, len(x)))\nm = np.zeros(x.shape)\nfor i in xrange(len(x)):\n    h, e = np.histogram(Y[:,i], bins=np.arange(ymin, ymax, bin_width), density=True)\n    H[:,i] = h\n    m[i] = np.median(Y[:,i])\nhb = ndimage.gaussian_filter(H, sigma=1)\nplt.imshow(-hb, cmap='gray', aspect='auto', origin='lower',\n           extent=(min(x)[0], max(x)[0], ymin, ymax))\nplt.plot(x, m, 'b:')\na = plt.gca()\na.set_ylim(-10, 15)\nplt.title('Bootstrap density plot')\nplt.xlabel('$x$')\nplt.ylabel('$f(x)$')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": "<matplotlib.text.Text at 0x109f59450>"
      },
      {
       "output_type": "display_data",
       "png": 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O0ges+kM7OBjy4PslS4RHQXE3E+8nks/nMTjYhXnzkigWi3A4HPD5fHC73bDZ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\nc6wFgPrf7I6ilUGuF7q7yioUDkJwsYDoDQxFIPSZGwDUa0qlUkUQWxc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       "text": "<matplotlib.figure.Figure at 0x1111c3910>"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}

## bootstrap.py
# -*- coding: utf-8 -*-
# <nbformat>3.0</nbformat>

# <codecell>

import numpy as np
import matplotlib.pyplot as plt
from scipy import ndimage
from sklearn.gaussian_process import GaussianProcess

# <codecell>

def pdense(x, y, sigma, M=1000):
    """ Plot probability density of y with known stddev sigma
    """
    assert len(x) == len(y) and len(x) == len(sigma)
    N = len(x)
    # TODO: better y ranging
    ymin, ymax = min(y - 2 * sigma), max(y + 2 * sigma)
    yy = np.linspace(ymin, ymax, M)
    a = [np.exp(-((Y - yy) / s) ** 2) / s for Y, s in zip(y, sigma)]
    A = np.array(a)
    A = A.reshape(N, M)
    plt.imshow(-A.T, cmap='gray', aspect='auto',
               origin='lower', extent=(min(x)[0], max(x)[0], ymin, ymax))
    plt.title('Density plot')

# <codecell>

def gpr(seed=0, N=20, M=1000, sigma=1.0):
    """ from scikits.learn demo
    """
    np.random.seed(seed)

    def f(x):
        """The function to predict."""
        return x * np.sin(x)

    X = np.linspace(0.1, 9.9, 20)
    X = np.atleast_2d(X).T
    y = f(X).ravel()
    y = np.random.normal(y, sigma)
    x = np.atleast_2d(np.linspace(0, 10, M)).T
    nugget = (sigma / y) ** 2
    gp = GaussianProcess(corr='squared_exponential', theta0=1e-1,
                         thetaL=1e-1, thetaU=1.0,
                         nugget=nugget,
                         random_start=100)
    gp.fit(X, y)
    y2, MSE = gp.predict(x, eval_MSE=True)
    s2 = np.sqrt(MSE)
    return X, y, x, y2, s2

# <codecell>

X, y, x, y2, s2 = gpr(seed=0)
plt.figure(1)
pdense(x, y2, s2, M=1000)
plt.plot(X, y, 'r.')
plt.plot(x, y2, 'b:')
a = plt.gca()
a.set_ylim(-10, 15)
plt.xlabel('$x$')
plt.ylabel('$f(x)$')
plt.show()

# <codecell>

# Run the experiment many times
N = 200
Y = np.nan * np.ones((N, len(x)))
s = np.nan * np.ones((N, len(x)))
print 'Running trial',
for i in xrange(N):
    X, y, x, y2, s2 = gpr(seed=i)
    Y[i,:] = y2
    s[i,:] = s2
    print i,
print '\nDone!'
plt.plot(x, Y.T, 'b', alpha=0.15)
a = plt.gca()
a.set_ylim(-10, 15)
plt.title('Bootstrap spaghetti plot')
plt.xlabel('$x$')
plt.ylabel('$f(x)$')
plt.show()

# <codecell>

ymin, ymax = -10, 15
bin_width = 0.15
y_bins = np.arange(ymin, ymax, bin_width)
H = np.zeros((len(y_bins)-1, len(x)))
m = np.zeros(x.shape)
for i in xrange(len(x)):
    h, e = np.histogram(Y[:,i], bins=np.arange(ymin, ymax, bin_width), density=True)
    H[:,i] = h
    m[i] = np.median(Y[:,i])
hb = ndimage.gaussian_filter(H, sigma=1)
plt.imshow(-hb, cmap='gray', aspect='auto', origin='lower',
           extent=(min(x)[0], max(x)[0], ymin, ymax))
plt.plot(x, m, 'b:')
a = plt.gca()
a.set_ylim(-10, 15)
plt.title('Bootstrap density plot')
plt.xlabel('$x$')
plt.ylabel('$f(x)$')

# <codecell>
	# -- coding: utf-8 --
	# <nbformat>3.0</nbformat>

	# <codecell>

	import numpy as np
	import matplotlib.pyplot as plt
	from scipy import ndimage
	from sklearn.gaussian_process import GaussianProcess

	# <codecell>

	def pdense(x, y, sigma, M=1000):
	""" Plot probability density of y with known stddev sigma
	"""
	assert len(x) == len(y) and len(x) == len(sigma)
	N = len(x)
	# TODO: better y ranging
	ymin, ymax = min(y - 2 * sigma), max(y + 2 * sigma)
	yy = np.linspace(ymin, ymax, M)
	a = [np.exp(-((Y - yy) / s) ** 2) / s for Y, s in zip(y, sigma)]
	A = np.array(a)
	A = A.reshape(N, M)
	plt.imshow(-A.T, cmap='gray', aspect='auto',
	origin='lower', extent=(min(x)[0], max(x)[0], ymin, ymax))
	plt.title('Density plot')

	# <codecell>

	def gpr(seed=0, N=20, M=1000, sigma=1.0):
	""" from scikits.learn demo
	"""
	np.random.seed(seed)

	def f(x):
	"""The function to predict."""
	return x * np.sin(x)

	X = np.linspace(0.1, 9.9, 20)
	X = np.atleast_2d(X).T
	y = f(X).ravel()
	y = np.random.normal(y, sigma)
	x = np.atleast_2d(np.linspace(0, 10, M)).T
	nugget = (sigma / y) ** 2
	gp = GaussianProcess(corr='squared_exponential', theta0=1e-1,
	thetaL=1e-1, thetaU=1.0,
	nugget=nugget,
	random_start=100)
	gp.fit(X, y)
	y2, MSE = gp.predict(x, eval_MSE=True)
	s2 = np.sqrt(MSE)
	return X, y, x, y2, s2

	# <codecell>

	X, y, x, y2, s2 = gpr(seed=0)
	plt.figure(1)
	pdense(x, y2, s2, M=1000)
	plt.plot(X, y, 'r.')
	plt.plot(x, y2, 'b:')
	a = plt.gca()
	a.set_ylim(-10, 15)
	plt.xlabel('$x$')
	plt.ylabel('$f(x)$')
	plt.show()

	# <codecell>

	# Run the experiment many times
	N = 200
	Y = np.nan * np.ones((N, len(x)))
	s = np.nan * np.ones((N, len(x)))
	print 'Running trial',
	for i in xrange(N):
	X, y, x, y2, s2 = gpr(seed=i)
	Y[i,:] = y2
	s[i,:] = s2
	print i,
	print '\nDone!'
	plt.plot(x, Y.T, 'b', alpha=0.15)
	a = plt.gca()
	a.set_ylim(-10, 15)
	plt.title('Bootstrap spaghetti plot')
	plt.xlabel('$x$')
	plt.ylabel('$f(x)$')
	plt.show()

	# <codecell>

	ymin, ymax = -10, 15
	bin_width = 0.15
	y_bins = np.arange(ymin, ymax, bin_width)
	H = np.zeros((len(y_bins)-1, len(x)))
	m = np.zeros(x.shape)
	for i in xrange(len(x)):
	h, e = np.histogram(Y[:,i], bins=np.arange(ymin, ymax, bin_width), density=True)
	H[:,i] = h
	m[i] = np.median(Y[:,i])
	hb = ndimage.gaussian_filter(H, sigma=1)
	plt.imshow(-hb, cmap='gray', aspect='auto', origin='lower',
	extent=(min(x)[0], max(x)[0], ymin, ymax))
	plt.plot(x, m, 'b:')
	a = plt.gca()
	a.set_ylim(-10, 15)
	plt.title('Bootstrap density plot')
	plt.xlabel('$x$')
	plt.ylabel('$f(x)$')

	# <codecell>