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PMR tutorial 2 questions 4 and 5
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"cell_type": "markdown",
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"source": [
"Question 4\n",
"==========\n",
"\n",
"Plotting bivariate Gaussians, with the following density function:\n",
"\n",
"$$\n",
"p(\\mathbf{x}) = \\frac{1}{( 2\\pi )^{d/2} |\\Sigma |^{1/2} } \\exp \\left( - \\frac{1}{2} \\mathbf{x}^{T} \\Sigma^{-1} \\mathbf{x} \\right)\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import scipy.stats as st"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sigma11 = 1\n",
"sigma12 = -0.5\n",
"sigma21 = sigma12\n",
"sigma22 = 1\n",
"Sigma = np.array([[sigma11,sigma12],\n",
" [sigma21,sigma22]])\n",
"# zero mean implied\n",
"mu = np.zeros((2))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 68
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X,Y = np.meshgrid(np.linspace(-3,3,100),np.linspace(-3,3,100))\n",
"X.shape\n",
"p = np.zeros(X.shape)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 69
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import itertools"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 70
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mu.shape[0]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 71,
"text": [
"2"
]
}
],
"prompt_number": 71
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mvnormal = st.multivariate_normal(mean=mu,cov=Sigma)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 72
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"for i,j in itertools.product(range(X.shape[0]),range(Y.shape[1])):\n",
" p[i,j] = mvnormal.pdf(np.array([X[i,j],Y[i,j]]))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 73
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib import cm\n",
"from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 74
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# 3d plot\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection=\"3d\")\n",
"surf = ax.plot_surface(X, Y, p, rstride=1, cstride=1, cmap=cm.coolwarm,\n",
" linewidth=0, antialiased=False)\n",
"ax.zaxis.set_major_locator(LinearLocator(10))\n",
"ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
"fig.colorbar(surf, shrink=0.5, aspect=5)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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8bORNMoFqqOA6h/AFjLoBraxj6S8vQOMTX5nYWJNAi0z0lRS5J7WfGbTINo2U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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f58da402f98>"
]
}
],
"prompt_number": 75
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.cm as cm\n",
"import matplotlib.mlab as mlab\n",
"import matplotlib.pyplot as plt"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 76
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# contour plot\n",
"plt.figure()\n",
"CS = plt.contour(X, Y, p)\n",
"plt.clabel(CS, inline=1, fontsize=10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 77,
"text": [
"<a list of 6 text.Text objects>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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6AUxH9R26RzPQ3HXxNh+HpIGQ0Akyp+GKK425g+d5ida0YTUrmMJkIoiwuRQX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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f58db0d5f98>"
]
}
],
"prompt_number": 77
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Question 5\n",
"==========\n",
"\n",
"Using the Cholesky decomposition to generate points from arbitrary multivariate Gaussians. This was a question in last year's NIP assignment, here's my answer:\n",
"\n",
"> For two uncorrelated random variables $x_{1}$ and $x_{2}$ the covariance matrix is defined as $\\mathbb{E}[\\vec{x}\\vec{x}^{T}]$, where $\\vec{x} = (\\begin{matrix} x_{1} & x_{2} \\end{matrix} )$.\n",
"As they are uncorrelated $\\mathbb{E}[\\vec{x}\\vec{x}^{T}] = \\mathbf{I} $.\n",
"For an arbitrary covariance matrix $\\Sigma$ between these two, in this case:\n",
"> \n",
"> $$ \\Sigma = \\left(\\begin{matrix} \\sigma^{2} & c \\sigma^{2} \\\\ c \\sigma^{2} & \\sigma^{2} \\end{matrix} \\right) $$\n",
">\n",
"> This matrix can be decomposed using the Cholesky decomposition to form a matrix $C$ such that $\\Sigma = C C^{T}$.\n",
"> If the vector of $\\vec{x}$ is multiplied by this the covariance between $x_{1}$ and $x_{2}$ becomes:\n",
">\n",
"> $$ \\mathbb{E}\\left[(C\\vec{x}) (C\\vec{x})^{T} \\right] = \\mathbb{E}\\left[C\\vec{x}\\vec{x}^{T}C^{T} \\right] = C\\mathbb{E}\\left[\\vec{x}\\vec{x}^{T} \\right]C^{T} = C C^{T} = \\Sigma $$\n",
">\n",
">Therefore, by creating this matrix with the cholesky decomposition and applying it to adjacent samples in a series of Gaussian random variables it's possible to create a correlated random variable."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#create the transforming matrix\n",
"c = 0.9\n",
"s = 1.0\n",
"nsamples = 10000\n",
"covariance = np.array([[s**2, c*s**2],[c*s**2, s**2]])\n",
"#generate matrix\n",
"#covariance = zeros((nsamples,nsamples))\n",
"#for i in range(nsamples):\n",
"# for j in range(nsamples):\n",
"# if i == j:\n",
"# covariance[i,j] = s**2\n",
"# elif i == j+1 or i == j-1:\n",
"# covariance[i,j] = c*s**2\n",
"#print covariance\n",
"#decompose covariance\n",
"C = np.linalg.cholesky(covariance)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 79
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#generate vector of gaussian samples\n",
"samples = np.random.randn(nsamples,2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 84
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"correlated_samples = np.zeros(samples.shape)\n",
"for i,s in enumerate(samples):\n",
" correlated_samples[i,:] = np.dot(C,s)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 86
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting before and after 2D histograms:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.title(\"Uncorrelated\")\n",
"h=plt.hist2d(samples[:,0], samples[:,1], bins=40)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAW0AAAEKCAYAAADZ8ATAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAaAi/x9zKV+v4yfiEQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f58db4a9ba8>"
]
}
],
"prompt_number": 93
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.title(\"Correlated\")\n",
"h=plt.hist2d(correlated_samples[:,0], correlated_samples[:,1], bins=40)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f58d9ef3358>"
]
}
],
"prompt_number": 95
}
],
"metadata": {}
}
]
}
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