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@ljwolf
Created November 22, 2016 20:55
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This details what should be a method to sample from a multivariate normal in a spatial error model using only the precision matrix, instead of the covariance matrix.
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import scipy.linalg as scla\n",
"import numpy as np\n",
"import pysal as ps\n",
"# pip install numpy\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A common problem for simulating spatial stochastic systems is that the covariance matrix of the system requires the inversion of a large sparse matrix. For example, below we'll generate a covariance matrix for a model with simultaneous autoregressive errors at an arbitrary $\\lambda = .25$ level of spatial autoregression, assuming our unstructured variance is $1$. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"W = ps.weights.Queen.from_shapefile(ps.examples.get_path('NAT.shp'))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"W.transform = 'r'\n",
"Wm = W.sparse.toarray()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"precision = (np.eye(W.n) - .25*Wm).T.dot(np.eye(W.n) - .25*Wm)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While the precision $P$ is easy to state, the covariance $\\Sigma$ requires $P^{-1}$, which is often both dense and large. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"covariance = np.linalg.inv(precision)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Efficient simulation from multivariate normal distributions often involves the cholesky factor of the covariance. This relies on the idea that, for a multivariate normal vector $X$:\n",
"\n",
"$$ X \\sim \\mathcal{N}(\\mu, \\Sigma)$$\n",
"\n",
"implies\n",
"\n",
"$$ X = \\mu + Lz$$\n",
"\n",
"where $\\Sigma = LL'$, the cholesky decomposition of $\\Sigma$, and $z$ is a standard normal variate. Since drawing standard normal variates is quite simple, this strategy is often used to construct correlated samples from a normal distribution. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def chol_mvn(mean, covariance, seed=111211):\n",
" L = scla.cholesky(covariance, lower=True)\n",
" np.random.seed(seed)\n",
" e = np.random.normal(size=mean.shape)\n",
" return mean + L.dot(e)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Starting from $P$, the simplest way to sample using it is to just invert it directly to get $\\Sigma$, and sample using the same cholesky strategy. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def chol_prec_naive(mean, precision):\n",
" return chol_mvn(mean, np.linalg.inv(precision))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But, is there a way we can work with the precision directly? Inverting an $N \\times N$ matrix is not desirable. \n",
"\n",
"In fact, we can work with just $P$ and its cholesky factor. First, let's simplify our goal a bit, to sample $X \\sim \\mathcal{N}(0, \\Sigma)$, and we only have $P$. This means that: \n",
"\n",
"$$\\Sigma = P^{-1} = LL'$$\n",
"\n",
"Then, \n",
"\n",
"$$ P = (LL')^{-1} = L'^{-1}L^{-1} = QQ'$$\n",
"\n",
"where $Q = L'^{-1}$, and also happens to be the cholesky decomposition of the precision. Remember, we only have $P=\\Sigma^{-1}$, so we don't actually know $L$. to keep it that way, a sample from a multivariate normal distribution with precision $P$ can be made by solving the linear system:\n",
"\n",
"$$Q'x = z$$\n",
"\n",
"and then shifting to the appropriate mean. This works to structure $X$ with covariance $\\Sigma$ without ever inverting $P$ directly, since:\n",
"\n",
"$$ Q'x = (L'^{-1})'x = z$$\n",
"$$ x = L z$$\n",
"\n",
"Which is exactly the equation used above to sample using the covariance matrix when the mean is zero. While that solve isn't free, it is often simpler than inverting $P$ or $Q$ outright. \n",
"\n",
"Practically speaking, this means you can generate random draws from a simultaneous autoregressive model by dealing only with its precision matrix:\n",
"\n",
"$$ (I - \\lambda \\mathbf{W})'(I - \\lambda \\mathbf{W}) \\sigma^{-2}$$\n",
"\n",
"without having to invert it."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def chol_prec_smart(mean, precision, seed=111211):\n",
" Q = scla.cholesky(precision, lower=True)\n",
" np.random.seed(seed)\n",
" e = np.random.normal(size=mean.shape)\n",
" return mean + np.linalg.solve(Q.T, e)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"mean = np.zeros((W.n,1))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loop, best of 3: 1.4 s per loop\n"
]
}
],
"source": [
"%timeit np.linalg.inv(precision)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loop, best of 3: 281 ms per loop\n"
]
}
],
"source": [
"%timeit chol_mvn(mean, covariance)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, in total, if you have the precision and need to sample from the covariance, it'll take around 1.7 seconds. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loop, best of 3: 1.7 s per loop\n"
]
}
],
"source": [
"%timeit chol_prec_naive(mean, precision)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is confirmed in the naive version, since we're just integrating the inversion into the sampling step"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 loop, best of 3: 639 ms per loop\n"
]
}
],
"source": [
"%timeit chol_prec_smart(mean, precision)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But, if you use the sampling strategy discussed above, you get samples in just over a third of the time. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with_cov = [chol_mvn(mean, covariance, seed=i)\n",
" for i in range(100)]\n",
"with_prec = [chol_prec_smart(mean, precision, seed=i) \n",
" for i in range(100)]"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import seaborn as sns"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/ljw/anaconda3/envs/py3/lib/python3.5/site-packages/statsmodels/nonparametric/kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
" y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j\n"
]
},
{
"data": {
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4IjblLGduKMh266Mw+1zh/fakzAmXxpo1WEOKu5+/FVyOR2fCqPop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\nBEEQhIgnilZBEARBEAQh4v0/b0N/Q+F6f2sAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fe3238379b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for cov, prec in zip(with_cov, with_prec):\n",
" sns.kdeplot(cov.flatten(), color='slategrey')\n",
" sns.kdeplot(prec.flatten(), color='orangered')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [conda env:py3]",
"language": "python",
"name": "conda-env-py3-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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