{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import gpflow\n",
"import numpy as np\n",
"import matplotlib\n",
"%matplotlib inline\n",
"matplotlib.rcParams['figure.figsize'] = (12, 6)\n",
"plt = matplotlib.pyplot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A Simple Demonstration of Coregionalization\n",
"--\n",
"\n",
"*James Hensman 2016, 2017*\n",
"\n",
"In this notebook I'll demonstrate how to fit a simple model with two correlated outputs. For a little added complexity, the noise on the observations will have a heavy tail, so that there are outliers in the data. \n",
"\n",
"In GPflow, multiple output models are specified by adding an extra _input_ dimension. We'll augment the training data X with an extra column contining 1 or 0 to indicate which output an observation is associated with. This also works at prediction time: you have to specify two columns containing the location and the output of the prediction. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f681abd7828>]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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7us/p4QMn097a/fWly3r4wEmFa52ni1Z0QGlwfx87WpuTpVR7OtvH/a66JVgr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\n73v4n3VFdSjwk8iAUuW1pKq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"text/plain": [
"<matplotlib.figure.Figure at 0x7f681abd7860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# make a dataset with two outputs, correlated, heavy-tail noise. One has more noise than the other.\n",
"X1 = np.random.rand(100, 1)\n",
"X2 = np.random.rand(50, 1) * 0.5\n",
"Y1 = np.sin(6*X1) + np.random.standard_t(3, X1.shape)*0.03\n",
"Y2 = np.sin(6*X2+ 0.7) + np.random.standard_t(3, X2.shape)*0.1\n",
"\n",
"plt.plot(X1, Y1, 'x', mew=2)\n",
"plt.plot(X2, Y2, 'x', mew=2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To build a GP with correlated multiple outputs, we'll use a kernel of the form\n",
"\n",
"$$\\textrm{cov}(f_i(x), f_j(y)) = k_1(x, y) \\times B[i, j]$$\n",
"\n",
"The covariance of the i'th function at x and the j'th function at y is a kernel applied at x and y, times the i, j'th entry of a positive definite matrix B. This is known as the _intrinsic model of coregionalization_.\n",
"\n",
"To make sure that B is positive-definite, we parameterize is as\n",
"\n",
"$$B = W W^\\top + \\textrm{diag}(\\kappa)$$. These parameters will be formed by the Coregion kernel below."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# a Coregionalization kernel. The base kernel is Matern, and acts on the first ([0]) data dimension.\n",
"# the 'Coregion' kernel indexes the outputs, and actos on the second ([1]) data dimension\n",
"k1 = gpflow.kernels.Matern32(1, active_dims=[0])\n",
"coreg = gpflow.kernels.Coregion(1, output_dim=2, rank=1, active_dims=[1])\n",
"kern = k1 * coreg\n",
"\n",
"# build a variational model. This likelihood switches between Student-T noise with different variances:\n",
"lik = gpflow.likelihoods.SwitchedLikelihood([gpflow.likelihoods.StudentT(), gpflow.likelihoods.StudentT()])\n",
"\n",
"# Augment the time data with ones or zeros to indicate the required output dimension\n",
"X_augmented = np.vstack((np.hstack((X1, np.zeros_like(X1))), np.hstack((X2, np.ones_like(X2)))))\n",
"\n",
"# Augment the Y data to indicate which likeloihood we should use\n",
"Y_augmented = np.vstack((np.hstack((Y1, np.zeros_like(X1))), np.hstack((Y2, np.ones_like(X2)))))\n",
"\n",
"# now buld the GP model as normal\n",
"m = gpflow.models.VGP(X_augmented, Y_augmented, kern=kern, likelihood=lik, num_latent=1)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/james/miniconda3/envs/pio_gpu/lib/python3.5/site-packages/tensorflow/python/ops/gradients_impl.py:96: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
" \"Converting sparse IndexedSlices to a dense Tensor of unknown shape. \"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"INFO:tensorflow:Optimization terminated with:\n",
" Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
" Objective function value: -136.088330\n",
" Number of iterations: 839\n",
" Number of functions evaluations: 910\n"
]
}
],
"source": [
"# fit the covariance function parameters\n",
"gpflow.train.ScipyOptimizer().minimize(m)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's it: the model has trained. Let's plot the model fit to see what's happened."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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PgjjnAQmiJ38h2dBTxPacUrbnODmvRzKGYXDT9BUYhsGarCIKyj113uZay1xW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"text/plain": [
"<matplotlib.figure.Figure at 0x7f6818113cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_gp(x, mu, var, color='k'):\n",
" plt.plot(x, mu, color=color, lw=2)\n",
" plt.plot(x, mu + 2*np.sqrt(var), '--', color=color)\n",
" plt.plot(x, mu - 2*np.sqrt(var), '--', color=color)\n",
"\n",
"def plot(m):\n",
" xtest = np.linspace(0, 1, 100)[:,None]\n",
" line, = plt.plot(X1, Y1, 'x', mew=2)\n",
" mu, var = m.predict_f(np.hstack((xtest, np.zeros_like(xtest))))\n",
" plot_gp(xtest, mu, var, line.get_color())\n",
"\n",
" line, = plt.plot(X2, Y2, 'x', mew=2)\n",
" mu, var = m.predict_f(np.hstack((xtest, np.ones_like(xtest))))\n",
" plot_gp(xtest, mu, var, line.get_color())\n",
"\n",
"plot(m)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the plots we see:\n",
"\n",
" - The first function (blue) has low posterior variance everywhere because there are so many observations, and the noise variance is small. \n",
" - The second function (orange) has higher posterior variance near the data, because the data are more noisy, and very high posterior variance where there are no observations (x > 0.5). \n",
" - The model has done a reasonable job of estimating the noise variance and lengthscales.\n",
" - The model has done a poor job of estimating the correlation between functions: at x>0.5, the upturn of the blue function is not reflected in the orange function.\n",
" \n",
"To see why this is the case, we'll inspect the parameters of the kernel:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>class</th>\n",
" <th>prior</th>\n",
" <th>transform</th>\n",
" <th>trainable</th>\n",
" <th>shape</th>\n",
" <th>fixed_shape</th>\n",
" <th>value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>VGP/kern/matern32/variance</th>\n",
" <td>Parameter</td>\n",
" <td>None</td>\n",
" <td>+ve</td>\n",
" <td>True</td>\n",
" <td>()</td>\n",
" <td>True</td>\n",
" <td>1.1298311967013703</td>\n",
" </tr>\n",
" <tr>\n",
" <th>VGP/kern/matern32/lengthscales</th>\n",
" <td>Parameter</td>\n",
" <td>None</td>\n",
" <td>+ve</td>\n",
" <td>True</td>\n",
" <td>()</td>\n",
" <td>True</td>\n",
" <td>0.5756759653605009</td>\n",
" </tr>\n",
" <tr>\n",
" <th>VGP/kern/coregion/W</th>\n",
" <td>Parameter</td>\n",
" <td>None</td>\n",
" <td>(none)</td>\n",
" <td>True</td>\n",
" <td>(2, 1)</td>\n",
" <td>True</td>\n",
" <td>[[0.0], [0.0]]</td>\n",
" </tr>\n",
" <tr>\n",
" <th>VGP/kern/coregion/kappa</th>\n",
" <td>Parameter</td>\n",
" <td>None</td>\n",
" <td>+ve</td>\n",
" <td>True</td>\n",
" <td>(2,)</td>\n",
" <td>True</td>\n",
" <td>[0.763638779944, 1.28142494162]</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" class prior transform trainable shape \\\n",
"VGP/kern/matern32/variance Parameter None +ve True () \n",
"VGP/kern/matern32/lengthscales Parameter None +ve True () \n",
"VGP/kern/coregion/W Parameter None (none) True (2, 1) \n",
"VGP/kern/coregion/kappa Parameter None +ve True (2,) \n",
"\n",
" fixed_shape value \n",
"VGP/kern/matern32/variance True 1.1298311967013703 \n",
"VGP/kern/matern32/lengthscales True 0.5756759653605009 \n",
"VGP/kern/coregion/W True [[0.0], [0.0]] \n",
"VGP/kern/coregion/kappa True [0.763638779944, 1.28142494162] "
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m.kern.as_pandas_table()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the W matrix has entries of zero. This is a caused by a saddle point in the objective: re-initializing the matrix to random entries should give a better result."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"m.kern.coregion.W = np.random.randn(2, 1)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/james/miniconda3/envs/pio_gpu/lib/python3.5/site-packages/tensorflow/python/ops/gradients_impl.py:96: UserWarning: Converting sparse IndexedSlices to a dense Tensor of unknown shape. This may consume a large amount of memory.\n",
" \"Converting sparse IndexedSlices to a dense Tensor of unknown shape. \"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"INFO:tensorflow:Optimization terminated with:\n",
" Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n",
" Objective function value: -139.010940\n",
" Number of iterations: 1001\n",
" Number of functions evaluations: 1082\n"
]
}
],
"source": [
"gpflow.train.ScipyOptimizer().minimize(m)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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V0I0brEpfEq+E0FZV11/3Nix8XL2g8Xqq+jhDVau9iPZw+8KqkFuWD7u+VRs8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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f681b688e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(m)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot is much more satisfying. The model now recognises the correlation between the two functions and is able to suggest (with uncertainty) that as x > 0.5 the orange curve should follow the blue curve (which we know to be the truth from the data generating procedure above). "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"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": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}