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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Gaussian Process"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"\n",
"[Gaussian process](https://en.wikipedia.org/wiki/Gaussian_process) has been used in supervised, unsupervised, and even reinforcement learning problems. It has a beautiful mathematical theory (for an overview of the subject, see [1]). In particular, its distribution can be considered as a distribution over functions. Many machine learning models give specific predictions, not how uncertainty the predictions are. Gaussian process particularly helps us solve such problems. Currently, there is a simple implementation of Gaussian process regression model at `pyro.contrib.gp` module. We will try to use it in this tutorial. The model is defined as\n",
"$$f \\sim \\mathcal{GP}\\left(0, \\mathbf{K}_f(x, x')\\right)$$\n",
"and\n",
"$$y = f + \\epsilon,\\quad \\epsilon \\sim \\mathcal{N}\\left(0, \\beta^{-1}\\mathbf{I}\\right).$$\n",
"\n",
"We will use [radial basis function kernel](https://en.wikipedia.org/wiki/Radial_basis_function_kernel) (RBF kernel) as the kernel of Gaussian process:\n",
"$$ k(x,x') = \\sigma^2 \\exp\\left(-\\frac{\\|x-x'\\|^2}{2l^2}\\right),$$\n",
"where $\\sigma^2$ is variance and $l$ is lengthscale of the RBF kernel."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Prepare"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we need import necessary modules."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import torch\n",
"\n",
"import pyro\n",
"from pyro.contrib.gp.kernels import RBF\n",
"from pyro.contrib.gp.models import GPRegression, SparseGPRegression, SparseVariationalGP\n",
"from pyro.contrib.gp.likelihoods import Gaussian\n",
"import pyro.distributions as dist\n",
"from pyro.infer import SVI\n",
"from pyro.optim import Adam\n",
"pyro.set_rng_seed(0)\n",
"\n",
"import os\n",
"smoke_test = True # Flaky MVN constraint checking issue - see:https://github.com/uber/pyro/issues/953 \n",
"pyro.enable_validation(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is better to make visualizations for Gaussian process' implementation. So we create a convenient function to plot."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"MEAN, COV = 0, 0"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def plot(model=None, n_sample=0, variational=False):\n",
" global MEAN\n",
" global COV\n",
" plt.figure(figsize=(12, 6))\n",
" plt.plot(X.numpy(), y.numpy(), 'kx') # plot data\n",
" if model is not None:\n",
" Xnew = torch.linspace(-0.5, 5.5, 100) # new input\n",
" with torch.no_grad():\n",
" # mean and variance of output's Gaussian distribution\n",
" if variational:\n",
" mean, cov = model(Xnew, full_cov=True)\n",
" noise = model.likelihood.get_param(\"variance\")\n",
" cov = cov + noise.expand(mean.size(0)).diag()\n",
" else:\n",
" mean, cov = model(Xnew, full_cov=True, noiseless=False)\n",
" sd = cov.diag().sqrt() # standard derivation at each input\n",
" plt.plot(Xnew.numpy(), mean.numpy(), 'r', lw=2) # plot the mean\n",
" plt.fill_between(Xnew.numpy(), mean.numpy() - 2*sd.numpy(), mean.numpy() + 2*sd.numpy(),\n",
" color='C0', alpha=0.3) # fill the interval (mean-2.sd, mean+2.sd)\n",
" if n_sample > 0: # plot the samples\n",
" n_sample = n_sample if not smoke_test else 1\n",
" MEAN = mean\n",
" COV = cov\n",
" samples = dist.MultivariateNormal(mean, covariance_matrix=cov) \\\n",
" .sample(sample_shape=torch.Size([n_sample]))\n",
" plt.plot(Xnew.numpy(), samples.numpy().T, 'C0', lw=2, alpha=0.4)\n",
" plt.xlim(-0.5, 5.5)\n",
" plt.ylim(-3, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data consists of $20$ points sampled from\n",
"$$ y = 0.5\\sin(3x) + \\epsilon, \\quad \\epsilon \\sim \\mathcal{N}(0, 0.5).$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# source: http://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_noisy.html\n",
"N = 20\n",
"X = dist.Uniform(torch.zeros(N), torch.ones(N)*5).sample()\n",
"y = 0.5 * torch.sin(3*X) + dist.Normal(torch.zeros(N), torch.ones(N)*0.5).sample()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf207f2cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define model"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"kernel = RBF(input_dim=1, variance=torch.tensor(10.), lengthscale=torch.tensor(10.))\n",
"gpr = GPRegression(X, y, kernel, noise=torch.tensor(1.))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf505297f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(gpr, n_sample=5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inference"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"optim = Adam({\"lr\": 0.001})\n",
"svi = SVI(gpr.model, gpr.guide, optim, loss=\"ELBO\")\n",
"losses = []\n",
"num_steps = 1000 if not smoke_test else 2\n",
"for i in range(num_steps):\n",
" losses.append(svi.step())"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fdf1c224a58>]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1d331f28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# look at the loss\n",
"plt.plot(losses[-500:])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1c1ba0b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# see the inference result; because we initiated the `lengthscale=10`,\n",
"# which is so large comparing to the data range (0, 5), it is hard to make the model learn\n",
"plot(gpr, n_sample=5)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"GPR$$$noise \n",
"1.00000e-03 *\n",
" -2.0010\n",
"[torch.FloatTensor of size ()]\n",
"\n",
"RBF$$$variance \n",
" 2.3006\n",
"[torch.FloatTensor of size ()]\n",
"\n",
"RBF$$$lengthscale \n",
" 2.3046\n",
"[torch.FloatTensor of size ()]\n",
"\n"
]
}
],
"source": [
"# observe the parameters\n",
"for param, value in pyro.get_param_store().named_parameters():\n",
" print(param, value)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In some cases, the inference will make `variance` or `lengthscale` become negative numbers. To solve that problem, we have to force these parameters to be positive. Thankfully, from version `0.4`, Pytorch supports a very generic way to put constraints to parameters (see [docs](http://pytorch.org/docs/master/distributions.html#module-torch.distributions.constraints)). Most Gaussian Process parameters in Pyro use constraints by default. To see the constrained value, we will use `get_param(...)` method."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 9.9800\n",
"[torch.FloatTensor of size ()]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gpr.kernel.get_param(\"variance\")"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 10.0200\n",
"[torch.FloatTensor of size ()]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gpr.kernel.get_param(\"lengthscale\")"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 0.9980\n",
"[torch.FloatTensor of size ()]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gpr.get_param(\"noise\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With RBF kernel, the larger lengthscale, we get the smoother samples (this can be deduced from the formula of $K$: the larger lengthscale, the more likeliness that $K$ will approach $1$, which in turn reflects the values of two points $x$ and $x'$ are similar). Variance parameter controls the derivation from the mean (besides the noise). Comparing the initial plot with the last plot, we can see that the second plot is less variant."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fit the model using MAP"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We need to define the priors for parameters. Beside it is more reliable approach, it will also help dealing with the constraints of parameters."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1d31a898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gpr.kernel.set_prior(\"lengthscale\", dist.LogNormal(torch.zeros(1), torch.ones(1)))\n",
"gpr.kernel.set_prior(\"variance\", dist.LogNormal(torch.zeros(1), torch.ones(1)))\n",
"# we fix the noise to 0.01\n",
"gpr.fix_param(\"noise\", torch.ones(1) * 0.01)\n",
"# we need to reset param store\n",
"pyro.clear_param_store()\n",
"optim = Adam({\"lr\": 0.001})\n",
"svi = SVI(gpr.model, gpr.guide, optim, loss=\"ELBO\")\n",
"losses = []\n",
"num_steps = 1000 if not smoke_test else 2\n",
"for i in range(num_steps):\n",
" losses.append(svi.step())\n",
"plot(gpr, n_sample=5)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1d37f5f8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(losses[-500:]);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that the model might still learn. We will run more iterations. However, it might cause \"overfitting\"."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1c1d50f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"num_steps = 4000 if not smoke_test else 2\n",
"for i in range(num_steps):\n",
" svi.step()\n",
"plot(gpr, n_sample=5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, look at the parameters, we can see that the names of parameters have been changed. The reason is that: when we put priors to parameters of our kernel, they become random variables (not `torch.nn.Parameter` anymore). Inference will learn the parameters with trailing `_MAP` at the end."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RBF$$$lengthscale_MAP \n",
" 1.6447\n",
"[torch.FloatTensor of size (1,)]\n",
"\n",
"RBF$$$variance_MAP \n",
" 1.6527\n",
"[torch.FloatTensor of size (1,)]\n",
"\n"
]
}
],
"source": [
"for param, value in pyro.get_param_store().named_parameters():\n",
" print(param, value)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sparse Approximation\n",
"\n",
"In case the number of data is large, using the Gaussian Process Regression model is computationally ineffective (see Section 2.2 of [1]). So we will use `SparseGPRegression` model, which helps reduce time consuming significantly.\n",
"\n",
"First, we generate more data."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1c1417b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 1000\n",
"X = dist.Uniform(torch.zeros(N), torch.ones(N)*5).sample()\n",
"y = 0.5 * torch.sin(3*X) + dist.Normal(torch.zeros(N), torch.ones(N)*0.5).sample()\n",
"plot()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the sparse version is quite similar to the original version. We just need to add an extra parameter $Xu$, which plays the role of inducing points."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"# initiate the position of inducing inputs\n",
"Xu = torch.tensor([0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5])\n",
"\n",
"# initiate the kernel and model\n",
"kernel = RBF(input_dim=1)\n",
"sgpr = SparseGPRegression(X, y, kernel, Xu=Xu)\n",
"sgpr.fix_param(\"noise\", torch.ones(1) * 0.01)\n",
"\n",
"# the learning steps are similar to learning GPRegression\n",
"pyro.clear_param_store()\n",
"optim = Adam({\"lr\": 0.001})\n",
"svi = SVI(sgpr.model, sgpr.guide, optim, loss=\"ELBO\")\n",
"losses = []\n",
"num_steps = 1000 if not smoke_test else 2\n",
"for i in range(num_steps):\n",
" losses.append(svi.step())"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RBF$$$variance \n",
"1.00000e-03 *\n",
" -1.9991\n",
"[torch.FloatTensor of size ()]\n",
"\n",
"RBF$$$lengthscale \n",
"1.00000e-03 *\n",
" 1.9993\n",
"[torch.FloatTensor of size ()]\n",
"\n",
"SGPR$$$Xu \n",
" 0.4980\n",
" 0.9980\n",
" 1.4980\n",
" 1.9980\n",
" 2.4980\n",
" 3.0020\n",
" 3.5020\n",
" 4.0020\n",
" 4.5020\n",
"[torch.FloatTensor of size (9,)]\n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1c170c18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for param, value in pyro.get_param_store().named_parameters():\n",
" print(param, value)\n",
"plot(sgpr, n_sample=5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that the model learns this data pretty well. There are three versions, which are currently implemented in Pyro, for sparse approximation: \"DTC\" (Deterministic Training\n",
"Conditional), \"FITC\" (Partially Independent Training Conditional), and \"VFE\" (Variational Free Energy). By default, `SparseGPRegression` will use \"VFE\" as the main inference method. We can use other methods by changing the `approx` parameter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sparse Variational Gaussian Process"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The noise in regression model plays the role of Gaussian likelihood. To deal with general likelihood (for example, we use Bernoulli likelihood for classification problems), we will use variational inference. In this section, we will give an example on how to use `SparseVariationGP` module."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "The parameter precision_matrix has invalid values",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-22-446a12bec6bd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mlosses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msvi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 21\u001b[0;31m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msvgp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_sample\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvariational\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m<ipython-input-3-52833dee312f>\u001b[0m in \u001b[0;36mplot\u001b[0;34m(model, n_sample, variational)\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0mMEAN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0mCOV\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcov\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m \u001b[0msamples\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMultivariateNormal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcovariance_matrix\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcov\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msample_shape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn_sample\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 25\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mXnew\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msamples\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'C0'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlw\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 26\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/pytorch/torch/distributions/multivariate_normal.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, loc, covariance_matrix, precision_matrix, scale_tril, validate_args)\u001b[0m\n\u001b[1;32m 145\u001b[0m \u001b[0mbatch_shape\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_batch_shape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprecision_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 146\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mloc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 147\u001b[0;31m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mMultivariateNormal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch_shape\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mevent_shape\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalidate_args\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvalidate_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 148\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 149\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mlazy_property\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/pytorch/torch/distributions/distribution.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, batch_shape, event_shape, validate_args)\u001b[0m\n\u001b[1;32m 31\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mconstraints\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_dependent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mconstraint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 32\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mconstraint\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparam\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 33\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The parameter {} has invalid values\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparam\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 34\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 35\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: The parameter precision_matrix has invalid values"
]
},
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fdf1c1e37f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# initiate the position of inducing inputs\n",
"# here, we just use 9 inducing points\n",
"# we recommend to increase the number of inducing points for better inference\n",
"Xu = torch.tensor([0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5])\n",
"\n",
"# initiate the kernel, likelihood, and model\n",
"kernel = RBF(input_dim=1)\n",
"likelihood = Gaussian()\n",
"svgp = SparseVariationalGP(X, y, kernel, Xu=Xu, likelihood=likelihood, jitter=1e-5)\n",
"# fix the noise to 0.01\n",
"svgp.likelihood.fix_param(\"variance\", torch.ones(1) * 0.01)\n",
"\n",
"pyro.clear_param_store()\n",
"optim = Adam({\"lr\": 0.01})\n",
"svi = SVI(svgp.model, svgp.guide, optim, loss=\"ELBO\")\n",
"losses = []\n",
"num_steps = 1000 if not smoke_test else 2\n",
"for i in range(num_steps):\n",
" losses.append(svi.step())\n",
" \n",
"plot(svgp, n_sample=5, variational=True)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"1.00000e-03 *\n",
" 8.9618\n",
" 9.7060\n",
" 9.8814\n",
" 9.9117\n",
" 9.9400\n",
" 9.9562\n",
" 9.9692\n",
" 9.9718\n",
" 9.9925\n",
" 9.9930\n",
"[torch.FloatTensor of size (10,)]"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"torch.symeig(COV, eigenvectors=False)[0][:10]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" -0.1942\n",
" 0.0046\n",
" 0.0394\n",
" 0.0770\n",
" 0.1185\n",
" 0.1196\n",
" 0.1215\n",
" 0.1240\n",
" 0.1272\n",
" 27.3152\n",
"[torch.FloatTensor of size (10,)]"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"PRE = COV.inverse()\n",
"torch.symeig(PRE, eigenvectors=False)[0][:10]"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 1.0151e-04\n",
" 6.4418e-04\n",
" 5.0923e-02\n",
" 8.2185e-02\n",
" 1.1836e-01\n",
" 1.1987e-01\n",
" 1.2166e-01\n",
" 1.2196e-01\n",
" 1.2625e-01\n",
" 2.7373e+01\n",
"[torch.FloatTensor of size (10,)]"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tril = COV.potrf(upper=False)\n",
"inv_tril = tril.inverse()\n",
"pre = inv_tril.t().matmul(inv_tril)\n",
"torch.symeig(pre, eigenvectors=False)[0][:10]"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[10475.6748046875,\n",
" 1592.6982421875,\n",
" 19.64120864868164,\n",
" 12.166779518127441,\n",
" 8.448244094848633,\n",
" 8.33909797668457,\n",
" 8.220293045043945,\n",
" 8.201311111450195,\n",
" 7.919301986694336,\n",
" 0.03658361732959747]"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Observe last 10 eigenvalues of COV, their inverses should be first 10\n",
"# eigenvalues of PRE. We can see that they agree with pre, not PRE.\n",
"torch.symeig(COV, eigenvectors=False)[0][-10:].tolist()[::-1]"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 62.9640 -28.3960 -21.6028 -15.1882 -10.1265\n",
"-28.4817 76.1766 -19.0169 -14.3258 -10.9178\n",
"-21.6333 -19.0190 83.3549 -13.9009 -10.7673\n",
"-15.0291 -14.4609 -13.9514 86.9465 -11.6730\n",
" -9.9698 -10.9113 -10.8822 -11.7358 89.1492\n",
"[torch.FloatTensor of size (5,5)]"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# test if PRE and pre agree\n",
"PRE[:5, :5]"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 63.8152 -28.9406 -21.6453 -15.4043 -10.2576\n",
"-28.9406 76.4909 -19.0414 -14.1877 -10.6904\n",
"-21.6453 -19.0414 83.3674 -13.9562 -10.9693\n",
"-15.4043 -14.1877 -13.9562 87.0176 -11.4562\n",
"-10.2576 -10.6904 -10.9693 -11.4562 89.1598\n",
"[torch.FloatTensor of size (5,5)]"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pre[:5, :5]"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"467 µs ± 4.91 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"# not related: current PositiveDefinite constraint's speed can be improved\n",
"# with flag eigenvectors=False\n",
"# https://github.com/pytorch/pytorch/blob/master/torch/distributions/constraints.py#L209\n",
"%timeit torch.symeig(COV, eigenvectors=True)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"141 µs ± 1.6 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
]
}
],
"source": [
"%timeit torch.symeig(COV, eigenvectors=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that the model predicts well the target $y = 0.5\\sin(3x)$ despite of noisy data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Some remarks\n",
"\n",
"+ In Gaussian Process, we usually have to solve the equation $Kx = y$, where $K$ is a positive covariance matrix. An efficiency and numerically-stable method to obtain the solution is to use [Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition). First, we decompose $K = LL^T$, where $L$ is a lower triangular matrix. Then, we solve in turn $Lz = y$ and $L^Tx = z$.\n",
"\n",
"+ The Cholesky decomposition `torch.potrf` usually throws the `RuntimeError`: \"Lapack Error in potrf : the leading minor of order {} is not positive definite\". The error tells itself: while decomposing, some eigenvalues of covariance matrix are approximately $0$ (and turn out to be negative). To deal with such error, one way is to cast our model's parameters to `DoubleTensor` (by calling `.double` from our model). Another way is to introduce the notion `jitter`. We will add a small positive term (named `jitter`) into the diagonal part of $K$ before decomposing the covariance matrix. Due to the `noise` component, all eigenvalues will be positive. Adding `jitter` is necessary when using Gaussian Process in variational framework. By default, in each model, we set `jitter=1e-6`. When getting that error, we recommend increasing `jitter` to a higher value."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reference\n",
"\n",
"[1] `Deep Gaussian processes and variational propagation of uncertainty`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
"Andreas Damianou\n",
"\n",
"[2] `A unifying framework for sparse Gaussian process approximation using power expectation propagation`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
"Thang D. Bui, Josiah Yan, and Richard E. Turner\n",
"\n",
"[3] `Scalable variational Gaussian process classification`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
"James Hensman, Alexander G. de G. Matthews, and Zoubin Ghahramani\n",
"\n",
"[4] `Gaussian Processes for Machine Learning`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
"Carl E. Rasmussen, and Christopher K. I. Williams\n",
"\n",
"[5] `A Unifying View of Sparse Approximate Gaussian Process Regression`,<br />&nbsp;&nbsp;&nbsp;&nbsp;\n",
"Joaquin Quinonero-Candela, and Carl E. Rasmussen"
]
}
],
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