{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Latent Function Inference with Pyro + QPyTorch (Low-Level Interface)\n", "\n", "## Overview\n", "\n", "In this example, we will give an overview of the low-level Pyro-QPyTorch integration.\n", "The low-level interface makes it possible to write QP models in a Pyro-style -- i.e. defining your own `model` and `guide` functions.\n", "\n", "These are the key differences between the high-level and low-level interface:\n", "\n", "**High level interface**\n", "\n", "- Base class is `qpytorch.models.PyroQEP`.\n", "- QPyTorch automatically defines the `model` and `guide` functions for Pyro.\n", "- Best used when *prediction* is the primary goal\n", "\n", "**Low level interface**\n", "\n", "- Base class is `qpytorch.models.ApproximateQEP`.\n", "- User defines the `model` and `guide` functions for Pyro.\n", "- Best used when *inference* is the primary goal" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import math\n", "import torch\n", "import pyro\n", "import tqdm\n", "import qpytorch\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example uses a QEP to infer a latent function $\\lambda(x)$, which parameterises the exponential distribution:\n", "\n", "$$y \\sim \\text{Exponential} (\\lambda),$$\n", "\n", "where:\n", "\n", "$$\\lambda = \\exp(f) \\in (0,+\\infty)$$\n", "\n", "is a QEP link function, which transforms the latent gaussian process variable:\n", "\n", "$$f \\sim QEP \\in (-\\infty,+\\infty).$$\n", "\n", "\n", "In other words, given inputs $X$ and observations $Y$ drawn from exponential distribution with $\\lambda = \\lambda(X)$, we want to find $\\lambda(X)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "<>:14: SyntaxWarning: invalid escape sequence '\\l'\n", "<>:14: SyntaxWarning: invalid escape sequence '\\l'\n", "/var/folders/4m/ffmpvs751fg60zck9593w5sc0000gn/T/ipykernel_75437/2610451266.py:14: SyntaxWarning: invalid escape sequence '\\l'\n", " lambdaf.set_ylabel('$\\lambda$')\n", "/var/folders/4m/ffmpvs751fg60zck9593w5sc0000gn/T/ipykernel_75437/2610451266.py:19: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n", " Y[i] = np.random.exponential(scale(x), 1)\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'Samples from exp. distrib.')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here we specify a 'true' latent function lambda\n", "scale = lambda x: np.sin(2 * math.pi * x) + 1 \n", "\n", "# Generate synthetic data\n", "# here we generate some synthetic samples\n", "NSamp = 100\n", "\n", "X = np.linspace(0, 1, 100) \n", "\n", "fig, (lambdaf, samples) = plt.subplots(1, 2, figsize=(10, 3))\n", "\n", "lambdaf.plot(X,scale(X))\n", "lambdaf.set_xlabel('x')\n", "lambdaf.set_ylabel('$\\lambda$')\n", "lambdaf.set_title('Latent function')\n", "\n", "Y = np.zeros_like(X)\n", "for i,x in enumerate(X):\n", " Y[i] = np.random.exponential(scale(x), 1)\n", "samples.scatter(X,Y)\n", "samples.set_xlabel('x')\n", "samples.set_ylabel('y')\n", "samples.set_title('Samples from exp. distrib.')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "train_x = torch.tensor(X).float()\n", "train_y = torch.tensor(Y).float()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the low-level Pyro/QPyTorch interface\n", "\n", "The low-level iterface should look familiar if you've written Pyro models/guides before. We'll use a `qpytorch.models.ApproximateQEP` object to model the QEP. To use the low-level interface, this object needs to define 3 functions:\n", "\n", "- `forward(x)` - which computes the prior QEP mean and covariance at the supplied times.\n", "- `guide(x)` - which defines the approximate QEP posterior.\n", "- `model(x)` - which does the following 3 things\n", "\n", " - Computes the QEP prior at `x`\n", " - Converts QEP function samples into scale function samples, using the link function defined above.\n", " - Sample from the observed distribution `p(y | f)`. (This takes the place of a qpytorch `Likelihood` that we would've used in the high-level interface)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "POWER = 2.0\n", "class PVQEPRegressionModel(qpytorch.models.ApproximateQEP):\n", " def __init__(self, num_inducing=64, name_prefix=\"mixture_qep\"):\n", " self.power = torch.tensor(POWER)\n", " self.name_prefix = name_prefix\n", " \n", " # Define all the variational stuff\n", " inducing_points = torch.linspace(0, 1, num_inducing)\n", " variational_strategy = qpytorch.variational.VariationalStrategy(\n", " self, inducing_points,\n", " qpytorch.variational.CholeskyVariationalDistribution(num_inducing_points=num_inducing, power=self.power)\n", " )\n", " \n", " # Standard initializtation\n", " super().__init__(variational_strategy)\n", " \n", " # Mean, covar, likelihood\n", " self.mean_module = qpytorch.means.ConstantMean()\n", " self.covar_module = qpytorch.kernels.ScaleKernel(qpytorch.kernels.RBFKernel())\n", "\n", " def forward(self, x):\n", " mean = self.mean_module(x)\n", " covar = self.covar_module(x)\n", " return qpytorch.distributions.MultivariateQExponential(mean, covar, power=self.power)\n", " \n", " def guide(self, x, y):\n", " # Get q(f) - variational (guide) distribution of latent function\n", " function_dist = self.pyro_guide(x)\n", "\n", " # Use a plate here to mark conditional independencies\n", " with pyro.plate(self.name_prefix + \".data_plate\", dim=-1):\n", " # Sample from latent function distribution\n", " pyro.sample(self.name_prefix + \".f(x)\", function_dist)\n", " \n", " def model(self, x, y):\n", " pyro.module(self.name_prefix + \".qep\", self)\n", " \n", " # Get p(f) - prior distribution of latent function\n", " function_dist = self.pyro_model(x)\n", " \n", " # Use a plate here to mark conditional independencies\n", " with pyro.plate(self.name_prefix + \".data_plate\", dim=-1):\n", " # Sample from latent function distribution\n", " function_samples = pyro.sample(self.name_prefix + \".f(x)\", function_dist)\n", " \n", " # Use the link function to convert QEP samples into scale samples\n", " scale_samples = function_samples.exp()\n", "\n", " # Sample from observed distribution\n", " return pyro.sample(\n", " self.name_prefix + \".y\",\n", " pyro.distributions.Exponential(scale_samples.reciprocal()), # rate = 1 / scale\n", " obs=y\n", " )" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "model = PVQEPRegressionModel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Performing inference with Pyro\n", "\n", "Unlike all the other examples in this library, `PyroQEP` models use Pyro's inference and optimization classes (rather than the classes provided by PyTorch).\n", "\n", "If you are unfamiliar with Pyro's inference tools, we recommend checking out the [Pyro SVI tutorial](http://pyro.ai/examples/svi_part_i.html)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "18dae2ce8e03477bbba9b6b7ef253fef", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/200 [00:00" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# visualize the result\n", "fig, (func, samp) = plt.subplots(1, 2, figsize=(12, 3))\n", "line, = func.plot(test_x, mean.detach().cpu().numpy(), label='GP prediction')\n", "func.fill_between(\n", " test_x, lower.detach().cpu().numpy(),\n", " upper.detach().cpu().numpy(), color=line.get_color(), alpha=0.5\n", ")\n", "\n", "func.plot(test_x, scale(test_x), label='True latent function')\n", "func.legend()\n", "\n", "# sample from p(y|D,x) = \\int p(y|f) p(f|D,x) df (doubly stochastic)\n", "samp.scatter(train_x, train_y, alpha = 0.5, label='True train data')\n", "samp.scatter(train_x, y_sim.cpu().detach().numpy(), alpha=0.5, label='Sample from the model')\n", "samp.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Next steps\n", "\n", "This example probably could've also been done (slightly easier) using the high-level Pyro integration, or using QPyTorch's native SVQEP implementation. The low-level interface really comes in handy when a gpytorch Likelihood is difficult to define. For an example of this, see the [next example](./Cox_Process_Example.ipynb) which uses the low-level interface to infer the intensity function of a Cox process." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 4 }