{ "cells": [ { "cell_type": "markdown", "id": "f3da35c6-12ae-40e9-b663-2fa3ad1c2bb5", "metadata": {}, "source": [ "# Introduction to Q-Exponential Process (QEP)\n", "\n", "In this notebook, we will introduce the q-exponential process (QEP) as a novel stochastic process which imposes regularization (through a parameter `q>0`) on function spaces and includes Gaussian process as a special case (with `q=2`). This is mainly due to [Li, Shuyi, Michael O’Connor, Shiwei Lan (2023)](https://papers.nips.cc/paper_files/paper/2023/hash/e6bfdd58f1326ff821a1b92743963bdf-Abstract-Conference.html).\n", "\n", "In particular, we will explain:\n", "\n", "- What is q-exponential process?\n", "- Why do we need q-exponential process?\n", "- How do we fit QEP models in QPyTorch?" ] }, { "cell_type": "markdown", "id": "4cf68eba-157a-4b9c-957c-bdc6236f8fc7", "metadata": {}, "source": [ "## What is Q-Exponential Process (QEP)?\n", "\n", "Q-Exponential process (QEP), denoted as $\\mathcal{Q}(\\mu, \\mathcal C)$, is a stochastic process parameterized by three parameters:\n", "\n", "- mean function $\\mu$;\n", "- covariance kernel $\\mathcal C$;\n", "- power parameter $q>0$.\n", "\n", "It is defined as a collection of random variables whose any subsect follows a (scaled) multivariate q-exponential distribution. Given any finite points $x_1,\\cdots, x_d$, a function $u(x)\\sim \\mathcal{Q}(\\mu, \\mathcal C)$ from QEP evaluated on these points, ${\\bf u}=(u(x_1),\\cdots, u(x_d))$ follows $d$-dimensional (scaled) q-exponential distribution, denoted as ${\\bf u}\\sim \\mathcal{Q}_d(\\boldsymbol{\\mu}, {\\bf C})$, which has the following probability density:\n", "\n", "\\begin{equation*}\n", "p({\\bf u}|\\boldsymbol{\\mu}, {\\bf C}, q) = \\frac{q}{2} (2\\pi)^{-\\frac{d}{2}} |{\\bf C}|^{-\\frac{1}{2}} r^{(\\frac{q}{2}-1)\\frac{d}{2}} \\exp\\left\\{-\\frac{r^\\frac{q}{2}}{2}\\right\\}, \\quad\n", "r({\\bf u}) = ({\\bf u}-\\boldsymbol{\\mu})^\\top {\\bf C}^{-1} ({\\bf u}-\\boldsymbol{\\mu})\n", "\\end{equation*}\n", "\n", "In practice, we define QEP $u(\\cdot)$ with scaled ${\\bf u}$ by a factor, ${\\bf u}^*=d^{\\frac{1}{2}-\\frac{1}{q}}{\\bf u}$, which has asymptotically finite covariance. **When q=2, it reduces to Gaussian**.\n", "\n", "In QPyTorch, we have `qpytorch.distributions.QExponential` and `qpytorch.distributions.MultivaraiteQExponential` for univariate and multivariate q-exponential random variables resepectively. We can plot their densities for different $q$s. " ] }, { "cell_type": "code", "execution_count": 1, "id": "bd43935d-fc93-451c-96e1-b08bf468a868", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# import pacakges\n", "import numpy as np\n", "import torch\n", "import qpytorch\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "fig, ax = plt.subplots(1, 4, figsize=(12, 3))\n", "\n", "n = 100\n", "x = torch.linspace(-3,3, n)\n", "qep = qpytorch.distributions.QExponential(torch.tensor(0), torch.tensor(1), torch.tensor(1.0))\n", "for q in [0.5, 1, 1.5, 2.0]:\n", " qep.power = torch.tensor(q)\n", " ax[0].plot(x, qep.log_prob(x))\n", "ax[0].legend(['q='+str(i) for i in [0.5, 1, 1.5, 2.0]], frameon=False)\n", "ax[0].set_title('log-densities')\n", "\n", "nx = ny = 50\n", "x = torch.linspace(-3,3, nx)\n", "y = torch.linspace(-3,3, ny)\n", "\n", "X, Y = torch.meshgrid(x, y, indexing='ij')\n", "qep = qpytorch.distributions.MultivariateQExponential(torch.zeros(2), torch.eye(2), torch.tensor(1.0))\n", "for i, q in enumerate([0.5, 1, 2.0]):\n", " qep.power = torch.tensor(q)\n", " Z = qep.log_prob(torch.stack([X.flatten(), Y.flatten()], dim=1)).reshape(nx, ny)\n", " contf = ax[i+1].contourf(X, Y, Z, levels=10)\n", " ax[i+1].contour(contf, levels=contf.levels[::2], colors='r')\n", " ax[i+1].set_title('q='+str(q))\n", " fig.colorbar(contf, ax=ax[i+1])\n", "\n", "plt.subplots_adjust(wspace=0.3)\n", "\n", "None" ] }, { "cell_type": "markdown", "id": "fc0b90a5-7e4e-49ef-ab65-89a2ea30afb4", "metadata": {}, "source": [ "When $02$, the density is log-concave in $r$ and light-tailed. Negative log-density is dominated by some weighted $L_q$ norm of ${\\bf u}-\\boldsymbol{\\mu}$, i.e. $\\Vert {\\bf u}-\\boldsymbol{\\mu}\\Vert_{\\bf C}$, which serves as an $L_q$ regularization term when QEP is used as a prior in Bayesian modeling." ] }, { "cell_type": "markdown", "id": "c065b27e-fecb-4c76-b61e-673a2e14d3d6", "metadata": {}, "source": [ "### Bayesian Modeling with Q-Exponential Process\n", "\n", "Consider the generic Bayesian regression model:\n", "\n", "\\begin{align*}\n", "y &= u(x)+\\epsilon, \\quad \\epsilon \\sim L(\\cdot;0,\\Sigma) \\\\\n", "u &\\sim \\mu_0(du)\n", "\\end{align*}\n", "\n", "where $L(\\cdot;0,\\Sigma)$ denotes some likelihood model with zero mean and covariance $\\Sigma$, and the mean function $u$ is given a QEP prior.\n", "Theorem 3.5 in Li et~al (2023) proves the following tractable posterior predictive formula.\n", "\n", "[**Posterior Prediction Theorem**]\n", "Given covariates ${\\bf x}=\\{x_i\\}_{i=1}^N$ and observations ${\\bf y}=\\{y_i\\}_{i=1}^N$ following mutlivariate q-exponential distribution, i.e., $L(\\cdot;0,\\Sigma) \\sim \\mathcal{Q}(0, \\Sigma)$, in the above model with QEP prior for the same $q>0$, we have the following posterior predictive distribution for $u(x_*)$ at (a) new point(s) $x_*$:\n", "\n", "\\begin{align*}\n", "u(x_*)|{\\bf y,{\\bf x},x_* \\sim \\mathcal{Q}(\\boldsymbol{\\mu}^*, {\\bf C}^*), \\quad\n", "\\boldsymbol{\\mu}^* = {\\bf C}^\\top_* ({\\bf C} + \\Sigma)^{-1} {\\bf y}, \\quad\n", "{\\bf C}^* = {\\bf C}_{**} - \\{\\bf C}^\\top_* ({\\bf C} + \\Sigma)^{-1} {\\bf C}_*\n", "\\end{align*}\n", "\n", "where ${\\bf C}=\\mathcal{C}({\\bf x},{\\bf x})$, ${\\bf C}_*=\\mathcal{C}({\\bf x},x_*)$, and ${\\bf C}_{**}=\\mathcal{C}(x_*,x_*)$." ] }, { "cell_type": "markdown", "id": "81cb967e-9e9d-4404-ac3e-9545e3dbf1b3", "metadata": {}, "source": [ "### Sampling\n", "\n", "When $L(\\cdot;0,\\Sigma)$ is not q-exponential, there is no conjugacy in general. We could apply Bayesian inference methods for which q-exponential random vector ${\\bf u}\\sim \\mathcal Q_d(\\boldsymbol{\\mu}, {\\bf C})$ can be sampled as follows:\n", "\n", "\\begin{equation*}\n", "{\\bf u} \\overset{d}{=} \\boldsymbol{\\mu} + R {\\bf L} S \n", "\\end{equation*}\n", "\n", "where $S\\sim \\mathrm{unif}(\\mathcal{S}^{d+1})$ uniformly distributed on the unit-sphere $\\mathcal{S}^{d+1}$, ${\\bf L}$ is the Cholesky factor of ${\\bf C}$ such that ${\\bf C}={\\bf L}{\\bf L}^\\top$, $R\\perp S$ and $R^q\\sim \\chi^2(d)$." ] }, { "cell_type": "markdown", "id": "e6412d3f-8790-4796-89e2-99f047524cd1", "metadata": {}, "source": [ "## Why Q-Exponential Process?\n", "\n", "Despite the popularity, GP tends to oversmooth modeling objects, e.g. edges in an image.\n", "When $q<2$, QEP imposes stronger regularization than GP as a prior. Numerically, QEP has advantages over GP in modeling inhomogeneous objects with abrupt changes or sharp contrast. For example, in imaging analysis, QEP is often adopted with $q=1$ as an edge-preserving prior.\n", "\n", "For example, we want to reconstruct an image of satellite from the following blurred observation.\n", "\n", "\n", "\n", "\n", "\n", "\n", "When using QEP as a prior, smaller $q$ tends to impose stronger regularization and hence yields sharper reconstruction.\n", "\n", "\n", "\n", "\n", "\n", "\n", "QEP is closed under linear combination, i.e. linear combination of q-exponential random variables is still q-exponential. Therefore, QEP can be used to model objects with derivative information as GP. Since QEP imposes stronger regularization on gradients with $q<2$, it also outperforms GP in modeling with derivatives. One can check this example of [2d modeling with derivative infornation](../078_QEP_Modeling_with_Derivatives/Simple_QEP_Regression_Derivative_Information_2d.ipynb) for more details.\n", "\n", "\n", "Therefore, QEP can find its applications in many statistics and machinear learning problems and is superior than GP in modeling inhomogeneous objects:\n", "\n", "* Bayesian modeling [Li, S., M. O'Connor, and S. Lan. \"Bayesian Learning via Q-Exponential Process.\" NIPS (2023)](https://papers.nips.cc/paper_files/paper/2023/hash/e6bfdd58f1326ff821a1b92743963bdf-Abstract-Conference.html)\n", "* Regularizing latent representations [Obite, C. P., Z. Chang, K. Wu, and S. Lan. \"Bayesian Regularization on Latent Representation.\" ICLR (2025)](https://openreview.net/pdf?id=VOoJEQlLW5)\n", "* Deep probabilistic models [Chang, Z., C. P. Obite, S. Zhou, and S. Lan. \"Deep Q-Exponential Processes. \" AABI (2025)](https://openreview.net/pdf?id=gV82fQTpqq)\n", "* Modeling with derivatives and solving PDEs [Yu, G., and S. Lan. \"Solving and Learning Partial Differential Equations with Variational Q-Exponential Processes\" NIPS (2025)](https://openreview.net/pdf?id=WjhS0EpJH7)\n", "* and so on...\n" ] }, { "cell_type": "markdown", "id": "25231b7f-e12c-426b-a5bc-83365b2eacf5", "metadata": {}, "source": [ "## How to fit QEP models in QPyTorch?\n", "\n", "QPyTorch is built on [PyTorch](https://pytorch.org) and [GPyTorch](https://gpytorch.ai) and provides comprehensive defining classes and modules. In particular, QPyTorch closely follows GPyTorch (which implements GP models) and mainly bases its inference on variational Bayes. Inherited from GPyTorch, QPyTorch can also run on [GPU](../02_Scalable_Exact_QEPs/index.html#exact-qeps-with-gpu-acceleration) and provides integration with [NUTS](../01_Exact_QEPs/QEP_Regression_Fully_Bayesian.ipynb) and Pyro (not fully tested).\n", "\n", "Interested users can start from this [QPyTorch Regression Tutorial](../01_Exact_QEPs/Simple_QEP_Regression.ipynb)." ] } ], "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": "3.10.18" } }, "nbformat": 4, "nbformat_minor": 5 }