$\pi$VAE: a stochastic process prior for Bayesian deep learning with MCMC

• URL: http://arxiv.org/abs/2002.06873v6
• Date: Tue, 13 Sep 2022 19:02:14 GMT
• Title: $\pi$VAE: a stochastic process prior for Bayesian deep learning with MCMC
• Authors: Swapnil Mishra, Seth Flaxman, Tresnia Berah, Harrison Zhu, Mikko Pakkanen, Samir Bhatt
• Abstract summary: We propose a novel variational autoencoder called the prior encodingal autoencoder ($pi$VAE) We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference. Perhaps most usefully, we demonstrate that the low dimensional distributed latent space representation learnt provides an elegant and scalable means of performing inference for processes within programming languages such as Stan.
• Score: 2.4792948967354236
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($\pi$VAE). The $\pi$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $\pi$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $\pi$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.

Related papers

• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Tractable and Provably Efficient Distributional Reinforcement Learning with General Value Function Approximation [8.378137704007038]
  We present a regret analysis for distributional reinforcement learning with general value function approximation. Our theoretical results show that approximating the infinite-dimensional return distribution with a finite number of moment functionals is the only method to learn the statistical information unbiasedly.
  arXiv  Detail & Related papers  (2024-07-31T00:43:51Z)
• Stochastic Q-learning for Large Discrete Action Spaces [79.1700188160944]
  In complex environments with discrete action spaces, effective decision-making is critical in reinforcement learning (RL) We present value-based RL approaches which, as opposed to optimizing over the entire set of $n$ actions, only consider a variable set of actions, possibly as small as $mathcalO(log(n)$)$. The presented value-based RL methods include, among others, Q-learning, StochDQN, StochDDQN, all of which integrate this approach for both value-function updates and action selection.
  arXiv  Detail & Related papers  (2024-05-16T17:58:44Z)
• Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization [55.98760097296213]
  We introduce a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations $(x_t sim p, x'_t sim q)$ are observed over time. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.
  arXiv  Detail & Related papers  (2023-11-03T13:20:11Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes [7.5991638205413325]
  For $N$ training points, exact inference has $O(N3)$ cost; with $M ll N$ features, state of the art sparse variational methods have $O(NM2)$ cost. Recently, methods have been proposed using more sophisticated features; these promise $O(M3)$ cost, with good performance in low dimensional tasks such as spatial modelling, but they only work with a very limited class of kernels, excluding some of the most commonly used. In this work, we propose integrated Fourier features, which extends these performance benefits to a very broad class of stationary co
  arXiv  Detail & Related papers  (2023-08-27T15:44:28Z)
• Exact Bayesian Inference on Discrete Models via Probability Generating Functions: A Probabilistic Programming Approach [7.059472280274009]
  We present an exact Bayesian inference method for discrete statistical models. We use a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events. Our inference method is provably correct and fully automated.
  arXiv  Detail & Related papers  (2023-05-26T16:09:59Z)
• Generalized Differentiable RANSAC [95.95627475224231]
  $nabla$-RANSAC is a differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. $nabla$-RANSAC is superior to the state-of-the-art in terms of accuracy while running at a similar speed to its less accurate alternatives.
  arXiv  Detail & Related papers  (2022-12-26T15:13:13Z)
• Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization [88.0031283949404]
  Many real-world problems have complicated non functional constraints and use a large number of data points. Our proposed method outperforms an existing method with the previously best-known result.
  arXiv  Detail & Related papers  (2022-12-19T14:48:54Z)
• Bayesian Learning via Q-Exponential Process [10.551294837978363]
  Regularization is one of the most fundamental topics in optimization, statistics and machine learning. In this work, we generalize the $q$-exponential distribution (with density proportional to) $exp( frac12|u|q)$ to a process named $Q$-exponential (Q-EP) process that corresponds to the $L_q$ regularization of functions.
  arXiv  Detail & Related papers  (2022-10-14T17:37:14Z)
• Quadruply Stochastic Gaussian Processes [10.152838128195466]
  We introduce a variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in the kernel approximation, $m$. We demonstrate accurate inference on large classification and regression datasets using GPs and relevance vector machines with up to $m = 107$ basis functions.
  arXiv  Detail & Related papers  (2020-06-04T17:06:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.