Adaptive variational Bayes: Optimality, computation and applications

• URL: http://arxiv.org/abs/2109.03204v4
• Date: Mon, 11 Mar 2024 04:29:15 GMT
• Title: Adaptive variational Bayes: Optimality, computation and applications
• Authors: Ilsang Ohn, Lizhen Lin
• Abstract summary: We propose a novel adaptive variational Bayes framework, which can operate on a collection of models. We show that the adaptive variational Bayes attains optimal contraction rates adaptively under very general conditions.
• Score: 2.4022340214033915
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally tractable variational Bayes method that performs adaptive inference. To fill this gap, we propose a novel adaptive variational Bayes framework, which can operate on a collection of models. The proposed framework first computes a variational posterior over each individual model separately and then combines them with certain weights to produce a variational posterior over the entire model. It turns out that this combined variational posterior is the closest member to the posterior over the entire model in a predefined family of approximating distributions. We show that the adaptive variational Bayes attains optimal contraction rates adaptively under very general conditions. We also provide a methodology to maintain the tractability and adaptive optimality of the adaptive variational Bayes even in the presence of an enormous number of individual models, such as sparse models. We apply the general results to several examples, including deep learning and sparse factor models, and derive new and adaptive inference results. In addition, we characterize an implicit regularization effect of variational Bayes and show that the adaptive variational posterior can utilize this.

Related papers

• Adaptive sparse variational approximations for Gaussian process regression [6.169364905804677]
  We construct a variational approximation to a hierarchical Bayes procedure, and derive upper bounds for the contraction rate of the variational posterior. Our theoretical results are accompanied by numerical analysis both on synthetic and real world data sets.
  arXiv  Detail & Related papers  (2025-04-04T09:57:00Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Quasi Black-Box Variational Inference with Natural Gradients for Bayesian Learning [84.90242084523565]
  We develop an optimization algorithm suitable for Bayesian learning in complex models. Our approach relies on natural gradient updates within a general black-box framework for efficient training with limited model-specific derivations.
  arXiv  Detail & Related papers  (2022-05-23T18:54:27Z)
• Loss function based second-order Jensen inequality and its application to particle variational inference [112.58907653042317]
  Particle variational inference (PVI) uses an ensemble of models as an empirical approximation for the posterior distribution. PVI iteratively updates each model with a repulsion force to ensure the diversity of the optimized models. We derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models.
  arXiv  Detail & Related papers  (2021-06-09T12:13:51Z)
• Transformation Models for Flexible Posteriors in Variational Bayes [0.0]
  In neural networks, variational inference is widely used to approximate difficult-to-compute posteriors. Transformation models are flexible enough to fit any distribution. TM-VI allows to accurately approximate complex posteriors in models with one parameter.
  arXiv  Detail & Related papers  (2021-06-01T14:43:47Z)
• A variational inference framework for inverse problems [0.39373541926236766]
  A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications. An image processing application and a simulation exercise motivated by biomedical problems reveal the computational advantage offered by variational Bayes.
  arXiv  Detail & Related papers  (2021-03-10T07:37:20Z)
• Sparse Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation [0.0]
  This paper develops a sparsity-inducing version of Bayesian Causal Forests. It is designed to estimate heterogeneous treatment effects using observational data.
  arXiv  Detail & Related papers  (2021-02-12T15:24:50Z)
• Robust, Accurate Stochastic Optimization for Variational Inference [68.83746081733464]
  We show that common optimization methods lead to poor variational approximations if the problem is moderately large. Motivated by these findings, we develop a more robust and accurate optimization framework by viewing the underlying algorithm as producing a Markov chain.
  arXiv  Detail & Related papers  (2020-09-01T19:12:11Z)
• Variational Variance: Simple, Reliable, Calibrated Heteroscedastic Noise Variance Parameterization [3.553493344868413]
  We propose critiques to test predictive mean and variance calibration and the predictive distribution's ability to generate sensible data. We find that our solution, to treat heteroscedastic variance variationally, sufficiently regularizes variance to pass these PPCs.
  arXiv  Detail & Related papers  (2020-06-08T19:58:35Z)
• Bayesian Deep Learning and a Probabilistic Perspective of Generalization [56.69671152009899]
  We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization. We also propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction.
  arXiv  Detail & Related papers  (2020-02-20T15:13:27Z)
• Decision-Making with Auto-Encoding Variational Bayes [71.44735417472043]
  We show that a posterior approximation distinct from the variational distribution should be used for making decisions. Motivated by these theoretical results, we propose learning several approximate proposals for the best model. In addition to toy examples, we present a full-fledged case study of single-cell RNA sequencing.
  arXiv  Detail & Related papers  (2020-02-17T19:23:36Z)

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.