Loss function based second-order Jensen inequality and its application to particle variational inference

• URL: http://arxiv.org/abs/2106.05010v2
• Date: Thu, 10 Jun 2021 00:43:30 GMT
• Title: Loss function based second-order Jensen inequality and its application to particle variational inference
• Authors: Futoshi Futami, Tomoharu Iwata, Naonori Ueda, Issei Sato, and Masashi Sugiyama
• Abstract summary: 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.
• Score: 112.58907653042317
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian model averaging, obtained as the expectation of a likelihood function by a posterior distribution, has been widely used for prediction, evaluation of uncertainty, and model selection. Various approaches have been developed to efficiently capture the information in the posterior distribution; one such approach is the optimization of a set of models simultaneously with interaction to ensure the diversity of the individual models in the same way as ensemble learning. A representative approach is particle variational inference (PVI), which 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. However, despite its promising performance, a theoretical understanding of this repulsion and its association with the generalization ability remains unclear. In this paper, we tackle this problem in light of PAC-Bayesian analysis. First, we provide a new second-order Jensen inequality, which has the repulsion term based on the loss function. Thanks to the repulsion term, it is tighter than the standard Jensen inequality. Then, we derive a novel generalization error bound and show that it can be reduced by enhancing the diversity of models. Finally, we derive a new PVI that optimizes the generalization error bound directly. Numerical experiments demonstrate that the performance of the proposed PVI compares favorably with existing methods in the experiment.

Related papers

• Variational Autoencoders for Efficient Simulation-Based Inference [0.3495246564946556]
  We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. We demonstrate the efficacy of these models on well-established benchmark problems, achieving results comparable to flow-based approaches.
  arXiv  Detail & Related papers  (2024-11-21T12:24:13Z)
• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• Moreau-Yoshida Variational Transport: A General Framework For Solving Regularized Distributional Optimization Problems [3.038642416291856]
  We consider a general optimization problem of minimizing a composite objective functional defined over a class probability distributions. We propose a novel method, dubbed as Moreau-Yoshida Variational Transport (MYVT), for solving the regularized distributional optimization problem.
  arXiv  Detail & Related papers  (2023-07-31T01:14:42Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• Optimal regularizations for data generation with probabilistic graphical models [0.0]
  Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models. We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
  arXiv  Detail & Related papers  (2021-12-02T14:45:16Z)
• PSD Representations for Effective Probability Models [117.35298398434628]
  We show that a recently proposed class of positive semi-definite (PSD) models for non-negative functions is particularly suited to this end. We characterize both approximation and generalization capabilities of PSD models, showing that they enjoy strong theoretical guarantees. Our results open the way to applications of PSD models to density estimation, decision theory and inference.
  arXiv  Detail & Related papers  (2021-06-30T15:13:39Z)
• Posterior-Aided Regularization for Likelihood-Free Inference [23.708122045184698]
  Posterior-Aided Regularization (PAR) is applicable to learning the density estimator, regardless of the model structure. We provide a unified estimation method of PAR to estimate both reverse KL term and mutual information term with a single neural network.
  arXiv  Detail & Related papers  (2021-02-15T16:59:30Z)
• Efficient Semi-Implicit Variational Inference [65.07058307271329]
  We propose an efficient and scalable semi-implicit extrapolational (SIVI) Our method maps SIVI's evidence to a rigorous inference of lower gradient values.
  arXiv  Detail & Related papers  (2021-01-15T11:39:09Z)
• 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.