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Automatically Marginalized MCMC in Probabilistic Programming
Feb 01, 2023
Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, which often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.
Variational Marginal Particle Filters
Sep 30, 2021
Variational inference for state space models (SSMs) is known to be hard in general. Recent works focus on deriving variational objectives for SSMs from unbiased sequential Monte Carlo estimators. We reveal that the marginal particle filter is obtained from sequential Monte Carlo by applying Rao-Blackwellization operations, which sacrifices the trajectory information for reduced variance and differentiability. We propose the variational marginal particle filter (VMPF), which is a differentiable and reparameterizable variational filtering objective for SSMs based on an unbiased estimator. We find that VMPF with biased gradients gives tighter bounds than previous objectives, and the unbiased reparameterization gradients are sometimes beneficial.
Optimal Mixture Weights for Off-Policy Evaluation with Multiple Behavior Policies
Nov 29, 2020
Off-policy evaluation is a key component of reinforcement learning which evaluates a target policy with offline data collected from behavior policies. It is a crucial step towards safe reinforcement learning and has been used in advertisement, recommender systems and many other applications. In these applications, sometimes the offline data is collected from multiple behavior policies. Previous works regard data from different behavior policies equally. Nevertheless, some behavior policies are better at producing good estimators while others are not. This paper starts with discussing how to correctly mix estimators produced by different behavior policies. We propose three ways to reduce the variance of the mixture estimator when all sub-estimators are unbiased or asymptotically unbiased. Furthermore, experiments on simulated recommender systems show that our methods are effective in reducing the Mean-Square Error of estimation.
On the Necessity and Effectiveness of Learning the Prior of Variational Auto-Encoder
May 31, 2019
Using powerful posterior distributions is a popular approach to achieving better variational inference. However, recent works showed that the aggregated posterior may fail to match unit Gaussian prior, thus learning the prior becomes an alternative way to improve the lower-bound. In this paper, for the first time in the literature, we prove the necessity and effectiveness of learning the prior when aggregated posterior does not match unit Gaussian prior, analyze why this situation may happen, and propose a hypothesis that learning the prior may improve reconstruction loss, all of which are supported by our extensive experiment results. We show that using learned Real NVP prior and just one latent variable in VAE, we can achieve test NLL comparable to very deep state-of-the-art hierarchical VAE, outperforming many previous works with complex hierarchical VAE architectures.