2014/11/06 by Yutian Chen, Chen, Yutian, Vikash K. Mansinghka +4 · 1 citation
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (stat.ML) #Machine Learning and Algorithms #Markov Chains and Monte Carlo Methods #stat.ML
paper · pdf · doi:10.48550/arxiv.1411.1690
openalex publication_date 2014/11/06 · arxiv created 2015/03/09 · arxiv updated 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time in the number of observations. This paper describes a sublinear-time algorithm for making Metropolis-Hastings (MH) updates to latent variables in probabilistic programs. The approach generalizes recently introduced approximate MH techniques: instead of subsampling data items assumed to be independent, it subsamples edges in a dynamically constructed graphical model. It thus applies to a broader class of problems and interoperates with other general-purpose inference techniques. Empirical results, including confirmation of sublinear per-transition scaling, are presented for Bayesian logistic regression, nonlinear classification via joint Dirichlet process mixtures, and parameter estimation for stochastic volatility models (with state estimation via particle MCMC). All three applications use the same implementation, and each requires under 20 lines of probabilistic code.