2016/09/03 by Ari Pakman, Pakman, Ari, Dar Gilboa +5 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.1609.00770
openalex publication_date 2016/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a novel stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear. The algorithm is based on simulating first arrival times in a doubly stochastic Poisson process using the thinning method, and allows efficient sampling of Bayesian posteriors in big datasets. We prove that in the BPS no bias is introduced by noisy evaluations of the log-likelihood gradient. On the other hand, we argue that efficiency considerations favor a small, controllable bias in the construction of the thinning proposals, in exchange for faster mixing. We introduce a simple regression-based proposal intensity for the thinning method that controls this trade-off. We illustrate the algorithm in several examples in which it outperforms both unbiased, but slowly mixing stochastic versions of BPS, as well as biased stochastic gradient-based samplers.