2015/06/09 by Bo Dai, Niao He, Dai, Bo +5 · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Gaussian Processes and Bayesian Inference #Statistical Methods and Bayesian Inference #cs.LG #stat.CO #stat.ML
paper · pdf · doi:10.48550/arxiv.1506.03101
38 pages, 26 figures
arxiv created 2016/05/05 · arxiv updated 2016/05/09
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack either scalability or rigorous guarantees. To tackle this challenge, we propose a simple yet provable algorithm, Particle Mirror Descent (PMD), to iteratively approximate the posterior density. PMD is inspired by stochastic functional mirror descent where one descends in the density space using a small batch of data points at each iteration, and by particle filtering where one uses samples to approximate a function. We prove result of the first kind that, with m particles, PMD provides a posterior density estimator that converges in terms of KL-divergence to the true posterior in rate O(1/√(m)). We demonstrate competitive empirical performances of PMD compared to several approximate inference algorithms in mixture models, logistic regression, sparse Gaussian processes and latent Dirichlet allocation on large scale datasets.