Bayesian Conditional Density Filtering

Authors: 
Rajarshi Guhaniyogi*, Shaan Qamar*, David B. Dunson
UC Santa Cruz, Duke University

Oct 14 2014

We propose a Conditional Density Filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts MCMC sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by propagating surrogate conditional sufficient statistics (a function of data and parameter estimates) as new data arrive. These quantities eliminate the need to store or process the entire dataset simultaneously and offer a number of desirable features. Often, these include a reduction in memory requirements and runtime and improved mixing, along with state-of-the-art parameter inference and prediction. These improvements are demonstrated through several illustrative examples including an application to high dimensional compressed regression. Finally, we show that C-DF samples converge to the target posterior distribution asymptotically as sampling proceeds and more data arrives.

* These authors contributed equally to this work.

Keywords: 

Approximate MCMC, Big data, Density filtering, Dimension reduction, Streaming data, Sequential inference, Sequential Monte Carlo