Bayesian Conditional Density Filtering
This addresses the challenge of scalable Bayesian inference for practitioners dealing with streaming data, though it is an incremental improvement over existing MCMC methods.
The paper tackles the problem of efficient online Bayesian inference by proposing a Conditional Density Filtering (C-DF) algorithm, which achieves state-of-the-art parameter inference and prediction with reduced memory and runtime requirements, as demonstrated in examples like high-dimensional compressed regression.
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.