Informed Subsampling MCMC: Approximate Bayesian Inference for Large Datasets
Florian Maire (University College Dublin)
Friday 17th February, 2017 15:00-16:00 Maths 204
We develop a framework for speeding up Bayesian inference conducted in presence of large datasets. Inspired by the Approximate Bayesian Computation (ABC) literature, we design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. The subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Subsampling-MCMC, is a generic and flexible approach which, contrarily to existing methodologies, preserves the simplicity of the Metropolis--Hastings algorithm. Even though the stationary distribution of the chain is an approximation of the posterior of interest, we show how the informed subsampling controls the error. We will provide some illustrations on digit recognition and time series inference.
This is joint work with Nial Friel (UCD) and Pierre Alquier (ENSAE ParisTech).