Spectral Subsampling MCMC for Stationary Time Series

TL;DR

This paper introduces a spectral subsampling MCMC method that accelerates Bayesian inference for large stationary time series datasets by operating in the frequency domain, achieving significant speedups with minimal bias.

Contribution

The paper presents a novel spectral subsampling approach for MCMC in time series, incorporating variance reduction techniques like data grouping and coreset constructions.

Findings

Speedup of up to two orders of magnitude in MCMC sampling.

Negligible bias compared to full-data MCMC.

Effective variance reduction methods for spectral subsampling.

Abstract

Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of independence. We propose a novel technique for speeding up MCMC for time series data by efficient data subsampling in the frequency domain. For several challenging time series models, we demonstrate a speedup of up to two orders of magnitude while incurring negligible bias compared to MCMC on the full dataset. We also propose alternative control variates for variance reduction based on data grouping and coreset constructions.