Ergodic Inference: Accelerate Convergence by Optimisation

TL;DR

This paper introduces Ergodic Inference, a hybrid approach that combines MCMC and variational inference, using gradient-based optimization to reduce bias and accelerate convergence in statistical inference tasks.

Contribution

It proposes a novel hybrid method that optimizes MCMC hyper-parameters to generate low-biased samples efficiently, improving upon existing inference algorithms.

Findings

Produces promising results on benchmark datasets

Balances bias reduction with computational efficiency

Outperforms recent hybrid MCMC-VI methods

Abstract

Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods may have large bias. In this work, we aim to improve upon MCMC and VI by a novel hybrid method based on the idea of reducing simulation bias of finite-length MCMC chains using gradient-based optimisation. The proposed method can generate low-biased samples by increasing the length of MCMC simulation and optimising the MCMC hyper-parameters, which offers attractive balance between approximation bias and computational efficiency. We show that our method produces promising results on popular benchmarks when compared to recent hybrid methods of MCMC and VI.