The Theory and Algorithm of Ergodic Inference

TL;DR

This paper introduces ergodic inference, a new theoretical framework based on ergodic transformations, aiming to improve the scalability and efficiency of approximate inference methods in machine learning.

Contribution

It establishes the foundational theory of ergodic inference, providing a basis for developing practical algorithms beyond traditional VI and MCMC methods.

Findings

Proposes ergodic inference as a novel framework

Establishes theoretical foundation for future algorithms

Addresses limitations of existing VI and MCMC methods

Abstract

Approximate inference algorithm is one of the fundamental research fields in machine learning. The two dominant theoretical inference frameworks in machine learning are variational inference (VI) and Markov chain Monte Carlo (MCMC). However, because of the fundamental limitation in the theory, it is very challenging to improve existing VI and MCMC methods on both the computational scalability and statistical efficiency. To overcome this obstacle, we propose a new theoretical inference framework called ergodic Inference based on the fundamental property of ergodic transformations. The key contribution of this work is to establish the theoretical foundation of ergodic inference for the development of practical algorithms in future work.