Stochastic Gradient Annealed Importance Sampling for Efficient Online Marginal Likelihood Estimation

TL;DR

This paper introduces SGAIS, a novel online method for estimating marginal likelihood efficiently using stochastic gradient techniques and adaptive annealing, suitable for real-time model evaluation.

Contribution

We propose SGAIS, a new stochastic gradient-based annealed importance sampling method that enables fast, online marginal likelihood estimation with stable accuracy.

Findings

SGAIS is significantly faster than traditional methods.

It maintains accuracy comparable to existing techniques.

Supports online data processing for real-time applications.

Abstract

We consider estimating the marginal likelihood in settings with independent and identically distributed (i.i.d.) data. We propose estimating the predictive distributions in a sequential factorization of the marginal likelihood in such settings by using stochastic gradient Markov Chain Monte Carlo techniques. This approach is far more efficient than traditional marginal likelihood estimation techniques such as nested sampling and annealed importance sampling due to its use of mini-batches to approximate the likelihood. Stability of the estimates is provided by an adaptive annealing schedule. The resulting stochastic gradient annealed importance sampling (SGAIS) technique, which is the key contribution of our paper, enables us to estimate the marginal likelihood of a number of models considerably faster than traditional approaches, with no noticeable loss of accuracy. An important benefit of our approach is that the marginal likelihood is calculated in an online fashion as data becomes available, allowing the estimates to be used for applications such as online weighted model combination.