Targeted stochastic gradient Markov chain Monte Carlo for hidden Markov models with rare latent states

TL;DR

This paper introduces TASS, a targeted sub-sampling method for hidden Markov models that over-samples rare latent states, improving inference accuracy and efficiency in imbalanced data scenarios.

Contribution

The paper proposes a novel targeted sub-sampling approach that over-samples rare states and uses clustering to reduce gradient variance in stochastic gradient MCMC.

Findings

Significant improvements in predictive accuracy on real data.

Enhanced inference quality for rare latent states.

Reduced variance in gradient estimates leading to better sampling efficiency.

Abstract

Markov chain Monte Carlo (MCMC) algorithms for hidden Markov models often rely on the forward-backward sampler. This makes them computationally slow as the length of the time series increases, motivating the development of sub-sampling-based approaches. These approximate the full posterior by using small random subsequences of the data at each MCMC iteration within stochastic gradient MCMC. In the presence of imbalanced data resulting from rare latent states, subsequences often exclude rare latent state data, leading to inaccurate inference and prediction/detection of rare events. We propose a targeted sub-sampling (TASS) approach that over-samples observations corresponding to rare latent states when calculating the stochastic gradient of parameters associated with them. TASS uses an initial clustering of the data to construct subsequence weights that reduce the variance in gradient estimation. This leads to improved sampling efficiency, in particular in settings where the rare latent states correspond to extreme observations. We demonstrate substantial gains in predictive and inferential accuracy on real and synthetic examples.