Bayesian Active Learning for Discrete Latent Variable Models

Active learning seeks to reduce the number of samples required to estimate the parameters of a model, thus forming an important class of techniques in modern machine learning. However, past work on active learning has largely overlooked latent variable models, which play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines. Here we address this gap in the literature and propose a novel framework for maximum-mutual-information input selection for learning discrete latent variable regression models. We first examine a class of models known as "mixtures of linear regressions" (MLR). This example is striking because it is well known that active learning confers no advantage for standard least-squares regression. However, we show -- both in simulations and analytically using Fisher information -- that optimal input selection can nevertheless provide dramatic gains for mixtures of regression models; we also validate this on a real-world application of MLRs. We then consider a powerful class of temporally structured latent variable models known as Input-Output Hidden Markov Models (IO-HMMs), which have recently gained prominence in neuroscience. We show that our method substantially speeds up learning, and outperforms a variety of approximate methods based on variational and amortized inference.