Practical Algorithms for Latent Variable Models

Abstract

Latent variables allow researchers and engineers to encode assumptions into their statistical models. A latent variable might, for example, represent an unobserved covariate, measurement error, or a missing class label. Inference is challenging because one must account for the conditional dependence structure induced by these variables, and marginalization is often intractable. In this thesis, I present several practical algorithms for inferring latent structure in probabilistic models used in computational biology, neuroscience, and time-series analysis. First, I present a multi-view framework that combines neural networks and probabilistic canonical correlation analysis to estimate shared and view-specific latent structure of paired samples of histological images and gene expression levels. The model is trained end-to-end to estimate all parameters simultaneously, and we show that the latent variables capture interpretable structure, such as tissue-specific and morphological variation. Next, I present a family of nonlinear dimension-reduction models that use random features to support non-Gaussian data likelihoods. By approximating a nonlinear relationship between the latent variables and observations with a function that is linear with respect to random features, we induce closed-form gradients of the posterior distribution with respect to the latent variables. This allows for gradient-based nonlinear dimension-reduction models for a variety of data likelihoods. Finally, I discuss lowering the computational cost of online Bayesian filtering of time series with abrupt changes in structure, called changepoints. We consider settings in which a time series has multiple data sources, each with an associated cost. We trade the cost of a data source against the quality or "fidelity" of that source and how its fidelity affects the estimation of changepoints. Our framework makes cost-sensitive decisions about which data source to use based on minimizing the information entropy of the posterior distribution over changepoints.