Spectral learning of Bernoulli latent dynamical system models for decision-making

A central problem in systems neuroscience is to understand the relationship between sensory stimuli, neural activity, and decision-making behavior. Latent linear dynamical systems (LDS) models are one powerful framework for characterizing these relationships. For example, LDS models can be used to describe the hidden dynamics that govern how an animal's decision-making strategy evolves continuously over time. However, fitting LDS models to data using standard methods such as the expectation-maximization (EM) algorithm is computationally expensive and prone to local optima. We address these shortcomings by developing a spectral learning method for fast, efficient fitting of input-driven LDS models with Bernoulli observations. Our method addresses gaps in the field by providing an efficient estimator (BErnoulli SpecTral Linear Dynamical System or bestLDS) for the setting of binary time series data driven by external inputs. Our approach extends traditional subspace identification (SSID) methods (van Overschee & Moore, Automatica 1994; Ho & Kalman, Regelungstechnik 1966) to the Bernoulli setting via a transformation of the first and second sample moments. The result is a fixed-cost estimator that avoids the hazards of local optima and the long computation time of fitting procedures like EM. In regimes where data is limited or assumptions about the statistical structure of the data are not met, bestLDS provides good initializations for standard approximate EM fitting. Finally, we show that our estimator provides substantial benefits in application to binary choice data from mice performing a sensory decision-making task.