  Latent linear dynamical systems with Bernoulli observations provide a
powerful modeling framework for identifying the temporal dynamics underlying
binary time series data, which arise in a variety of contexts such as binary
decision-making and discrete stochastic processes (e.g., binned neural spike
trains). Here we develop a spectral learning method for fast, efficient fitting
of probit-Bernoulli latent linear dynamical system (LDS) models. Our approach
extends traditional subspace identification methods to the Bernoulli setting
via a transformation of the first and second sample moments. This results in a
robust, fixed-cost estimator that avoids the hazards of local optima and the
long computation time of iterative fitting procedures like the
expectation-maximization (EM) algorithm. In regimes where data is limited or
assumptions about the statistical structure of the data are not met, we
demonstrate that the spectral estimate provides a good initialization for
Laplace-EM fitting. Finally, we show that the estimator provides substantial
benefits to real world settings by analyzing data from mice performing a
sensory decision-making task.
