Transactions on Machine Learning Research 2835-8856 (2023).
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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 such as 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.
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