Spectral learning of Bernoulli linear dynamical systems models

• URL: http://arxiv.org/abs/2303.02060v2
• Date: Wed, 26 Jul 2023 22:29:21 GMT
• Title: Spectral learning of Bernoulli linear dynamical systems models
• Authors: Iris R. Stone, Yotam Sagiv, Il Memming Park, Jonathan W. Pillow
• Abstract summary: We develop a learning method for fast, efficient fitting of latent linear dynamical system models. Our approach extends traditional subspace identification methods to the Bernoulli setting. We show that the estimator provides real world settings by analyzing data from mice performing a sensory decision-making task.
• Score: 21.3534487101893
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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