Spectral learning of Bernoulli linear dynamical systems models
| Autor: | Stone, Iris R., Sagiv, Yotam, Park, Il Memming, Pillow, Jonathan W. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Transactions on Machine Learning Research (2023) |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Published in Transactions on Machine Learning Research (https://jmlr.org/tmlr/papers/) |
| Databáze: | arXiv |
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