Spectral learning of shared dynamics between generalized-linear processes

Lucine L Oganesian, Omid G. Sani, Maryam Shanechi

Primary Area: applications to neuroscience & cognitive science

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Keywords: state space models, subspace identification, dynamical systems, neural coding

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Abstract: Across various science and engineering applications, there often arises a need to predict the dynamics of one data stream from another. Further, these data streams may have different statistical properties. Studying the dynamical relationship between such processes, especially for the purpose of predicting one from the other, requires accounting for their distinct statistics while also dissociating their shared dynamical subspace. Existing analytical modeling approaches, however, do not address both of these needs. Here we propose a path forward by deriving a novel analytical multi-step subspace identification algorithm that can learn a model for a primary generalized-linear process (called ``predictor"), while also dissociating the dynamics shared with a secondary process. We demonstrate a specific application of our approach for modeling discrete Poisson point-processes activity, while finding the dynamics shared with continuous Gaussian processes. In simulations, we show that our algorithm accurately prioritizes identification of shared dynamics. Further, we also demonstrate that the method can additionally model the disjoint dynamics that exist only in the predictor Poisson data stream, if desired. Similarly, we apply our algorithm on a biological dataset to learn models of dynamics in Poisson neural population spiking streams that predict dynamics in movement streams. Compared with existing Poisson subspace identification methods, models learned with our method decoded movements better and with lower-dimensional latent states. Lastly, we discuss regimes in which our assumptions might not be met and provide recommendations and possible future directions of investigation.

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Submission Number: 7049