CCF: Medium: Inference with dynamic deep probabilistic models

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The dynamics of complex systems are often studied by processing multivariate time signals that are produced by these systems. Improved understanding of the systems from such signals hinges on working with accurate models of the systems. The rationale of the proposed methodology for making inference from multivariate time signals stands on three important principles: algorithmic compressibility, locality, and deep probabilistic modeling. With algorithmic compressibility, one interprets seemingly complex high-dimensional data in much lower dimensional spaces. With locality, one exploits the fact that in nature the most influential events to an event are its local events. With deep probabilistic modeling, one aims at finding algorithmic compressibilities. These principles are used for developing novel models with little prior knowledge about the dynamics of the observed system. Another challenging problem of interest in the project is discovering causes and effects based on the adopted models. The developed methods are tested on multivariate local field potentials acquired from patients with epilepsy. Based on these signals, the objective is to find the zones in the brain that cause seizures in the patients. Finding these zones and removing them by surgery often cures the patients. The project conceptualizes a principled approach to building deep state-space models with deep probabilistic modeling. The research includes the development of theory and methods for estimating the unknowns of these models, investigation of methods for estimating the structures of the models, extension of the new methods to models that capture regime switching, development of theory and methods for discovering causalities among multivariate time signals, and identification of states that cause seizures in patients with epilepsy. The research is based on minimal assumptions about the models and is carried out within the Bayesian framework. The methodology is not data hungry, and all the produced results are probabilistic in nature. This research on deep probabilistic models and causal discovery considerably extends the capabilities for modeling multivariate time signals, which not only facilitates our understanding of complex systems but also offers new paradigms that extend the horizons and scope of signal processing and machine learning. The applications in medicine and neurosurgery, such as identifying the pathological zones in the brain of epilepsy patients that cause seizures stand on their merit.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.