Model Reduction of High Dimensional Hidden Markov Models and Markov Decision Processes

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Intellectual Merit: We currently live in an era where data is a major currency promising a transformative change to our society. Consequently, there has been a surge in the use of machine learning (ML) algorithms on high dimensional data producing unstructured stochastic models. Such models tend to be of very high dimensions limiting their utility in various applications involving optimization or decision systems. This proposal focuses on developing a foundational theory for model reduction applied to classes of stochastic models, in particular, Hidden Markov Models (HMMs); these are stochastic models that are described by underlying finite dimensional state space. Broader Impact: Ultimately, a model reduction theory will impact many fundamental aspects related to complex stochastic models including simulation, prediction, coding, robust learning, decision design and reinforcement learning. This research will develop new insights to address similar questions for other stochastic models including jump linear systems, and graphical models with latent variables and will have a direct impact on problems related to artificial intelligence and reinforcement learning. The latter is emerging as a popular approach for many decision-systems applications involving social behavior-- where simple mechanistic models do not exist. Examples of such problems are critical infrastructures and smart services where high dimensional unstructured data is available in real time. Models emerging in such approaches tend to have very high dimensions. A foundational theory for model reduction will affect the way we learn and utilize complex stochastic models. As a result, this development will enter our courses at MIT in a fashion similar to how model reduction theory impacted courses in linear system theory. The development should affect classes in stochastic models, machine learning, and statistical learning theory, reinforcement learning, and AI. We also intend to incorporate the connection between model reduction and statistical learning in our new MIT micromasters in statistics and data science.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.