Enhanced Statistical Learning for Physical Systems Exploiting Non-Standard Constraints

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Real world systems are often naturally constrained by physical laws or human behavioral patterns, and understanding of such systems can be significantly enhanced by incorporating said constraints into the inferential mechanism. However, the presence of multiple constraints can complicate the process of statistical learning. This project aims to develop novel statistical methods to help solve real world problems where a multitude of complex constraints pose inferential challenges. Motivations are drawn directly from three concrete applications: i) extracting the radius of proton from electric form-factor data, a fundamental problem in atomic physics which is of high relevance due to anomalies between results from different modes of experimentation, ii) describing the relationship between wind velocity and power derived from wind-turbines, which is one of the fastest growing renewable sources of energy and iii) describing the traffic flow pattern with traffic speed, a key object of research in traffic engineering. The project will bring together ideas from machine learning and Bayesian nonparametrics to develop statistically sound and computationally efficient methods of inference in constrained decision problems. The project aims to develop a principled probabilistic approach towards inference in scientific and engineering applications where various physical constraints provide a priori knowledge regarding key objects of inference. Such objects may correspond to a single curve or a collection of curves or density functions. The PI and co-PI will develop novel statistical methods for simultaneous incorporation of multiple shape constraints motivated by real scientific and engineering applications, while being broadly generalizable beyond the considered applications. Emphasis is laid on obtaining equivalent representations of various constraints within a flexible nonparametric Bayesian model, and developing novel prior distributions on these constrained spaces. The Bayesian approach is attractive to obtain uncertainty estimates, and the PI and co-PI aim to develop rigorous theoretical guarantees for the frequentist validity of Bayesian uncertainty measures in the present setting. In addition, the PI and co-PI propose to demonstrate that including the constraints diminishes the uncertainty which will subsequently lead to better scientific conclusions. The methodological developments will be accompanied by efficient computation algorithms that meet the scalability demanded by the specific applications and beyond. To maximize the impact of the methodology developed, the PI and co-PI will closely collaborate with domain experts for the specific applications.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.