CIF: Small: Sensing-Aware Decision Making for High-Dimensional Signals

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There has been an explosion in our ability to sense and record the world around us. This has led to new discoveries and allowed us to consider new paradigms in nearly every walk of life. While the promise of these developments is significant, the explosion of sensing has also created substantial challenges. These challenges include high-dimensionality of observations and the associated ``curse of dimensionality'', non-trivial relationships between the observations and the latent variables we care about, poor understanding of models, and lack of sufficient training data from which to learn these models. Motivated by such problems, this research studies an approach which we term ``sensing-aware inferencing'' that leverages knowledge about the underlying structure of the sensing process for data-driven inferencing. Such problems are at the frontier of statistical signal processing and advance this frontier by contributing to signal processing theory and practice.This research involves both analysis of the fundamental limits to the performance of, as well as the development of new methods for, decision making and inference from high-dimensional data when the data are related to latent variables through a underlying sensing structure. The methods being developed explicitly acknowledge and account for the underlying sensing process in a unified and optimal way. Research is being advanced along two major thrusts: 1) theoretical investigation of the fundamental limits of classification performance as dimension grows faster than available training data under various states of sensing knowledge, 2) development of methods for inference in high-dimensional problems exploiting sensing structure in a unified way. Throughout, the samples available for such learning are severely limited relative to the dimensionality of the observations.