High-dimensional nonparametric models of complex physical phenomena have facilitated a myriad of scientific and engineering developments. A wide variety of important applications, however, rely upon our ability to perform fast and accurate inference on these models using a meager supply of event-based data. Such data arise when indirect observations of a physical phenomenon are collected by measuring discrete events (such as photons hitting a detector, neurons firing, or people interacting in a social network). The challenge here is to use extremely small numbers of random events to perform inference on the underlying high-dimensional phenomenon (e.g., the distribution of light in a scene or influences within a network).
In this talk I will describe point process models and inference for three physical systems. First, we will examine electron microscopy data used in materials science and use low-dimensional models of material structure to mitigate the effects of low-count observations. Second, we will examine photon-limited compressive optical imaging systems and how physical models play a critical role in their characterization. Finally, we will examine dynamical system identification using count data in the context of social and biological neural networks. Underlying these methods are techniques at the intersection of statistical signal processing, learning theory, sparse coding, nonlinear approximation theory, optical engineering, and optimization theory.