Denison Scientific Association: Stochastic Dynamical Systems: Rare Events and Machine Learning for Nonlinear Dynamics

In this talk I will present recent work in two areas of statistics and probability.

First, I will discuss large deviations theory and its application to self-interacting processes. Large deviations theory quantifies the probability of rare events that significantly deviate from a system’s typical behavior and explains how quickly these probabilities decrease over time. Self-interacting processes arise in ecological models and Monte Carlo (i.e., randomized) algorithms, where large deviations help assess the risk of unusually poor algorithm performance.

Next, I will discuss nonlinear time series data, which arises in settings such as epidemiology, finance, and neuroscience. After introducing linear and nonlinear time series models, I will discuss a statistical machine learning method that can be used to learn the relationships within such data sets. This method is flexible enough to learn a general class of nonlinear relationships, but is structured enough to have provable performance guarantees.

These topics are both centered around characterizing the long-term behavior of random perturbations of deterministic systems.