Large deviations in data science: some initial examples

The theory of large deviations has become a cornerstone of modern probability theory. It has proven particularly useful in the analysis and design of efficient stochastic numerical methods. Examples include methods for rare-event sampling and general-purpose Markov chain Monte Carlo methods. Large deviations are also a natural way to analyze gradient flows, which are now being used extensively within data science. Despite the successful use of tools for large deviations, and their connections to stochastic control, in a range of areas within applied probability, they are largely unexplored in the data science setting. In this talk, we will discuss some initial attempts at bringing large deviation theory into the data science context. We will consider several examples, including some recent algorithms proposed for finding mixed equilibria in zero-sum games and stochastic approximation methods.

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