Morgane Austern is an assistant professor of Statistics at Harvard University. She is interested in understanding the behavior of algorithms and statistical estimators in the presence of a large amount of dependence. Her work consists in developing new probability tools, and in using those to establish the properties of learning algorithms in structured and dependent data contexts. She graduated with a PhD in statistics from Columbia University in 2019 where she worked in collaboration with Peter Orbanz and Arian Maleki on limit theorems for dependent and structured data. For two years (2019-2021), She was a postdoctoral researcher at Microsoft Research New England. In 2022, Morgane was named a Kavli fellow by the National Academy of science.
Her research has notably extended limit theorems for dependent data and matrices, studied graph representation learning, proposed new methods to obtain concentration inequalities, and established the properties of resampling methods such as the cross-validation and bootstrap method. Her current work is motivated by high-dimensional statistics, stable matching problems and random matrix theory.
Talk: Transport distances and novel concentration inequalities
Abstract: Concentration inequalities for the sample mean, like those due to Bernstein and Hoeffding, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. In this talk, motivated by applications to reinforcement learning we develop new results on transport and information theoretic distances. This allows us to obtain new computable concentration inequalities with asymptotically optimal size, finite-sample validity, and sub-Gaussian decay. These bounds enable the construction of efficient confidence intervals with correct coverage for any sample size. We derive our inequalities by tightly bounding the Hellinger distance, non-uniform Kolmogorov distance, and Wasserstein distance to a Gaussian. We then explore how these results could be extended to dependent data such as random fields and locally dependent data. Beyond empirical averages we study polynomial functions of independent high-dimensional random vectors, with the dimension of the vectors and the degree of the polynomial growing with the sample size. We bound the Kolmogorov-Smirnov distance between those and a polynomial of Gaussian random variables and show that the rate is nearly optimal.