The Statistics Seminar speaker for Wednesday, February 19, 2020 is Ashwin Pananjady, a PhD student in the Department of Electrical Engineering and Computer Sciences at the University of California Berkeley, advised by Martin Wainwright and Thomas Courtade. His interests lie broadly in statistics, machine learning, information theory, and optimization, and include ranking and permutation estimation, high-dimensional and non-parametric statistics, high-dimensional probability, and reinforcement learning. He is a recipient of the inaugural Lawrence Brown PhD student award from the Institute of Mathematical Statistics, an Outstanding Graduate Student Instructor award from UC Berkeley, and the Governor's Gold Medal from IIT Madras
Talk: Statistics meets computation: Exploring the interface between parametric and non-parametric modeling
Abstract: Modeling and tractable computation form two fundamental but competing pillars of data science; indeed, fitting good models to data is often computationally challenging in modern applications. Focusing on the canonical tasks of ranking and regression, I introduce problems where this tension is immediately apparent, and present methodological solutions that are both statistically sound and computationally tractable.
I begin by describing a class of “permutation-based" models as a flexible alternative to parametric modeling in a host of inference problems including ranking from ordinal data. I introduce procedures that narrow a conjectured statistical-computational gap, demonstrating that carefully chosen non-parametric structure can significantly improve robustness to mis-specification while maintaining interpretability. Next, I address a complementary question in the context of convex regression, where I show that the curse of dimensionality inherent to non-parametric modeling can be mitigated via parametric approximation. Our provably optimal methodology demonstrates that it is often possible to enhance the interpretability of non-parametric models while maintaining important aspects of their flexibility.