Event Date
Speaker: Alden Green, Stein Fellow, Stanford University
Title: "The Voronoigram and the Graph KS test: Two optimal approaches to TV regularization"
Abstract: Bounded total variation (TV) is a useful modeling assumption for functions which display spatially inhomogeneous kinds of smoothness and may even be discontinuous. This talk will discuss methods that use TV smoothness to tackle two classic statistical problems – nonparametric regression and two-sample testing – in a multivariate setting.
- For regression, the Voronoigram solves a penalized least squares problem where the penalty involves TV, and the optimization is over functions that are piecewise constant on cells in the Voronoi diagram.
- For testing, the graph KS statistic is a maximum mean discrepancy in which the maximum difference in sample means is computed over a TV smoothness class.
In each case, I will discuss worst-case rates of convergence, give matching upper and lower bounds that show the methods are nearly optimal under natural TV modeling assumptions, and explain why some obvious competitors are suboptimal.
Based on joint work with Addison Hu, Sivaraman Balakrishnan, and Ryan Tibshirani.
Speaker's webpage (external link): https://statistics.stanford.edu/people/alden-green
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Seminar date/time: Thursday March 16, 2023, 4:10pm
Location: MSB 1147 (Colloquium Room)
Refreshments: 3:30pm MSB 1147 courtyard