Fall Seminar - Nikita Zhivotovskiy

In this talk I will discuss the finite sample behavior of likelihood ratios in logistic regression. Classical theory, through Wilks theorem, predicts a simple dimension dependent scale in regular asymptotic settings. For arbitrary fixed designs, the worst case likelihood ratio can be larger by a logarithmic factor, and this factor is unavoidable. The low dimensional cases exhibit a different behavior, while Gaussian random designs recover the classical scale. The results are uniform over all target parameters and do not require existence of the maximum likelihood estimator. Nikita Zhivotovskiy is an Assistant Professor in the Department of Statistics at the University of California Berkeley. He previously held postdoctoral positions at ETH Zürich in the department of mathematics hosted by Afonso Bandeira, and at Google Research, Zürich hosted by Olivier Bousquet. He also spent time at the Technion I.I.T. mathematics department hosted by Shahar Mendelson. Nikita completed his thesis at Moscow Institute of Physics and Technology under the guidance of Vladimir Spokoiny and Konstantin Vorontsov.