BIU learning club – Amichai Painsky – Inferring the Unseen

Location:

Engineering building (1103), room 329

Title:

Inferring the Unseen

Abstract:

Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics and related fields, which was extensively studied in the context of point estimation. In this work we introduce a novel interval estimation scheme for unobserved events. Our proposed framework applies selective inference, as we construct confidence intervals (CIs) for the desired set of parameters. Interestingly, we show that obtained CIs are dimension-free, as they do not grow with the alphabet size. Further, we show that our CIs are (almost) tight, in the sense that they cannot be further improved without violating the prescribed coverage rate. We demonstrate the performance of our proposed scheme in synthetic and real-world experiments, showing a significant improvement over alternatives. Finally, we apply our proposed scheme to large alphabet modeling. We introduce a novel simultaneous CI scheme for large alphabet distributions which outperforms currently known methods while maintaining the prescribed coverage rate.

Short Bio:

Dr. Amichai Painsky is an Assistant Professor at Tel Aviv University.  Amichai received his B.Sc. in EE from Tel Aviv University (2007), his Masters in EE from Princeton University (2009) and his Ph.D. in Statistics from Tel Aviv University (2016). Following his graduation, Amichai  spent two years as a Post Doctoral Fellow, jointly affiliated with the Israeli Center of Research Excellence (I-CORE) and the Signals, Information and Algorithms Lab at MIT. His research interests include statistical inference and learning, with an emphasis on high-dimensional and large scale problems.