Tata Institute of Fundamental Research

The Optimal Approximation Factor in the Hypothesis Selection Problem

STCS Student Seminar
Speaker: Eeshan Modak (TIFR)
Organiser: Varun Ramanathan
Date: Friday, 3 Nov 2023, 16:00 to 17:30
Venue: A-201 (STCS Seminar Room)

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Abstract: 

Consider the following problem: Given a collection of probability distributions (q_1,...,q_n) and a sample access to an unknown target distribution p, find which q_i is closest to p in total variation. Turns out that this problem in general is not tractable. However, we can output a q_i such that TV(q_i,p) <= \beta OPT + \epsilon. Here OPT is the TV between p and best candidate in our collection.

In this talk, we will see that the approximation factor \beta has to be at least 3.

PS: If you attended Klim Efrimenko's talk then he cited this result but did not go into the proof.