Lecture Announcement
Date: Wednesday, June 1, 2022 Time: 11:45 am.
Venue: CMI seminar Hall
PAC Mode Estimation using PPR Martingale Confidence Sequences
Shivaram Kalyanakrishnan
IIT Mumbai.
01-06-22

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Abstract

We consider the problem of correctly identifying the MODE of a discrete distribution $\mathcal{P}$ with sufficiently high probability by observing a sequence of i.i.d. samples drawn from $\mathcal{P}$. This problem reduces to the estimation of a single parameter when $\mathcal{P}$ has a support set of size K = 2. After noting that this special case is tackled very well by prior-posterior-ratio (PPR) martingale confidence sequences (Waudby-Smith and Ramdas, 2020), we propose a generalisation to mode estimation, in which $\mathcal{P}$ may take K >= 2 values. To begin, we show that the "one-versus-one" principle to generalise from K = 2 to K > 2 classes is more efficient than the "one-versus-rest” alternative. We then prove that our resulting stopping rule, denoted PPR-1v1, is asymptotically optimal (as the mistake probability is taken to $0$). PPR-1v1 is parameter-free and computationally light, and incurs significantly fewer samples than competitors even in the non-asymptotic regime. We demonstrate its gains in two practical applications of sampling: election forecasting and verification of smart contracts in blockchains.