PAC Mode Estimation using PPR Martingale Confidence Sequences

• URL: http://arxiv.org/abs/2109.05047v1
• Date: Fri, 10 Sep 2021 18:11:38 GMT
• Title: PAC Mode Estimation using PPR Martingale Confidence Sequences
• Authors: Shubham Anand Jain, Sanit Gupta, Denil Mehta, Inderjeet Jayakumar Nair, Rohan Shah, Jian Vora, Sushil Khyalia, Sourav Das, Vinay J. Ribeiro, Shivaram Kalyanakrishnan
• Abstract summary: We consider the problem of correctly identifying the mode of a discrete distribution $mathcalP$ with sufficiently high probability. We propose a generalisation to mode estimation, in which $mathcalP$ may take $K geq 2$ values. Our resulting stopping rule, denoted PPR-ME, is optimal in its sample complexity up to a logarithmic factor.
• Score: 5.623190096715942
• License: http://creativecommons.org/licenses/by/4.0/
• 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 according to $\mathcal{P}$. This problem reduces to the estimation of a single parameter when $\mathcal{P}$ has a support set of size $K = 2$. Noting the efficiency of prior-posterior-ratio (PPR) martingale confidence sequences for handling this special case, we propose a generalisation to mode estimation, in which $\mathcal{P}$ may take $K \geq 2$ values. We observe that the "one-versus-one" principle yields a more efficient generalisation than the "one-versus-rest" alternative. Our resulting stopping rule, denoted PPR-ME, is optimal in its sample complexity up to a logarithmic factor. Moreover, PPR-ME empirically outperforms several other competing approaches for mode estimation. We demonstrate the gains offered by PPR-ME in two practical applications: (1) sample-based forecasting of the winner in indirect election systems, and (2) efficient verification of smart contracts in permissionless blockchains.

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