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A Near-Optimal Adaptive Algorithm for Estimating Binary Mixtures of Unknown Coins

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If you have a question about this talk, please contact Dr Thomas Sauerwald.

Given a mixture between two populations of coins: “positive” coins that have (unknown and potentially different) probabilities of heads at least 1/2+Δ and “negative” coins with probabilities at most 1/2-Δ, we consider the task of estimating the fraction ρ of coins of each type to within additive error ε, with a constant probability of success.

In this talk, we will focus on the construction of an algorithm with sample complexity O((ρ/ε²Δ²)(1+ρ log 1/ε)), which matches the fully-adaptive lower bound of Ω(ρ/ε²Δ²) shown in our paper, except for the regime where ρ = ω(1/log 1/ε).

The fine-grained adaptive flavour of both our algorithm and lower bound contrasts with much previous work in distributional testing and learning.

Joint work with Paul Valiant, available on arXiv at https://arxiv.org/abs/1904.09228

This talk is part of the Cambridge Algorithms talks series.

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