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Activity Number:
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146
- Statistical Physics, Information Theory, and Statistics
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Type:
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Invited
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Date/Time:
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Monday, July 30, 2018 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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Abstract #327031
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Title:
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Covering Probability Simplex with Divergence Balls
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Author(s):
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Yuri Polyanskiy*
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Companies:
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MIT
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Keywords:
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Abstract:
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We discuss a question of covering a (large-dimensional) probability simplex with a net of M points $Q_j, j \in [M]$ such that for any distribution $P$ there exists a $Q_j$ with $D(P||Q_j)\le \epsilon$, where $D$ is the Kullback-Leibler divergence. Depending on $\epsilon$ the number $M$ scales exponentially or polynomially in dimension. We prove upper and lower bounds on the minimal required $M$. Applications in data-driven universal compression and prediction are discussed. Joint work with M. Feder, J. Tang and Y. Wu.
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Authors who are presenting talks have a * after their name.
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