Acharya, J and Canonne, CL and Tyagi, H (2020) Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction. In: IEEE Transactions on Information Theory, 66 (12). pp. 7835-7855.
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Abstract
Multiple players are each given one independent sample, about which they can only provide limited information to a central referee. Each player is allowed to describe its observed sample to the referee using a channel from a family of channels \mathcal W , which can be instantiated to capture, among others, both the communication- and privacy-constrained settings. The referee uses the players' messages to solve an inference problem on the unknown distribution that generated the samples. We derive lower bounds for the sample complexity of learning and testing discrete distributions in this information-constrained setting. Underlying our bounds is a characterization of the contraction in chi-square distance between the observed distributions of the samples when information constraints are placed. This contraction is captured in a local neighborhood in terms of chi-square and decoupled chi-square fluctuations of a given channel, two quantities we introduce. The former captures the average distance between distributions of channel output for two product distributions on the input, and the latter for a product distribution and a mixture of product distribution on the input. Our bounds are tight for both public- and private-coin protocols. Interestingly, the sample complexity of testing is order-wise higher when restricted to private-coin protocols. © 1963-2012 IEEE.
| Item Type: | Journal Article |
|---|---|
| Publication: | IEEE Transactions on Information Theory |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to the Author(S). |
| Keywords: | Information theory, Chi Square distance; Discrete distribution; Independent samples; Inference problem; Limited information; Local neighborhoods; Product distributions; Sample complexity, Computer applications |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems |
| Date Deposited: | 10 Jan 2023 05:08 |
| Last Modified: | 10 Jan 2023 05:08 |
| URI: | https://eprints.iisc.ac.in/id/eprint/78971 |
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