Sahasranand, KR and Tyagi, H (2021) Communication Complexity of Distributed High Dimensional Correlation Testing. In: IEEE Transactions on Information Theory, 67 (9). pp. 6082-6095.
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Abstract
We consider a two-party distributed hypothesis testing problem for correlated Gaussian random variables. For a d -dimensional random vector X and a scalar random variable Y , where X and Y are jointly Gaussian with an unknown correlation vector rho , parties {mathcal P}{1} and {mathcal P}{2} observe independent copies of X and Y , respectively. The parties seek to test if their observations are correlated or not, namely they seek to test if |rho |{2} exceeds tau or is it 0. To that end, they communicate interactively and declare the test output. We show that roughly order d/tau {2} bits of communication are sufficient and necessary for resolving the distributed correlation testing problem above. Furthermore, we establish a lower bound of roughly d{2}/tau {2} bits for the communication needed for distributed estimation of rho , implying that distributed correlation testing requires less communication than distributed estimation. Both our lower bounds for testing and estimation hold for an arbitrary d and interactive communication with shared randomness, while our distributed test requires only one-way communication with shared randomness. For the one-dimensional case, with one-way communication and with probability of one of the error-types fixed, our bounds are more refined in the dependence on the other error-type and are tight even in the constant.
| 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 Authors. |
| Keywords: | Random processes; Random variables, Communication complexity; Correlated Gaussian random variables; Correlation vectors; Distributed estimation; Distributed hypothesis testing; High-dimensional; Interactive communications; Random vectors, Block codes |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 15 May 2023 09:56 |
| Last Modified: | 15 May 2023 09:56 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81648 |
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