First, we consider a two-party distributed hypothesis testing problem for correlated Gaussian random variables. For a d-dimensional random vector X and a scalar 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. Towards the end, we shall discuss briefly a streaming signal compression problem where access to samples is limited, and another recent work wherein we provide partial resolution to a 27-year-old conjecture regarding the capacity of queue channels by considering a limited form of feedback.
Bio: Sahasranand is currently a postdoctoral fellow at Telecom Paris. He has completed his PhD from ECE, IISc in 2022. His research interests include statistical inference, information theory, and signal processing.
