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Title: Hypothesis Testing under Communication Constraints
Speaker: Ankit Pensia
Abstract: Simple hypothesis testing is a fundamental problem in statistics and it is well-known that its sample complexity is characterized by the Hellinger distance between the two candidate distributions. In this talk, we discuss the problem of simple hypothesis testing under communication constraints, wherein each sample is mapped to a message from a finite set of messages before being revealed to the statistician. We show that it is possible to map samples to messages such that the sample complexity is only an extra logarithmic factor larger than the non-constrained setting. Our proofs rely on a reverse data processing inequality and a reverse Markov’s inequality, which might be of independent interest. This is joint work with Po-Ling Loh and Varun Jog.
Bio: Ankit Pensia is a graduate student in the CS department. He is interested in robust statistics, learning theory, and high-dimensional statistics. Website: https://ankitp.net

Title: Streaming Algorithms for High-Dimensional Robust Statistics
Speaker: Thanasis Pittas
Abstract: We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust statistics tasks. Unfortunately, all previous algorithms require storing the entire dataset, incurring memory at least quadratic in the dimension. In this work, we develop the first efficient streaming algorithms for high-dimensional robust statistics with near-optimal memory requirements (up to logarithmic factors). Our main result is for the task of high-dimensional robust mean estimation in (a strengthening of) Huber’s contamination model. We give an efficient single-pass streaming algorithm for this task with near-optimal error guarantees and space complexity nearly-linear in the dimension. As a corollary, we obtain streaming algorithms with near-optimal space complexity for several more complex tasks, including robust covariance estimation, robust regression, and more generally robust stochastic optimization.
Bio: Thanasis Pittas is a PhD student at the University of Wisconsin-Madison, advised by Prof. Ilias Diakonikolas. He works on theoretical machine learning and robust statistics. Thanasis was an IFDS RA during the summer of 2021. He did his undergraduate studies in Greece, at the National Technical University of Athens.

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