Matthew Brennan

TL;DR: Detailed studies of cellular biochemistry at the single-cell level now show that cells responding en masse may have quite varied behaviors when examined individually, raising the question of how precisely signaling pathways can control a cell's actions.

TL;DR: In this paper, a set of techniques for average-case reductions are introduced to maintain the level of signal in an instance of a problem, alter its planted structure, and map two initial high-dimensional distributions simultaneously to two target distributions approximately under total variation.

TL;DR: This work gives the first evidence that an expanded set of hardness assumptions, such as for secret leakage planted clique, may be a key first step towards a more complete theory of reductions among statistical problems.

TL;DR: This paper studies two of the most popular restricted computational models, the statistical query framework and low-degree polynomials, in the context of high-dimensional hypothesis testing, and finds that under mild conditions on the testing problem, the two classes of algorithms are essentially equivalent in power.