JProf David Gross

Abstract:
Our quantum physics group has worked on various data analysis projects over the past years. In some cases, because ever-larger quantum experiments call for non-trivial statistical tools. Mainly, however, because methods developed in mathematical physics proved well-suited to tackle certain ill-defined estimation problems. I will touch on the following topics: 1) Our main contribution has been the introduction of greatly simplified proof techniques for the theory of low-rank matrix recovery - a matrix-analogue of compressed sensing. 2) Phase retrieval is the problem of recovering a signal from quadratic measurements. In 2012 new, randomized, algorithms for this problem have been introduced (partly building on our low-rank methods). Very recently, we have described a partial de-randomization based on quantum information ideas. 3) A novel line of research within the group concerns methods for causal inference from information-theoretic data. While the initial motivation stemmed from quantum non-locality problems, we are investigating applications to classical statistics.

References:
Low-rank recovery: http://arxiv.org/abs/0910.1879
Phase retrieval: http://arxiv.org/abs/1310.2267
Causal inference: http://arxiv.org/abs/1310.0284
Physics applications: http://arxiv.org/abs/1205.2300