skip to main content

Search for: All records

Award ID contains: 2008868

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Uniformity testing is one of the most well-studied problems in property testing, with many known test statistics, including ones based on counting collisions, singletons, and the empirical TV distance. It is known that the optimal sample complexity to distinguish the uniform distribution on m elements from any ϵ-far distribution with 1−δ probability is n=Θ(mlog(1/δ)√ϵ2+log(1/δ)ϵ2), which is achieved by the empirical TV tester. Yet in simulation, these theoretical analyses are misleading: in many cases, they do not correctly rank order the performance of existing testers, even in an asymptotic regime of all parameters tending to 0 or ∞. We explain this discrepancy by studying the \emph{constant factors} required by the algorithms. We show that the collisions tester achieves a sharp maximal constant in the number of standard deviations of separation between uniform and non-uniform inputs. We then introduce a new tester based on the Huber loss, and show that it not only matches this separation, but also has tails corresponding to a Gaussian with this separation. This leads to a sample complexity of (1+o(1))mlog(1/δ)√ϵ2 in the regime where this term is dominant, unlike all other existing testers. 
    more » « less
  2. The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deepgenerative priors can be powerful tools for solving inverse problems.However, to date this framework has been empirically successful only oncertain datasets (for example, human faces and MNIST digits), and itis known to perform poorly on out-of-distribution samples. In thispaper, we present the first successful application of the CSGMframework on clinical MRI data. We train a generative prior on brainscans from the fastMRI dataset, and show that posterior sampling viaLangevin dynamics achieves high quality reconstructions. Furthermore,our experiments and theory show that posterior sampling is robust tochanges in the ground-truth distribution and measurement process.Our code and models are available at: \url{}. 
    more » « less