Abstract: We study the problem of certification: given queries to an n-variable boolean function f with certificate complexity k and an input x, output a size-k certificate for f's value on x. This abstractly models a problem of interest in explainable machine learning, where we think of f as a blackbox model that we seek to explain the predictions of. For monotone functions, classic algorithms of Valiant and Angluin accomplish this task with n queries to f. Our main result is…

Abstract: The development of CRISPR-based assays and small molecule screens holds the promise of engineering precise cell state transitions to move cells from one cell type to another or from a diseased state to a healthy state. The main bottleneck is the huge space of possible perturbations/interventions, where even with the breathtaking technological advances in single-cell biology it will never be possible to experimentally perturb all combinations of thousands of genes or compounds. This important biological problem calls for a…

Abstract:  Many new random matrix ensembles arise in learning and modern signal processing. As shown in recent studies, the spectral properties of these matrices help answer crucial questions regarding the training and generalization performance of neural networks, and the fundamental limits of high-dimensional signal recovery. As a result, there has been growing interest in precisely understanding the spectra and other asymptotic properties of these matrices. Unlike their classical counterparts, these new random matrices are often highly structured and are the…