We present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. We present computational guarantees for the method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We apply our method to the low-rank…

A independent set in a graph is a set of vertices that have no edges between them. How large can a independent set be in a random d-regular graph? How large can it be if we are to construct it using a (possibly randomized) algorithm that is local in nature? We will discuss a notion…

We consider the problem of influence maximization in fixed networks, for both stochastic and adversarial contagion models. In the stochastic setting, nodes are infected in waves according to linear threshold or independent cascade models. We establish upper and lower bounds for the influence of a subset of nodes in the network, where the influence is…

Classical approaches to causal inference largely rely on the assumption of “lack of interference”, according to which the outcome of each individual does not depend on the treatment assigned to others. In many applications, however, including healthcare interventions in schools, online education, and design of online auctions and political campaigns on social media, assuming lack…

ixture models represent the superposition of statistical processes, and are natural in machine learning and statistics. In mixed regression, the relationship between input and output is given by one of possibly several different (noisy) linear functions. Thus the solution encodes a combinatorial selection problem, and hence computing it is difficult in the worst case. Even…