<lb>We study statistical inference and robust solution methods for stochastic optimization prob-<lb>lems. We first develop an empirical likelihood framework for stochastic optimization. We show<lb>anâ€¦ (More)

Abstract Standard forms of coordinate and stochastic gradient methods do not adapt to structure in data; their good behavior under random sampling is predicated on uniformity in data. When gradientsâ€¦ (More)

We develop efficient solution methods for a robust empirical risk minimization problem designed to give calibrated confidence intervals on performance and provide optimal tradeoffs between bias andâ€¦ (More)

Neural networks are vulnerable to adversarial examples and researchers have proposed many<lb>heuristic attack and defense mechanisms. We take the principled view of distributionally ro-<lb>bustâ€¦ (More)

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading betweenâ€¦ (More)

We develop and analyze a robust stochastic optimization framework that learns a solution which is robust to perturbations in the underlying distribution. We formulate a convex procedure for theâ€¦ (More)

We study statistical inference of the rare event probability pm =<lb>P(Sm â‰¥ my) for fixed<lb>y > E[X] and Sm =<lb>âˆ‘n<lb>i=1Xi where Xiâ€™s are i.i.d. sub-exponential random variables. We con-<lb>siderâ€¦ (More)

Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens ofâ€¦ (More)

<lb>We study extensions of empirical likelihood where the log likelihood ratio is replaced with<lb>general f -divergences (which we call empirical divergences). First, we give a novel,â€¦ (More)