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High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless p/n → 0, a line of recent work has studied models with various types of low-dimensional structure, including sparse vectors, sparse and(More)
We consider the matrix completion problem under a form of row/column weighted entrywise sampling , including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with high probability, it satisfies a form of restricted strong convexity with respect to weighted Frobenius norm. Using(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract We analyze a class of estimators based on convex relaxation for(More)
We study an instance of high-dimensional inference in which the goal is to estimate a matrix Θ * ∈ R m 1 ×m 2 on the basis of N noisy observations. The unknown matrix Θ * is assumed to be either exactly low rank, or " near " low-rank, meaning that it can be well-approximated by a matrix with low rank. We consider a standard M-estimator based on(More)
We propose a general framework for increasing local stability of Artificial Neural Nets (ANNs) using Robust Optimization (RO). We achieve this through an alternating minimization-maximization procedure, in which the loss of the network is minimized over perturbed examples that are generated at each parameter update. We show that adversarial training of ANNs(More)
The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR's TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining a(More)
Given a collection of r ≥ 2 linear regression problems in p dimensions, suppose that the regression coefficients share partially common supports. This setup suggests the use of 1 // ∞-regularized regression for joint estimation of the p × r matrix of regression coefficients. We analyze the high-dimensional scaling of 1 // ∞-regularized quadratic programming(More)