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Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform ...
We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...
Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...
The currently adopted practice for uncertainty quantification of thermal-hydraulics code predictions is done through statistical sampling where the code is evaluated multiple times using different values of input parameters that are randomly generated acco ...
This work derives and analyzes an online learning strategy for tracking the average of time-varying distributed signals by relying on randomized coordinate-descent updates. During each iteration, each agent selects or observes a random entry of the observa ...
Inspired by the BBM formula and by work of G. Leoni and D. Spector, we analyze the asymptotic behavior of two sequences of convex nonlocal functionals (Psi(n)(u)) and (Phi(n)(u)) which converge formally to the BV-norm of u. We show that pointwise convergen ...
In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...
We present a new information-theoretic result which we call the Chaining Lemma. It considers a so-called "chain" of random variables, defined by a source distribution X-(0) with high min-entropy and a number (say, t in total) of arbitrary functions (T-1,.. ...
We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomi ...
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...
