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In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population…
We present further developments of the auxiliary master equation approach (AMEA), a numerical method to simulate many-body quantum systems in as well as out of equilibrium, and apply it to the Interacting Resonant Level Model (IRLM) to…
We consider the problem of learning convex aggregation of models, that is as good as the best convex aggregation, for the binary classification problem. Working in the stream based active learning setting, where the active learner has to…
We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs…
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…
Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We study non-convex distributed optimization problems where a set of agents collaboratively solve a separable optimization problem that is distributed over a time-varying network. The existing methods to solve these problems rely on (at…