Related papers: Fast algorithm for computing nonlocal operators wi…
A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…
We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…
We propose a nonlocal operator method for solving partial differential equations (PDEs). The nonlocal operator is derived from the Taylor series expansion of the unknown field, and can be regarded as the integral form "equivalent" to the…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…
Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them…
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…
In this paper we discuss a well known computing problem -- inference for models with intractable normalizing functions. Models with intractable normalizing functions arise in a wide variety of areas, for instance network models, models for…
Peridynamic (PD) theory is significant and promising in engineering and materials science; however, it imposes challenges owing to the enormous computational cost caused by its nonlocality. Our main contribution, which overcomes the…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
High-order finite-difference methods are commonly used in wave propagators for industrial subsurface imaging algorithms. Computational aspects of the reduced linear elastic vertical transversely isotropic propagator are considered. Thread…