相关论文: An Accelerated Newton-GMRES Method for Multilinear…

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…

Approximate nearest neighbor search (ANNS) is a fundamental problem in databases and data mining. A scalable ANNS algorithm should be both memory-efficient and fast. Some early graph-based approaches have shown attractive theoretical…

Deep learning and especially the use of Deep Neural Networks (DNNs) provides impressive results in various regression and classification tasks. However, to achieve these results, there is a high demand for computing and storing resources.…

Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it…

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Combinatorial Optimization problems are widespread in domains such as logistics, manufacturing, and drug discovery, yet their NP-hard nature makes them computationally challenging. Recent Neural Combinatorial Optimization methods leverage…

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…

Multiple network alignment is the problem of identifying similar and related regions in a given set of networks. While there are a large number of effective techniques for pairwise problems with two networks that scale in terms of edges,…

Deep Q-learning method is one of the most popularly used deep reinforcement learning algorithms which uses deep neural networks to approximate the estimation of the action-value function. Training of the deep Q-network (DQN) is usually…

We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi and Gauss-Seidel, or with Krylov methods, e.g., GMRES and…

We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…

Markov chains that describe interacting subsystems suffer, on the one hand, from state space explosion but lead, on the other hand, to highly structured matrices. In this work, we propose a novel tensor-based algorithm to address such…

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are…

Policy iteration enjoys a local quadratic rate of contraction, but its iterations are computationally expensive for Markov decision processes (MDPs) with a large number of states. In light of the connection between policy iteration and the…

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…

An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…