Related papers: ABS Methods and ABSPACK for Linear Systems and Opt…
Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability is limited when dealing with inconsistent systems or…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on…
Under-bagging (UB), which combines under-sampling and bagging, is a popular ensemble learning method for training classifiers on an imbalanced data. Using bagging to reduce the increased variance caused by the reduction in sample size due…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
Alternating Direction Method of Multipliers (ADMM) is a popular method for solving large-scale Machine Learning problems. Stochastic ADMM was proposed to reduce the per iteration computational complexity, which is more suitable for big data…
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
We present in this paper first-order alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most $O(1/\epsilon)$…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…
Augmented Lagrangian Method (ALM) combined with Burer-Monteiro (BM) factorization, dubbed ALM-BM, offers a powerful approach for solving large-scale low-rank semidefinite programs (SDPs). Despite its empirical success, the theoretical…
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…
A type of iterative orthogonally accumulated projection methods for solving linear system of equations are proposed in this paper. This type of methods are applications of accumulated projection(AP) technique proposed recently by authors.…
Computational implementations for solving systems of linear equations often rely on a one-size-fits-all approach based on LU decomposition of dense matrices stored in column-major format. Such solvers are typically implemented with the aid…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
Quantization and pruning are two effective Deep Neural Networks model compression methods. In this paper, we propose Automatic Prune Binarization (APB), a novel compression technique combining quantization with pruning. APB enhances the…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
This paper investigates the distributed computation of the well-known linear matrix equation in the form of $AXB = F$, with the matrices A, B, X, and F of appropriate dimensions, over multi-agent networks from an optimization perspective.…