相关论文: Polynomial Linear Programming with Gaussian Belief…

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…

Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…

In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP are based on either of the following three principles:…

Gaussian Mixture Models (GMMs) commonly arise in communication systems, particularly in bilinear joint estimation and detection problems. Although the product of GMMs is still a GMM, as the number of factors increases, the number of…

This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…

This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting…

Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local measurements/observations are scattered over a wide…

The belief propagation (BP) algorithm is an efficient way to solve "inference" problems in graphical models, such as Bayesian networks and Markov random fields. The system-state probability distribution of CSMA wireless networks is a Markov…

In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…

In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…

Gaussian Belief Propagation (BP) algorithm is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density…

Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…

In this study, calculations necessary to solve the large scale linear programming problems in two operating systems, Linux and Windows 7 (Win), are compared using two different methods. Relying on the interior-point methods,…

Loopy Belief Propagation (LBP) is a widely used approximate inference algorithm in probabilistic graphical models, with applications in computer vision, error correction codes, protein folding, program analysis, etc. However, LBP faces…

In the context of inference with expectation constraints, we propose an approach based on the "loopy belief propagation" algorithm LBP, as a surrogate to an exact Markov Random Field MRF modelling. A prior information composed of…

Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…

The max-product {belief propagation} (BP) is a popular message-passing heuristic for approximating a maximum-a-posteriori (MAP) assignment in a joint distribution represented by a graphical model (GM). In the past years, it has been shown…

Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and…