相关论文: Another view of the Gaussian algorithm

Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…

We consider a class of multivariate recurrences frequently arising in the worst case analysis of Davis-Putnam-style exponential time backtracking algorithms for NP-hard problems. We describe a technique for proving asymptotic upper bounds…

While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function…

The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…

We introduce a framework generalizing lattice reduction algorithms to module lattices in order to practically and efficiently solve the $\gamma$-Hermite Module-SVP problem over arbitrary cyclotomic fields. The core idea is to exploit the…

Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…

This work presents a novel lattice-based methodology for incorporating multidimensional constraints into continuous decision variables within a genetic algorithm (GA) framework. The proposed approach consolidates established transcription…

The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for these ensembles the BDD problem is NP-hard in the worst case.…

It is known that circularly symmetric Gaussian signals are the optimal input signals for the partial decode-and-forward (PDF) coding scheme in the Gaussian multiple-input multiple-output (MIMO) relay channel, but there is currently no…

Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the…

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…

Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…

Consider the setting where a $\rho$-sparse Rademacher vector is planted in a random $d$-dimensional subspace of $R^n$. A classical question is how to recover this planted vector given a random basis in this subspace. A recent result by…

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

We give a deterministic algorithm for solving the (1+eps)-approximate Closest Vector Problem (CVP) on any n dimensional lattice and any norm in 2^{O(n)}(1+1/eps)^n time and 2^n poly(n) space. Our algorithm builds on the lattice point…

Assume that f is a strict convex function with a unique minimum in R^n. We divide the vector of n-variables to d groups of vector subvariables with d at least two. We assume that we can find the partial minimum of f with respect to each…

A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…