Related papers: Convolution quadratures based on block generalized…

Deep neural networks have recently achieved state of the art performance thanks to new training algorithms for rapid parameter estimation and new regularization methods to reduce overfitting. However, in practice the network architecture…

The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held…

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…

In this paper we propose a distributed version of a randomized block-coordinate descent method for minimizing the sum of a partially separable smooth convex function and a fully separable non-smooth convex function. Under the assumption of…

We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the…

Recent several years have witnessed the surge of asynchronous (async-) parallel computing methods due to the extremely big data involved in many modern applications and also the advancement of multi-core machines and computer clusters. In…

We analyze the convergence rate of the randomized Newton-like method introduced by Qu et. al. (2016) for smooth and convex objectives, which uses random coordinate blocks of a Hessian-over-approximation matrix $\bM$ instead of the true…

There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…

The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature,…

In this paper, we establish the convergence of the proximal alternating direction method of multipliers (ADMM) and block coordinate descent (BCD) for nonseparable minimization models with quadratic coupling terms. The novel convergence…

A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial…

We discuss an elementary method for the evaluation of the convolution sums $\underset{\substack{ {(l,m)\in\mathbb{N}_{0}^{2}} \\ {\alpha\,l+\beta\,m=n} } }{\sum}\sigma(l)\sigma(m)$ for those $\alpha,\beta\in\mathbb{N}$ for which…

Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…

Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the…

In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…

This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Runge-Kutta method with repeated randomized low-rank…