相关论文: A local greedy algorithm and higher order extensio…

This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs…

We give criteria for finding the greedy $\beta$-expansion for $1$ for families of Salem numbers that approach a given Pisot number. We show that these expansions are related to the greedy expansion under the Pisot base. This expands on the…

We present various estimates for the Lebesgue constants of the thresholding greedy algorithm, in the case of general bases in Banach spaces. We show the optimality of these estimates in some situations. Our results recover and slightly…

The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective…

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large…

The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively…

We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…

In this effort we introduce and analyze a novel reduced basis approach, used to construct an approximating subspace for a given set of data. Our technique, which we call the Natural Greedy Algorithm (NGA), is based on a recursive approach…

We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…

This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…

We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few…

Coalition formation explores how to partition a set of $n$ agents into disjoint coalitions according to their preferences. We consider a cardinal utility model with an additively separable aggregation of preferences and study the online…

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…

We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically…

In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…

Methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods which is based on the $\mathcal{K}_1(\mathbb{D})$-norm of the solution. We show that the…

Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…

Certain solutions of autonomous PDEs without any boundary conditions describing the spatiotemporal evolution of a dependent variable in an unbounded spatial domain can be characterised as a travelling wave moving with constant speed. In the…