相关论文: Lebesgue inequalities for the greedy algorithm in …

We introduce the notion of a \textit{weight-almost greedy} basis and show that a basis for a real Banach space is $w$-almost greedy if and only if it is both quasi-greedy and $w$-democratic. We also introduce the notion of…

We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control…

In this paper we prove that there exists a function which $f(x)$ belongs to $L^1[0,1]$ such that a greedy algorithm with regard to the Walsh subsystem does not converge to $f(x)$ in $L^1[0,1]$ norm, i.e. the Walsh subsystem $\{W_{n_k}\}$ is…

The main results in this paper contribute to bring to the fore novel underlying connections between the contemporary concepts and methods springing from greedy approximation theory with the well established techniques of classical Banach…

Several recent deep neural networks experiments leverage the generalist-specialist paradigm for classification. However, no formal study compared the performance of different clustering algorithms for class assignment. In this paper we…

The main focus of this article is to provide a mathematical study of the algorithm proposed in \cite{boyaval2010variance} where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations…

We derive the non-improvable Grand Lebesgue Space norm estimations for multivariate and multidimensional operator of infimal convolution.

We establish the existence of a quantum lift of the greedy basis.

Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…

In this paper we analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special incoherence property. We apply a powerful nonlinear approximation method -- the Weak…

We analyze greedy algorithms for the Hierarchical Aggregation (HAG) problem, a strategy introduced in [Jia et al., KDD 2020] for speeding up learning on Graph Neural Networks (GNNs). The idea of HAG is to identify and remove redundancies in…

Identifying the structure of a partially observed causal system is essential to various scientific fields. Recent advances have focused on constraint-based causal discovery to solve this problem, and yet in practice these methods often face…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…

This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…

We consider the influence maximization problem (selecting $k$ seeds in a network maximizing the expected total influence) on undirected graphs under the linear threshold model. On the one hand, we prove that the greedy algorithm always…

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…

We perform an experimental study of algorithms for online bipartite matching under the known i.i.d. input model with integral types. In the last decade, there has been substantial effort in designing complex algorithms with the goal of…

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…

In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…

We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…