Related papers: Summability Methods for the Greedy Algorithm in Ba…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…
Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…
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…
We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First,…
We describe a greedy algorithm that approximates the Carleson constant of a collection of general sets. The approximation has a logarithmic loss in a general setting, but is optimal up to a constant with only mild geometric assumptions. The…
In this paper, for solving nonlinear systems we propose two pseudoinverse-free greedy block methods with momentum by combining the residual-based weighted nonlinear Kaczmarz and heavy ball methods. Without the full column rank assumptions…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: $(1)$ reduce the…
The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…
We study parallel algorithms for the problem of maximizing a non-negative submodular function. Our main result is an algorithm that achieves a nearly-optimal $1/2 -\epsilon$ approximation using $O(\log(1/\epsilon) / \epsilon)$ parallel…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
We investigate a Bayesian $k$-armed bandit problem in the \emph{many-armed} regime, where $k \geq \sqrt{T}$ and $T$ represents the time horizon. Initially, and aligned with recent literature on many-armed bandit problems, we observe that…
We show that, for quasi-greedy bases in Hilbert spaces, the associated conditionality constants grow at most as $O(\log N)^{1-\epsilon}$, for some $\epsilon>0$, answering a question by Temlyakov. We show the optimality of this bound with an…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a…
We continue the study initiated in [F. Albiac and P. Wojtaszczyk, Characterization of $1$-greedy bases, J. Approx. Theory 138 (2006), no. 1, 65-86] of properties related to greedy bases in the case when the constants involved are sharp,…
We consider the $X$-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in $L_p[0,1]$…
Greedy Sampling Methods (GSMs) are widely used to construct approximate solutions of Configuration Optimization Problems (COPs), where a loss functional is minimized over finite configurations of points in a compact domain. While effective…
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…
We use new methods, specific of non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$-Banach space for $0<p<1$ are democratic. The novel techniques we obtain permit to show in particular that all…
Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta…