Related papers: Greedy Rational Approximation for Frequency-Domain…
Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels…
In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…
This paper addresses resource allocation problem with a separable objective function under a single linear constraint, formulated as maximizing $\sum_{j=1}^{n}R_j(x_j)$ subject to $\sum_{j=1}^{n}x_j=k$ and $x_j\in\{0,\dots,m\}$. While…
Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$. One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on…
Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…
Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…
Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems…
Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…
We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple,…
In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…
We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end,…
Morphing attacks are an emerging threat to state-of-the-art Face Recognition (FR) systems, which aim to create a single image that contains the biometric information of multiple identities. Diffusion Morphs (DiM) are a recently proposed…
Slang interpretation has been a challenging downstream task for Large Language Models (LLMs) as the expressions are inherently embedded in contextual, cultural, and linguistic frameworks. In the absence of domain-specific training data, it…
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…
Greedy-GQ is an off-policy two timescale algorithm for optimal control in reinforcement learning. This paper develops the first finite-sample analysis for the Greedy-GQ algorithm with linear function approximation under Markovian noise. Our…
Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…
Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…
In a standard NP-complete optimization problem we introduce an interpolating algorithm between the quick decrease along the gradient (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that for a…