Related papers: Minimax separation of the Cauchy kernel

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration a) the orthogonal projection of a signal onto a reduced subspace and b) the index…

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The separable approximation exploits intrinsic decaying sensitivity…

Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…

We consider in this paper the optimal approximations of convex univariate functions with feed-forward Relu neural networks. We are interested in the following question: what is the minimal approximation error given the number of…

A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…

Low-rank decompositions to reduce the Coulomb operator to a pairwise form suitable for its quantum simulation are well-known in quantum chemistry, where the underlying basis functions are real-valued. We generalize the result of Motta…

Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…

We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

The need to compute small con-eigenvalues and the associated con-eigenvectors of positive-definite Cauchy matrices naturally arises when constructing rational approximations with a (near) optimally small $L^{\infty}$ error. Specifically,…

We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the…

This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…