相关论文: Reducing numerical work in non-linear parameter id…

We consider the problem of noiseless and noisy low-rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

In this paper, we focus on regression estimation in both the inductive and the transductive case. We assume that we are given a set of features (which can be a base of functions, but not necessarily). We begin by giving a deviation…

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

Few-shot learning is a relatively new technique that specializes in problems where we have little amounts of data. The goal of these methods is to classify categories that have not been seen before with just a handful of samples. Recent…

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

We introduce a new fundamental algorithm called Matrix-POAFD to solve the matrix least square problem. The method is based on the matching pursuit principle. The method directly extracts, among the given features as column vectors of the…

We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are…

The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks…

This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…

A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional…

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…

Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal…

We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…