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The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
We investigate the performance of distributed least-mean square (LMS) algorithms for parameter estimation over sensor networks where the regression data of each node are corrupted by white measurement noise. Under this condition, we show…
Imbalanced problems can arise in different real-world situations, and to address this, certain strategies in the form of resampling or balancing algorithms are proposed. This issue has largely been studied in the context of classification,…
Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and…
We propose a learning-based approach for estimating the spectrum of a multisinusoidal signal from a finite number of samples. A neural-network is trained to approximate the spectra of such signals on simulated data. The proposed methodology…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
We discuss techniques of estimation and inference for nonstationary nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator used in…
The logistic regression estimator is known to inflate the magnitude of its coefficients if the sample size $n$ is small, the dimension $p$ is (moderately) large or the signal-to-noise ratio $1/\sigma$ is large (probabilities of observing a…
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…
Is it possible to perform linear regression on datasets whose labels are shuffled with respect to the inputs? We explore this question by proposing several estimators that recover the weights of a noisy linear model from labels that are…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…