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A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…

Optimization and Control · Mathematics 2021-04-07 S. Bellavia , G. Gurioli , B. Morini , Ph. L. Toint

We consider the nonparametric estimation of the value of a quadratic functional evaluated at the density of a strictly positive random variable $X$ based on an iid. sample from an observation $Y$ of $X$ corrupted by an independent…

Statistics Theory · Mathematics 2024-08-14 Bianca Neubert , Fabienne Comte , Jan Johannes

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…

Statistics Theory · Mathematics 2007-06-13 A. B. Tsybakov , S. A. van de Geer

We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give…

Statistics Theory · Mathematics 2009-09-30 Stéphane Gaïffas , Agathe Guilloux

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

Statistics Theory · Mathematics 2008-07-31 Jean-Michel Loubes , Carenne Ludeña

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our…

Statistics Theory · Mathematics 2009-03-02 Leif Boysen , Angela Kempe , Volkmar Liebscher , Axel Munk , Olaf Wittich

In this paper we introduce a new methodology to determine an optimal coefficient of penalized functional regression. We assume the dependent, independent variables and the regression coefficients are functions of time and error dynamics…

Methodology · Statistics 2021-07-07 Paramahansa Pramanik , Alan M. Polansky

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

Statistics Theory · Mathematics 2009-09-29 Jérémie Bigot , Rolando Biscay , Jean-Michel Loubes , Lilian Muniz Alvarez

Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…

Methodology · Statistics 2017-05-17 James P. Long

We address the problem of adaptive minimax density estimation on $\bR^d$ with $\bL_p$--loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters…

Statistics Theory · Mathematics 2013-06-19 A. Goldenshluger , O. Lepski

The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of…

Machine Learning · Computer Science 2025-11-05 Nimrod Megiddo , Segev Wasserkrug , Orit Davidovich , Shimrit Shtern

We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed…

Statistics Theory · Mathematics 2021-12-01 Sergio Brenner Miguel , Fabienne Comte , Jan Johannes

We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely…

Machine Learning · Statistics 2017-10-17 Liyuan Xu , Junya Honda , Masashi Sugiyama

When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable.…

Statistics Theory · Mathematics 2022-01-06 Kyungchul Song

We consider the problem of constructing a regression model with a functional predictor and a functional response. We extend the functional linear model to the quadratic model, where the quadratic term also takes the interaction between the…

Methodology · Statistics 2020-06-01 Hidetoshi Matsui

This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a…

Statistics Theory · Mathematics 2007-09-12 Enno Mammen , Kyusang Yu

Optimal estimation is a promising tool for estimation of payloads' inertial parameters and localization of robots in the presence of multiple contacts. To harness its advantages in robotics, it is crucial to solve these large and…

Robotics · Computer Science 2025-02-21 Sergi Martinez , Robert J. Griffin , Carlos Mastalli

Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…

Quantum Physics · Physics 2012-06-05 Christopher Ferrie , Christopher E. Granade , D. G. Cory

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…

Statistics Theory · Mathematics 2009-03-09 Marianna Pensky , Theofanis Sapatinas

Free-energy-based adaptive biasing methods, such as Metadynamics, the Adaptive Biasing Force (ABF) and their variants, are enhanced sampling algorithms widely used in molecular simulations. Although their efficiency has been empirically…

Probability · Mathematics 2026-01-29 Tony Lelièvre , Xuyang Lin , Pierre Monmarché