Related papers: Empirical risk minimization in inverse problems: E…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the tails of the losses used. Starting with…

In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes. We do so by extending the seminal works of Mendelson [Men15, Men18] on the analysis of ERM with…

This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…

We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give…

We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…

We consider in this paper a Gaussian sequence model of observations $Y_i$, $i\geq 1$ having mean (or signal) $\theta_i$ and variance $\sigma_i$ which is growing polynomially like $i^\gamma$, $\gamma >0$. This model describes a large panel…

The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…

This paper proposes a novel framework of aggregated intersection of regression functions, where the target parameter is obtained by averaging the minimum (or maximum) of a collection of regression functions over the covariate space. Such…

It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…

In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…

We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…

The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…

Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…

We consider the model $Z_i=X_i+\varepsilon_i$, for i.i.d. $X_i$'s and $\varepsilon_i$'s and independent sequences $(X_i)_{i\in{\mathbb{N}}}$ and $(\varepsilon_i)_{i\in{\mathbb{N}}}$. The density $f_{\varepsilon}$ of $\varepsilon_1$ is…

Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

Statistical learning methods typically assume that the training and test data originate from the same distribution, enabling effective risk minimization. However, real-world applications frequently involve distributional shifts, leading to…

We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…

We study a standard method of regularization by projections of the linear inverse problem $Y=Af+\epsilon$, where $\epsilon$ is a white Gaussian noise, and $A$ is a known compact operator with singular values converging to zero with…