Related papers: Extensions of smoothing via taut strings

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…

We consider optimization algorithms that successively minimize simple Taylor-like models of the objective function. Methods of Gauss-Newton type for minimizing the composition of a convex function and a smooth map are common examples. Our…

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…

Let $X_1,\dots, X_n$ be i.i.d. random variables sampled from a normal distribution $N(\mu,\Sigma)$ in ${\mathbb R}^d$ with unknown parameter $\theta=(\mu,\Sigma)\in \Theta:={\mathbb R}^d\times {\mathcal C}_+^d,$ where ${\mathcal C}_+^d$ is…

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

In the context of global optimization of mixed-integer nonlinear optimization formulations, we consider smoothing univariate functions $f$ that satisfy $f(0)=0$, $f$ is increasing and concave on $[0,+\infty)$, $f$ is twice differentiable on…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…

The estimation of regression parameters in one dimensional broken stick models is a research area of statistics with an extensive literature. We are interested in extending such models by aiming to recover two or more intersecting…