Related papers: Multivariate convex regression: global risk bounds…

Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each…

The problem of constructing confidence sets that are adaptive in L^2-loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev…

Extending the results of Bellec, Lecu\'e and Tsybakov to the setting of sparse high-dimensional linear regression with unknown variance, we show that two estimators, the Square-Root Lasso and the Square-Root Slope can achieve the optimal…

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…

We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test…

The logistic loss function is often advocated in machine learning and statistics as a smooth and strictly convex surrogate for the 0-1 loss. In this paper we investigate the question of whether these smoothness and convexity properties make…

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…

This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…

Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature,…

This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the…

We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many…

We study the properties of nonparametric least squares regression using deep neural networks. We derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer of feedforward deep neural regression. Our error…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

Consider the heteroscedastic nonparametric regression model with random design \begin{align*} Y_i = f(X_i) + V^{1/2}(X_i)\varepsilon_i, \quad i=1,2,\ldots,n, \end{align*} with $f(\cdot)$ and $V(\cdot)$ $\alpha$- and $\beta$-H\"older smooth,…

We consider the problem of adversarial bandit convex optimization, that is, online learning over a sequence of arbitrary convex loss functions with only one function evaluation for each of them. While all previous works assume known and…

This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…