Related papers: Adaptive testing on a regression function at a poi…

Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of…

Optimization in engineering requires appropriate models. In this article, a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity…

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…

Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…

We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…

A class of estimating functions is introduced for the regression parameter of the Cox proportional hazards model to allow unknown failure statuses on some study subjects. The consistency and asymptotic normality of the resulting estimators…

We study the approximation capacity of deep ReLU recurrent neural networks (RNNs) and explore the convergence properties of nonparametric least squares regression using RNNs. We derive upper bounds on the approximation error of RNNs for…

Given a dictionary of $M_n$ initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse $q$-norm ($0 \leq q…

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…

For a given domain $\Omega \subset \Bbb{R}^n$, we consider the variational problem of minimizing the $L^1$-norm of the gradient on $\Omega$ of a function $u$ with prescribed continuous boundary values and satisfying a continuous lower…

We study in-context learning for nonparametric regression with $\alpha$-H\"older smooth regression functions, for some $\alpha>0$. We prove that, with $n$ in-context examples and $d$-dimensional regression covariates, a pretrained…

We estimate convex polytopes and general convex sets in $\mathbb R^d,d\geq 2$ in the regression framework. We measure the risk of our estimators using a $L^1$-type loss function and prove upper bounds on these risks. We show that, in the…

We show that every algorithm for testing $n$-variate Boolean functions for monotonicity must have query complexity $\tilde{\Omega}(n^{1/4})$. All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a…

This paper studies the statistical theory of batch data reinforcement learning with function approximation. Consider the off-policy evaluation problem, which is to estimate the cumulative value of a new target policy from logged history…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

For linear time-invariant systems having a state matrix with uncertain sign, we formulate a minimax adaptive control problem as a zero sum dynamic game. Explicit expressions for the optimal value function and the optimal control law are…

Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks. Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test…