Related papers: Optimal solutions to the isotonic regression probl…

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…

We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…

In this paper we deal with the regression problem in a random design setting. We investigate asymptotic optimality under minimax point of view of various Bayesian rules based on warped wavelets and show that they nearly attain optimal…

We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the…

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

We consider the $[0,1]$-valued regression problem in the i.i.d. setting. In a related problem called cost-sensitive classification, \citet{foster21efficient} have shown that the log loss minimizer achieves an improved generalization bound…

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…

A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…

In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some…

We consider a misspecified optimization problem that requires minimizing a function f(x;q*) over a closed and convex set X where q* is an unknown vector of parameters that may be learnt by a parallel learning process. In this context, We…

In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…

In many real-world applications of machine learning classifiers, it is essential to predict the probability of an example belonging to a particular class. This paper proposes a simple technique for predicting probabilities based on…

The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…

We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…