Related papers: Minimax rates without the fixed sample size assump…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than $n^{-1/2}$. The work on this subject has suggested…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, i.e., the rates faster than $n^{-1/2}$. The works on this subject suggested…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…
We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is…
Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…
We consider the classical problem of learning rates for classes with finite VC dimension. It is well known that fast learning rates up to $O\left(\frac{d}{n}\right)$ are achievable by the empirical risk minimization algorithm (ERM) if low…
There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in…
Machine learning models are often susceptible to adversarial perturbations of their inputs. Even small perturbations can cause state-of-the-art classifiers with high "standard" accuracy to produce an incorrect prediction with high…
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between…
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…
We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…
The empirical Orlicz norm based on a random sample is defined as a natural estimator of the Orlicz norm of a univariate probability distribution. A law of large numbers is derived under minimal assumptions. The latter extends readily to a…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
A rich line of recent work has studied distributionally robust learning approaches that seek to learn a hypothesis that performs well, in the worst-case, on many different distributions over a population. We argue that although the most…
Consider a setup in which a decision maker is informed about the population by a finite sample and based on that sample has to decide whether or not to apply a certain treatment. We work out finite sample minimax regret treatment rules…
The concept of a minimax classifier is well-established in statistical decision theory, but its implementation via neural networks remains challenging, particularly in scenarios with imbalanced training data having a limited number of…