Related papers: Minimax rates without the fixed sample size assump…

Practitioners often use data from a randomized controlled trial to learn a treatment assignment policy that can be deployed on a target population. A recurring concern in doing so is that, even if the randomized trial was well-executed…

For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…

We obtain estimation error rates for estimators obtained by aggregation of regularized median-of-means tests, following a construction of Le Cam. The results hold with exponentially large probability -- as in the gaussian framework with…

The underlying assumption of many machine learning algorithms is that the training data and test data are drawn from the same distributions. However, the assumption is often violated in real world due to the sample selection bias between…

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss of the predictor on the next point conditioned on the set…

Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms.…

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that…

This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…

Representations of data that are invariant to changes in specified factors are useful for a wide range of problems: removing potential biases in prediction problems, controlling the effects of covariates, and disentangling meaningful…

We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…

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…

Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…

In practice, there are often explicit constraints on what representations or decisions are acceptable in an application of machine learning. For example it may be a legal requirement that a decision must not favour a particular group.…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…

Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…

Supervised classification techniques use training samples to learn a classification rule with small expected 0-1 loss (error probability). Conventional methods enable tractable learning and provide out-of-sample generalization by using…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…