Related papers: Minimax testing in a statistical inverse problem w…
In hypothesis testing, the phenomenon of label noise, in which hypothesis labels are switched at random, contaminates the likelihood functions. In this paper, we develop a new method to determine the decision rule when we do not have…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…
Given a set of incomplete observations, we study the nonparametric problem of testing whether data are Missing Completely At Random (MCAR). Our first contribution is to characterise precisely the set of alternatives that can be…
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…
We consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according…
We consider the problem of testing whether an unknown and arbitrary set $S \subseteq \mathbb{R}^n$ (given as a black-box membership oracle) is convex, versus $\varepsilon$-far from every convex set, under the standard Gaussian distribution.…
This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…
We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived…
Minimax decentralized detection is studied under two scenarios: with and without a fusion center when the source of uncertainty is the Bayesian prior. When there is no fusion center, the constraints in the network design are determined.…
This paper studies the off-policy evaluation problem, where one aims to estimate the value of a target policy based on a sample of observations collected by another policy. We first consider the multi-armed bandit case, establish a minimax…
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…
This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
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:…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
We obtain the minimax rate for a mean location model with a bounded star-shaped set $K \subseteq \mathbb{R}^n$ constraint on the mean, in an adversarially corrupted data setting with Gaussian noise. We assume an unknown fraction $\epsilon…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…
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…
Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using…