相关论文: Robust Hypothesis Testing with a Relative Entropy …

This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and…

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…

We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…

This paper primarily considers the robust estimation problem under Wasserstein distance constraints on the parameter and noise distributions in the linear measurement model with additive noise, which can be formulated as an…

Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018b), show that if the inputs are drawn from a…

This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and Type-II). Uncertainty classes based on…

Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper…

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a non-parametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability…

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…

Randomly censored survival data are frequently encountered in applied sciences including biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to…

Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…

In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…

We study the rigidity of the volume entropy for weighted word metrics on hyperbolic groups, building on a recent convexity result due to Cantrell-Tanaka. Using ideas from small cancellation theory, we give conditions under which a…