Related papers: An Information Theoretic Analysis of Sequential De…
A nonparametric variant of the Kiefer--Weiss problem is proposed and investigated. In analogy to the classical Kiefer--Weiss problem, the objective is to minimize the maximum expected sample size of a sequential test. However, instead of…
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 propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these…
Information-theoretic generalization bounds based on the supersample construction are a central tool for algorithm-dependent generalization analysis in the batch i.i.d.~setting. However, existing supersample conditional mutual information…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses.…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic,…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
We propose a new, simple, and computationally inexpensive termination test for constant step-size stochastic gradient descent (SGD) applied to binary classification on the logistic and hinge loss with homogeneous linear predictors. Our…
New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do…