Related papers: Robust Kullback-Leibler Divergence and Universal H…
For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal…
We study a variant of the simple hypothesis testing problem where observed samples do not necessarily come from either of the specified distributions, but rather from a close variant of them. In this setting, we require a test that is…
We consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternate hypothesis $Q$, and only $P$…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
We propose a simple robust hypothesis test that has the same sample complexity as that of the optimal Neyman-Pearson test up to constants, but robust to distribution perturbations under Hellinger distance. We discuss the applicability of…
In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…
We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original $H$-theorem hypotheses do not fit here and the…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
We examine the estimation of the Kullback-Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate continuous distributions. Our starting point is the maximum entropy principle for Shannon entropy: among all…
Data collection is a critical step in statistical inference and data science, and the goal of statistical experimental design (ED) is to find the data collection setup that can provide most information for the inference. In this work we…
We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
The following detection problem is studied, in which there are $M$ sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains $n$ independent and identically distributed (i.i.d.) continuous…
The Kullback-Leibler (KL) divergence is a fundamental equation of information theory that quantifies the proximity of two probability distributions. Although difficult to understand by examining the equation, an intuition and understanding…
This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…