Related papers: Exponentially Consistent Statistical Classificatio…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different…
Machine learning has achieved tremendous success in a variety of domains in recent years. However, a lot of these success stories have been in places where the training and the testing distributions are extremely similar to each other. In…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
Several approaches to testing the hypothesis that two histograms are drawn from the same distribution are investigated. We note that single-sample continuous distribution tests may be adapted to this two-sample grouped data situation. The…
We provide the first convergence guarantees for the Consistency Models (CMs), a newly emerging type of one-step generative models that can generate comparable samples to those generated by Diffusion Models. Our main result is that, under…
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…
Suppose that we have two training sequences generated by parametrized distributions $P_{\theta^*}$ and $P_{\xi^*}$, where $\theta^*$ and $\xi^*$ are unknown true parameters. Given training sequences, we study the problem of classifying…
In this paper, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
We revisit $M$-ary classification of Gutman (TIT 1989), where one is tasked to determine whether a testing sequence is generated with the same distribution as one of the $M$ training sequences or not. Our main result is a two-phase test,…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple…
A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…
Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are…