Related papers: Exploring the Gap between Tolerant and Non-toleran…
We give nearly optimal bounds on the sample complexity of $(\widetilde{\Omega}(\epsilon),\epsilon)$-tolerant testing the $\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Determining whether an unknown distribution matches a known reference is a cornerstone problem in distributional analysis. While classical results establish a rigorous framework in the case of distributions over finite domains, real-world…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
We consider an acceptance-rejection sampler based on a deterministic driver sequence. The deterministic sequence is chosen such that the discrepancy between the empirical target distribution and the target distribution is small. We use…
We give the first tester-learner for halfspaces that succeeds universally over a wide class of structured distributions. Our universal tester-learner runs in fully polynomial time and has the following guarantee: the learner achieves error…
Out-of-distribution (OOD) detection aims to detect test samples outside the training category space, which is an essential component in building reliable machine learning systems. Existing reviews on OOD detection primarily focus on method…
Out-of-distribution (OOD) generalisation is considered a hallmark of human and animal intelligence. To achieve OOD through composition, a system must discover the environment-invariant properties of experienced input-output mappings and…
Given samples from two non-negative random variables, we propose a family of tests for the null hypothesis that one random variable stochastically dominates the other at the second order. Test statistics are obtained as functionals of the…
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…
With the rise of machine learning and deep learning based applications in practice, monitoring, i.e. verifying that these operate within specification, has become an important practical problem. An important aspect of this monitoring is to…
We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…
The relative-error property testing model was introduced in [CDHLNSY24] to facilitate the study of property testing for "sparse" Boolean-valued functions, i.e. ones for which only a small fraction of all input assignments satisfy the…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…