Related papers: Sharp Bounds for Generalized Uniformity Testing
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 are interested in testing properties of distributions with systematically mislabeled samples. Our goal is to make decisions about unknown probability distributions, using a sample that has been collected by a confused collector, such as…
Within the machine learning community, the widely-used uniform convergence framework has been used to answer the question of how complex, over-parameterized models can generalize well to new data. This approach bounds the test error of the…
We consider the problem of $L_p$-testing of class of bounded derivative properties over hypergrid domain with points distributed according to some product distribution. This class includes monotonicity, the Lipschitz property,…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
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…
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…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the $L^p$-norm of the difference between an empirical distribution function and its least concave…
Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…
Recently Shah et al., 2020 pointed out the pitfalls of the simplicity bias - the tendency of gradient-based algorithms to learn simple models - which include the model's high sensitivity to small input perturbations, as well as sub-optimal…
In this paper we study the problem of testing of constrained samplers over high-dimensional distributions with $(\varepsilon,\eta,\delta)$ guarantees. Samplers are increasingly used in a wide range of safety-critical ML applications, and…
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…
We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…
This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…
We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…