Related papers: Testing Shape Restrictions of Discrete Distributio…
In this paper, we study learning and testing decision tree of size and depth that are significantly smaller than the number of attributes $n$. Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms with…
For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on…
We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…
The Huge Object model is a distribution testing model in which we are given access to independent samples from an unknown distribution over the set of strings $\{0,1\}^n$, but are only allowed to query a few bits from the samples. We…
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,…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…
We construct a universally Bayes consistent learning rule that satisfies differential privacy (DP). We first handle the setting of binary classification and then extend our rule to the more general setting of density estimation (with…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…
Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…
Probabilistic model checking traditionally verifies properties on the expected value of a measure of interest. This restriction may fail to capture the quality of service of a significant proportion of a system's runs, especially when the…
We propose the test for distinguishing between two classes of distribution tails using only the largest order statistics of the sample and state its consistency. We do not assume belonging the corresponding distribution functions to any…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…
Many algorithms have been developed to estimate probability distributions subject to differential privacy (DP): such an algorithm takes as input independent samples from a distribution and estimates the density function in a way that is…