Related papers: Towards Testing Monotonicity of Distributions Over…
Alon and Shapira proved that every monotone class (closed under taking subgraphs) of undirected graphs is strongly testable, that is, under the promise that a given graph is either in the class or $\varepsilon$-far from it, there is a test…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
The dimension of a partially ordered set $P$ (poset for short) is the least positive integer $d$ such that $P$ is isomorphic to a subposet of $\mathbb{R}^d$ with the natural product order. Dimension is arguably the most widely studied…
Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on…
We prove a lower bound of $\tilde{\Omega}(n^{1/3})$ for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is monotone or far from monotone. This…
The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion…
We revisit classic balancing problems for linear extensions of a partially ordered set $P$, proving results that go far beyond many of the best earlier results on this topic. For example, with $p(x\prec y)$ the probability that $x$ precedes…
In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…
In this paper, we consider several property testing problems and ask how the query complexity depends on the distance parameter $\eps$. We achieve new lower bounds in this setting for the problems of testing whether a function is monotone…
For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
We study the question of closeness testing for two discrete distributions. More precisely, given samples from two distributions $p$ and $q$ over an $n$-element set, we wish to distinguish whether $p=q$ versus $p$ is at least $\eps$-far from…
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
We show that for any constant $c>0$, any (two-sided error) adaptive algorithm for testing monotonicity of Boolean functions must have query complexity $\Omega(n^{1/2-c})$. This improves the $\tilde\Omega(n^{1/3})$ lower bound of [CWX17] and…
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…