Related papers: Junta correlation is testable
A family of permutations $\mathcal{F} \subset S_{n}$ is said to be $t$-intersecting if any two permutations in $\mathcal{F}$ agree on at least $t$ points. It is said to be $(t-1)$-intersection-free if no two permutations in $\mathcal{F}$…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
We show a procedure that, given oracle access to a function $f\colon \{0,1\}^n\to\{0,1\}$, produces oracle access to a function $f'\colon \{0,1\}^{n'}\to\{0,1\}$ such that if $f$ is monotone, then $f'$ is monotone, and if $f$ is…
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been…
Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…
Uniformity testing is arguably one of the most fundamental distribution testing problems. Given sample access to an unknown distribution $\mathbf{p}$ on $[n]$, one must decide if $\mathbf{p}$ is uniform or $\varepsilon$-far from uniform (in…
Inspired by the classic problem of Boolean function monotonicity testing, we investigate the testability of other well-studied properties of combinatorial finite set systems, specifically \emph{intersecting} families and \emph{union-closed}…
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…
Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting where the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ with a certain property P and reject…
Standard Quantum Physics states that the outcome of measurements for some distant entangled subsystems are instantaneously statistically correlated, whatever their mutual distance. This correlation presents itself as if there were a…
We study the computational complexity of several problems connected with finding a maximal distance-$k$ matching of minimum cardinality or minimum weight in a given graph. We introduce the class of $k$-equimatchable graphs which is an edge…
Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
We consider the problem of enumerating relevant features hidden in other irrelevant information for multi-labeled data, which is formalized as learning juntas. A $k$-junta function is a function which depends on only $k$ coordinates of the…
The sensitivity conjecture which claims that the sensitivity complexity is polynomially related to block sensitivity complexity, is one of the most important and challenging problem in decision tree complexity theory. Despite of a lot of…
We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all…
A set family ${\cal F}$ is called intersecting if every two members of ${\cal F}$ intersect, and it is called uniform if all members of ${\cal F}$ share a common size. A uniform family ${\cal F} \subseteq \binom{[n]}{k}$ of $k$-subsets of…
Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far? This question of "identity testing" has received significant attention in the case of testing whether $p$ and $q$ are…
We show that the graph property of having a (very) large $k$-th Betti number $\beta_k$ for constant $k$ is testable with a constant number of queries in the dense graph model. More specifically, we consider a clique complex defined by an…
We perform a cosmological-model-independent test for the distance-duality (DD) relation $\eta(z)=D_L(z)(1+z)^{-2}/D_A(z)$, where $D_L$ and $D_A$ are the luminosity distance and angular diameter distance respectively, with a combination of…