Related papers: On active and passive testing

We study the Stochastic Boolean Function Certification (SBFC) problem, where we are given $n$ Bernoulli random variables $\{X_e: e \in U\}$ on a ground set $U$ of $n$ elements with joint distribution $p$, a Boolean function $f: 2^U \to \{0,…

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA).…

A new method, with an application program in Matlab code, is proposed for testing item performance models on empirical databases. This method uses data intraclass correlation statistics as expected correlations to which one compares simple…

In this paper we construct a cyclically invariant Boolean function whose sensitivity is $\Theta(n^{1/3})$. This result answers two previously published questions. Tur\'an (1984) asked if any Boolean function, invariant under some transitive…

A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The…

A Boolean function $f:\{0,1\}^d \mapsto \{0,1\}$ is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make…

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…

How many $k$-SAT functions on $n$ boolean variables are there? What does a typical such function look like? Bollob\'as, Brightwell, and Leader conjectured that, for each fixed $k \ge 2$, the number of $k$-SAT functions on $n$ variables is…

Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set…

Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…

In this paper, we consider the problem of tolerant junta testing for boolean function. Compared with the prior work by Blais et al., we provide improved results in terms of both the parameter gap and query complexity. Compared with the…

The study of the interplay between the testability of properties of Boolean functions and the invariances acting on their domain which preserve the property was initiated by Kaufman and Sudan (STOC 2008). Invariance with respect to…

Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…

Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…

A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = \{a + b : a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. Sumsets are central objects of study in additive combinatorics, featuring in several influential…

We study the problem of testing whether a function f:R^n->R is linear (i.e., both additive and homogeneous) in the distribution-free property testing model, where the distance between functions is measured with respect to an unknown…

Property testers form an important class of sublinear algorithms. In the standard property testing model, an algorithm accesses the input function via an oracle that returns function values at all queried domain points. In many realistic…

We present algorithms for testing if a $(0,1)$-matrix $M$ has Boolean/binary rank at most $d$, or is $\epsilon$-far from Boolean/binary rank $d$ (i.e., at least an $\epsilon$-fraction of the entries in $M$ must be modified so that it has…