Related papers: Relative-error testing of conjunctions and decisio…

We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given $2^{\tilde{O}(\sqrt{n}/\varepsilon)}$ uniformly random examples of an unknown function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$, our…

We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in…

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is…

We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…

We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…

We revisit the problem of property testing for convex position for point sets in $\mathbb{R}^d$. Our results draw from previous ideas of Czumaj, Sohler, and Ziegler (ESA 2000). First, the algorithm is redesigned and its analysis is revised…

Context: Most approaches to automated white-box testing consider the client side and the server side of a web application in isolation from each other. Such testers lack a whole-program perspective on the web application under test.…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

The noise sensitivity of a Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$ is one of its fundamental properties. A function of a positive noise parameter $\delta$, it is denoted as $NS_{\delta}[f]$. Here we study the algorithmic problem…

Recently it has been proved that simple GP systems can efficiently evolve the conjunction of $n$ variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the…

We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity…

The Consolidated Standards of Reporting Trials statement is the global benchmark for transparent and high-quality reporting of randomized controlled trials. Manual verification of CONSORT adherence is a laborious, time-intensive process…

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 give a non-adaptive algorithm that makes $2^{\tilde{O}(\sqrt{k\log(1/\varepsilon_2 - \varepsilon_1)})}$ queries to a Boolean function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$ and distinguishes between $f$ being $\varepsilon_1$-close to some…

We consider the problem of testing whether an unknown and arbitrary set $S \subseteq \mathbb{R}^n$ (given as a black-box membership oracle) is convex, versus $\varepsilon$-far from every convex set, under the standard Gaussian distribution.…

Let $f: T\to \{ 0,1 \}$ be a Boolean function on the Boolean half-slice, $T$, \ie elements of $\{0,1\}^n$ with Hamming weight $n/2$. We show that if $f(x)+f(y)=f(x+y)$ holds with probability $\frac{1+\delta}{2}$ over a uniform pair $(x,y)$…

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 nonparametric estimators built by minimizing the mean squared relative error are gaining in popularity for their robustness in the presence of outliers in comparison to the Nadaraya Watson estimators. In this paper we build a relative…

Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…

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…