Related papers: Testing Junta Truncation
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the $L^p$-norm of the difference between an empirical distribution function and its least concave…
We give an algorithm for learning symmetric k-juntas (boolean functions of $n$ boolean variables which depend only on an unknown set of $k$ of these variables) in the PAC model under the uniform distribution, which runs in time n^{O(k/\log…
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…
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…
A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is "close" to an isomorphism f_sigma of f, we can compute f_sigma(x) for any x in Z_2^n with good probability using…
Uniformity testing is one of the most well-studied problems in property testing, with many known test statistics, including ones based on counting collisions, singletons, and the empirical TV distance. It is known that the optimal sample…
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 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…
We study the problem of estimating the parameters of a Boolean product distribution in $d$ dimensions, when the samples are truncated by a set $S \subset \{0, 1\}^d$ accessible through a membership oracle. This is the first time that the…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
The (low soundness) linearity testing problem for the middle slice of the Boolean cube is as follows. Let $\varepsilon>0$ and $f$ be a function on the middle slice on the Boolean cube, such that when choosing a uniformly random quadruple…
A natural problem in high-dimensional inference is to decide if a classifier $f:\mathbb{R}^n \rightarrow \{-1,1\}$ depends on a small number of linear directions of its input data. Call a function $g: \mathbb{R}^n \rightarrow \{-1,1\}$, a…
This paper presents a set of Stata commands and Mata functions to evaluate different distributional quantities of the multivariate normal distribution, and a particular type of non-central multivariate t distribution. Specifically, their…
In this paper, we study adaptive and non-adaptive exact learning of Juntas from membership queries. We use new techniques to find new bounds, narrow some of the gaps between the lower bounds and upper bounds and find new deterministic and…
A test of uniformity on [0,1] is developed for the setting of a single observation recorded with sufficient precision. Although consistency against general alternatives is not attainable with only one draw in the classical large-sample…
We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of $k$-uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between…
We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…
Given a discrete-valued sample $X_1,...,X_n$ we wish to decide whether it was generated by a distribution belonging to a family $H_0$, or it was generated by a distribution belonging to a family $H_1$. In this work we assume that all…
In this note we establish a uniform bound for the distribution of a sum $S_n=X_1+\cdots+X_n$ of independent non-homogeneous Bernoulli trials. Specifically, we prove that $\sigma_n \mathbb{P}(S_n\!=\!j)\leq\eta$ where $\sigma_n$ denotes the…