Related papers: Is your function low-dimensional?

We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access…

A function f : {0, 1}^n -> {0, 1} is said to be k-monotone if it flips between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in…

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…

Given a Boolean function $f$ provided as a black-box with $n$ variables, this paper will propose a quantum algorithm for testing if a certain variable is junta or $\epsilon$-far from being junta. The proposed algorithm constructs another…

A Boolean function $f:\{0,1\}^n\to \{0,1\}$ is $k$-linear if it returns the sum (over the binary field $F_2$) of $k$ coordinates of the input. In this paper, we study property testing of the classes $k$-Linear, the class of all $k$-linear…

For a function $f \colon \{0,1\}^n \to \{0,1\}$, the junta testing problem asks whether $f$ depends on only $k$ variables. If $f$ depends on only $k$ variables, the feature selection problem asks to find those variables. We prove that these…

We study the question of local testability of low (constant) degree functions from a product domain $S_1 \times \dots \times {S}_n$ to a field $\mathbb{F}$, where ${S_i} \subseteq \mathbb{F}$ can be arbitrary constant sized sets. We show…

In this paper, we study classes of Boolean functions that are testable with $O(\psi+1/\epsilon)$ queries, where $\psi$ depends on the parameters of the class (e.g., the number of terms, the number of relevant variables, etc.) but not on the…

We consider the problem of determining which classes of functions can be tested more efficiently than they can be learned, in the distribution-free sample-based model that corresponds to the standard PAC learning setting. Our main result…

We study the problems of learning and testing junta distributions on $\{-1,1\}^n$ with respect to the uniform distribution, where a distribution $p$ is a $k$-junta if its probability mass function $p(x)$ depends on a subset of at most $k$…

Given a black-box representing an unknown Boolean function $f$ of $n$ variables, in this paper we propose a fast quantum algorithm to test whether or not a certain variable in the function $f$ is a junta variable. The proposed algorithm…

In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function $f$ on $n$ variables that only depends on $k$ variables, and, when restricted to them, equals some predefined…

We show that a Boolean degree $d$ function on the slice $\binom{[n]}{k}$ is a junta if $k \geq 2d$, and that this bound is sharp. We prove a similar result for $A$-valued degree $d$ functions for arbitrary finite $A$, and for functions on…

We provide an example of a monotone Boolean function on the hypercube given by a low depth decision tree that is not well approximated by any k-junta for small k.

We present a generalization of the well-known problem of learning k-juntas in R^n, and a novel tensor algorithm for unraveling the structure of high-dimensional distributions. Our algorithm can be viewed as a higher-order extension of…

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…

We investigate the approximability of several classes of real-valued functions by functions of a small number of variables ({\em juntas}). Our main results are tight bounds on the number of variables required to approximate a function…

In this paper, we investigate score function-based tests to check the significance of an ultrahigh-dimensional sub-vector of the model coefficients when the nuisance parameter vector is also ultrahigh-dimensional in linear models. We first…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…