Related papers: Testing Sparse Functions over the Reals
Many representations for sets are available in programming languages libraries. The paper focuses on sparse sets used, e.g., in some constraint solvers for representing integer variable domains which are finite sets of values, as an…
Recent work has shown the surprising power of low-degree sandwiching polynomial approximators in the context of challenging learning settings such as learning with distribution shift, testable learning, and learning with contamination. A…
A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every…
Despite its extensive development for multivariate data, semi-supervised learning remains underdeveloped for functional data. To address this challenge, we extend the Fermat distance, a density-sensitive metric aligning with the…
We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
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 consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…
We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures the distance between optimal IP and LP solutions. We create…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…
As a result of several successful applications in computer vision and image processing, sparse representation (SR) has attracted significant attention in multi-sensor image fusion. Unlike the traditional multiscale transforms (MSTs) that…
Sparse linear regression is a vast field and there are many different algorithms available to build models. Two new papers published in Statistical Science study the comparative performance of several sparse regression methodologies,…
Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…
This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of $\mathbb{R}^N$. We introduce the notion of linear-sleeve functions, whose function values only depend on…
The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different…
Given sparse collections of measurable sets $\mathcal S_k$, $k=1,2,\ldots ,N$, in a general measure space $(X,\mathfrak M,\mu)$, let $ \Lambda_{\mathcal S_k}$ be the sparse operator, corresponding to $\mathcal S_k$. We show that the maximal…
The Fourier-Walsh expansion of a Boolean function $f \colon \{0,1\}^n \rightarrow \{0,1\}$ is its unique representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if in the expansion of $f$, the total weight…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
This paper proposes a Kolmogorov-Smirnov type statistic and a Cram\'er-von Mises type statistic to test linearity in semi-functional partially linear regression models. Our test statistics are based on a residual marked empirical process…