Related papers: A $d^{1/2+o(1)}$ Monotonicity Tester for Boolean F…
In this paper, we study the stochastic probing problem under a general monotone norm objective. Given a ground set $U = [n]$, each element $i \in U$ has an independent nonnegative random variable $X_i$ with known distribution. Probing an…
This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…
We consider several related problems of estimating the 'sparsity' or number of nonzero elements $d$ in a length $n$ vector $\mathbf{x}$ by observing only $\mathbf{b} = M \odot \mathbf{x}$, where $M$ is a predesigned test matrix independent…
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
Outlier detection (OD) has a vast literature as it finds numerous real-world applications. Being an unsupervised task, model selection is a key bottleneck for OD without label supervision. Despite a long list of available OD algorithms with…
We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the…
We provide two sufficient and necessary conditions to characterize any $n$-bit partial Boolean function with exact quantum 1-query complexity. Using the first characterization, we present all $n$-bit partial Boolean functions that depend on…
Expansion testing aims to decide whether an $n$-node graph has expansion at least $\Phi$, or is far from any such graph. We propose a quantum expansion tester with complexity $\widetilde{O}(n^{1/3}\Phi^{-1})$. This accelerates the…
We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…
Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly…
We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in the literature identify properties of the measurement that…
We introduce a new framework for constructing tests of general semiparametric hypotheses which have nontrivial power on the $n^{-1/2}$ scale in every direction, and can be tailored to put substantial power on alternatives of importance. The…
Recent advances in randomized incremental methods for minimizing $L$-smooth $\mu$-strongly convex finite sums have culminated in tight complexity of $\tilde{O}((n+\sqrt{n L/\mu})\log(1/\epsilon))$ and $O(n+\sqrt{nL/\epsilon})$, where…
DFT-1/2 is an efficient band gap rectification method for density functional theory (DFT) under local density approximation (LDA) or generalized gradient approximation. It was suggested that non-self-consistent DFT-1/2 should be used for…
We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of…
We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement…
Estimating the length of the longest increasing subsequence (LIS) in an array is a problem of fundamental importance. Despite the significance of the LIS estimation problem and the amount of attention it has received, there are important…