Related papers: Efficiency analysis of simple perturbed pairwise c…
We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…
The basic motivation and primary goal of this paper is a qualitative evaluation of the performance of a new weighted statistic for a nonparametric test for stochastic dominance based on two samples, which was introduced in Ledwina and…
Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and…
We study the problem of allocating indivisible goods among agents with additive valuation functions to achieve both fairness and efficiency under the constraint that each agent receives exactly the same number of goods (the \emph{balanced…
Pairwise comparison matrices have received substantial attention in a variety of applications, especially in rank aggregation, the task of flattening items into a one-dimensional (and thus transitive) ranking. However, non-transitive…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto…
Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum…
Orthogonal weight matrices are used in many areas of deep learning. Much previous work attempt to alleviate the additional computational resources it requires to constrain weight matrices to be orthogonal. One popular approach utilizes…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to…
Weighted sieves are used to detect numbers with at most $S$ prime factors with $S \in \mathbb{N}$ as small as possible. When one studies problems with two variables in somewhat symmetric roles (such as Chen primes, that is primes $p$ such…
The power method is a basic method for computing the dominant eigenpair of a matrix. In this paper, we propose a structure-preserving power-like method for computing the dominant conjugate pair of purely imaginary eigenvalues and the…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
With the great success of deep neural networks, adversarial learning has received widespread attention in various studies, ranging from multi-class learning to multi-label learning. However, existing adversarial attacks toward multi-label…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…