相关论文: A Lower Bound on WAFOM

The Best-Worst Method (BWM) is a well-known Multi-Criteria Decision-Making (MCDM) method used to calculate criteria-weights in many real-life applications. It was observed that the decision judgments used to calculate weights in BWM may be…

In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…

Few-shot image classification is a challenging task in the field of machine learning, involving the identification of new categories using a limited number of labeled samples. In recent years, methods based on local descriptors have made…

This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $R^d$, which can be unbounded. Under…

Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…

To efficiently solve online problems with complicated constraints, projection-free algorithms including online frank-wolfe (OFW) and its variants have received significant interest recently. However, in the general case, existing efficient…

In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of…

Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…

When applying the quasi-Monte Carlo (QMC) method of numerical integration of univariate functions, Koksma's inequality provides a basic estimate of the error in terms of the discrepancy of the used evaluation points and the total variation…

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…

Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…

We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet…

Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct…

A weakly admissible mesh (WAM) on a continuum real-valued domain is a sequence of discrete grids such that the discrete maximum norm of polynomials on the grid is comparable to the supremum norm of polynomials on the domain. The asymptotic…

This article deals with the lower compactness property of a sequence of integrands and the use of this key notion in various domains: convergence theory, optimal control, non-smooth analysis. First about the interchange of the weak…

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…

We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…

To save energy and alleviate interferences in a wireless sensor network, the usage of virtual backbone was proposed. Because of accidental damages or energy depletion, it is desirable to construct a fault tolerant virtual backbone, which…

Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called \emph{star discrepancy}.…

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…