Related papers: Fast implementation of the Tukey depth
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
Depth from a monocular video can enable billions of devices and robots with a single camera to see the world in 3D. In this paper, we present an approach with a differentiable flow-to-depth layer for video depth estimation. The model…
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…
The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We present an efficient algorithm that computes the Minkowski sum of two polygons, which may have holes. The new algorithm is based on the convolution approach. Its efficiency stems in part from a property for Minkowski sums of polygons…
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program,…
This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function…
This paper describes a practical methodology for computing the Hardy function Z(t), using just O(((t/epsilon)^(1/3))*(log(t))^(2+o(1)))) standard computational operations, to a tolerance of epsilon in the relative error. The methodology is…
Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an $n\times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1,\ldots,v_n$, one by one. After seeing each vector $v_i$, we…
We propose learning a depth covariance function with applications to geometric vision tasks. Given RGB images as input, the covariance function can be flexibly used to define priors over depth functions, predictive distributions given…
We present a new algorithm to calculate exact hypervolumes. Given a set of $d$-dimensional points, it computes the hypervolume of the dominated space. Determining this value is an important subroutine of Multiobjective Evolutionary…
Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact…