相关论文: Two-dimensional projections of an hypercube
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
In this paper we provide an efficient computation of the projection onto the cone generated by the epigraph of the perspective of any convex lower semicontinuous function. Our formula requires solving only two scalar equations involving the…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
This research work aims to explore the distortions in distance in equidistant cylindrical projection. The horizontal bending that occurs in the projection process can be assessed by performing a geometric analysis using Tissot's…
The phase space slicing method of two cutoffs for next-to-leading-order Monte-Carlo style QCD corrections has been applied to many physics processes. The method is intuitive, simple to implement, and relies on a minimum of process dependent…
Two points are randomly selected inside a three-dimensional euclidian cube. The value l of their separation lies somewhere between zero and the length of a diagonal of the cube. The probability density P(l) of the separation is obtained…
Quadratic hypersurfaces are a natural generalization of affine subspaces, and projections are elementary blocks of algorithms in optimization and machine learning. It is therefore intriguing that no proper studies and tools have been…
Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…
An extension to the multiple-histogram method (sometimes referred to as the Ferrenberg-Swendsen method) for use in quantum Monte Carlo simulations is presented. This method is shown to work well for the 2D repulsive Hubbard model, allowing…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
In this work, we address the unsupervised classification issue by exploiting the general idea of Random Projection Ensemble. Specifically, we propose to generate a set of low dimensional independent random projections and to perform…
We present a novel variant of the multi-level Monte Carlo method that effectively utilizes a reserved computational budget on a high-performance computing system to minimize the mean squared error. Our approach combines concepts of the…
In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for…
We describe a Monte Carlo procedure for the simulation of dynamically triangulate random surfaces with a boundary (topology of a disk). The algorithm keeps the total number of triangles fixed, while the length of the boundary is allowed to…
A complete uncertainty analysis on a given fringe projection set-up has been performed using Monte-Carlo approach. In particular the calibration procedure is taken into account. Two applications are given: at a macroscopic scale, phase…