Related papers: Gaussian random projections for Euclidean membersh…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…
We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new…
We solve the Random Euclidean Matching problem with exponent 2 for the Gaussian distribution defined on the plane. Previous works by Ledoux and Talagrand determined the leading behavior of the average cost up to a multiplicative constant.…
This paper is aimed at presenting a systematic survey of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there are…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
The distributional analysis of Euclidean algorithms was carried out by Baladi and Vall\'{e}e. They showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
In this paper, we propose to study a new geometric optimization problem called "geometric prototype" in Euclidean space. Given a set of patterns, where each pattern is represented by a (weighted or unweighted) point set, the geometric…
In a recent paper the author proved a theorem to the effect that the matrix of normalized Euclidean distances on the set of specially distributed random points in the $n$-dimensional Euclidean space $\mathbb R^{n}$ with independent…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…
This paper provides a theorem to compare the minimum total cost of two different Euclidean Random Assignment Problems with the same number of points, using the stochastic order of the costs of one of the pairs in these two problems. The…