Related papers: Gaussian random projections for Euclidean membersh…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…
We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the problem in a compact set with the topology both of the interval…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…
Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.
The Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address…
We determine the probability that a random k-dimensional subspace of Euclidean n-space contains a positive vector.
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, this paper establishes Gaussian approximation results for high-dimensional fixed-order $U$-statistics whose kernels depend on the sample…
In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…
This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…
A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…