Related papers: Random projections beyond zero overlap
We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of…
We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional…
There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…
In the context of mod-Gaussian convergence, as defined previously in our work with J. Jacod, we obtain lower bounds for local probabilities for a sequence of random vectors which are approximately Gaussian with increasing covariance. This…
The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex…
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by the asymptotic behavior of the widths of compact subsets with…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for…
The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…
Spin glass theory studies the structure of sublevel sets and minima (or near-minima) of certain classes of random functions in high dimension. Near-minima of random functions also play an important role in high-dimensional statistics and…
We determine the expected curvature polynomial of random real projective varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group.…
In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.