The Kronecker-Gaussian Curvature of Hyperspace

A smooth Gaussian-Kronecker diffeomorphism

We construct a smooth Gaussian-Kronecker diffeomorphism T , on ”× [0, 1], where [0, 1] is the Hilbert cube. To obtain this diffeomorphism, we adapt a construction by De La Rue [6], which uses transformations of the planar Brownian motion.

Fast Kronecker Inference in Gaussian Processes with non-Gaussian Likelihoods

Gaussian processes (GPs) are a flexible class of methods with state of the art performance on spatial statistics applications. However, GPs require O(n) computations and O(n) storage, and popular GP kernels are typically limited to smoothing and interpolation. To address these difficulties, Kronecker methods have been used to exploit structure in the GP covariance matrix for scalability, while ...

Blitzkriging: Kronecker-structured Stochastic Gaussian Processes

We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales cubically in the number of ‘inducing inputs’, variables introduced to factorise the model. Blitzkriging shares state-of-the-art scaling with data, but reduces the ...

of non-positive Gaussian curvature

Existence of Convex Hypersurfaces with Prescribed Gauss-kronecker Curvature

Let f(x) be a given positive function in Rn+1. In this paper we consider the existence of convex, closed hypersurfaces X so that its GaussKronecker curvature at x ∈ X is equal to f(x). This problem has variational structure and the existence of stable solutions has been discussed by Tso (J. Diff. Geom. 34 (1991), 389–410). Using the Mountain Pass Lemma and the Gauss curvature flow we prove the ...