Cosmic mass functions from Gaussian stochastic diffusion processes

Stochastic Approximation of Score Functions for Gaussian Processes

We discuss the statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number of the covariance matrix, the approach achieves O(n) storage and nearly O(n) computational effort per optimization step, where n is the number of data sites....

Diffusion Equation and Stochastic Processes.

Contrastive Divergence In Gaussian Diffusion Processes

Contrastive Divergence (CD) is a recent learning rule found to work very well in practice despite its still unclear theoretical underpinnings (Carreira-Perpiñan and Hinton, 2005; Hinton, 2002; Hinton and Salakhutdinov, 2006; Hyvärinen, 2006; MacKay, 2001; Roth and Black, 2005; Williams and Agakov, 2002; Yuille, 2004). This paper presents a theoretical analysis of CD in Gaussian Diffusion Proces...

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 ...

Stochastic Integration with respect to Gaussian Processes

We construct a Stratonovitch-Skorohod-like stochastic integral for general Gaussian processes. We study its sample-paths regularity and one of its numerical approximating schemes. We also analyze the way it is transformed by an absolutely continuous change of probability and we give an Itô formula. c 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Intégrale stochasti...