Augmented Gaussian random field: Theory and computation

Gaussian free field and conformal field theory

In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie derivatives. Based on this approach, we explain some equations of conformal field theory and outline their relation to SLE theory.

Gaussian Process Latent Random Field

The Gaussian process latent variable model (GPLVM) is an unsupervised probabilistic model for nonlinear dimensionality reduction. A supervised extension, called discriminative GPLVM (DGPLVM), incorporates supervisory information into GPLVM to enhance the classification performance. However, its limitation of the latent space dimensionality to at most C − 1 (C is the number of classes) leads to ...

Gaussian Markov Random Fields: Theory and Applications

Autoregressive Gaussian Random Vectors of First Order

Random Matrix Theory, Numerical Computation and Applications

This paper serves to prove the thesis that a computational trick can open entirely new approaches to theory. We illustrate by describing such random matrix techniques as the stochastic operator approach, the method of ghosts and shadows, and the method of “Riccatti Diffusion/Sturm Sequences,” giving new insights into the deeper mathematics underneath random matrix theory.