Gaussian Process Regression Networks Supplementary Material

Supplementary material: Gaussian process nonparametric tensor estimator and its minimax optimality

In this supplementary material, we give the comprehensive proof and the generalized theorems. We consider a more general regression setting: yi = f (xi) + i, (S-1) where f : X → R is the unknown true function. We suppose that the true function f is well approximated by f∗ = ∑d∗ r=1 ∏K k=1 f ∗ r (k) (that is f ' f∗). When f = f∗, this generalized regression problem is equivalent to that in the m...

Supplementary Material: Uncertainty Propagation in Long-term Structured Regression on Evolving Networks

In order to model the distribution of input variables, a reasonable assumption is that input variables x are generated by some process u, and that process has a Gaussian error. Thus, the distribution of input variables can be presented as ppxq N pu,Σxq. The new data point for prediction will be annotated as x . In the general case, we predict on the entire set of points representing a single sn...

material for our Computational Statistics paper : ’ Modelling non - stationary dynamic gene regulatory processes with the BGM model ’

This paper provides the technical details, which for space restrictions could not be included in the main paper ’Modelling non-stationary dynamic gene regulatory processes with the BGM model’ submitted to the Computational Statistics journal. The three sections of this paper are organized as follows: In Section 1 we provide details about the Gaussian BGe scoring metric for static Bayesian netwo...

Multiresolution Gaussian Processes Supplementary Material

Supplementary Material for “Statistical test for consistent estimation of causal effects in linear non-Gaussian models”

This document contains supplementary material to the article ‘Statistical test for consistent estimation of causal effects in linear non-Gaussian models’, AISTATS 2012. A table of contents is given below.