An Explicit Representation of a Stationary Gaussian Process

Some Properties of Large Excursions of a Stationary Gaussian Process

The present work investigates two properties of level crossings of a stationary Gaussian process X(t) with autocorrelation function RX(τ). We show firstly that if RX(τ) admits finite second and fourth derivatives at the origin, the length of up-excursions above a large negative level −γ is asymptotically exponential as −γ → −∞. Secondly, assuming that RX(τ) admits a finite second derivative at ...

State Space representation of non-stationary Gaussian Processes

The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where n is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS representation of the most important kernels used in machine learning. The aim ...

An Explicit Representation of Forgetting

A pervasive, yet much ignored, factor in the analysis of processing-failures is the problem of misorganized knowledge. If a system’s knowledge is not indexed or organized correctly, it may make an error, not because it does not have either the general capability or specific knowledge to solve a problem, but rather because it does not have the knowledge sufficiently organized so that the appropr...

EXPECTED NUMBER OF CROSSINGS OF AN ARBITRARY CURVE BY A NON-STATIONARY GAUSSIAN PROCESS by

Sparse Representation for Gaussian Process Models

We develop an approach for a sparse representation for Gaussian Process (GP) models in order to overcome the limitations of GPs caused by large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the model. Experimental results on toy examples and large ...