Covariance function plays a critical role in functional and longitudinal data analysis. In this paper, we consider nonparametric covariance function estimation using a reproducing kernel Hilbert space framework. A regularization method is introduced through a careful characterization of the function space in which a covariance function resides. It is shown that the procedure enjoys desirable th...

Starting from scanning electron microscope images of some food products, we generate binary images of composite materials. After measuring the covariance and the probability for segments and for squares to be included in the dominant component, we develop a modelling of the microstructure from random sets obtained by thresholding Gaussian random functions. The covariance function of the underly...

In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based models such as SVM is, that the covariance function should be adapted to the modeled data. Frequently, the squared exponential covariance function is used as a default. However, this can lead to a...

Independent Slow Feature Analysis (ISFA) is an algorithm for performing nonlinear blind source separation, which combines linear ICA with Slow Feature Analysis (SFA). In its current form the objective function is based on time-delayed covariance matrices. While the algorithm performs well in general, we occasionally encountered cases in which the estimated sources are highly statistically depen...

Mixture of Probabilistic Principal Component Analyzers (MPPCA) is a seminal work in Machine Learning in that it was the first to use PCA to perform clustering and local dimensionality reduction. MPPCA is based upon the mixture of Factor Analyzers (MFA) which is similar to MPPCA except is uses Factor Analysis to estimate the covariance matrix. This algorithm is of interest to me because it is re...