Sequential, Bayesian geostatistics:a principled method for large data sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of “basis vectors” that best represent the “true” posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks

Hierarchical and Reweighting Cluster Kernels for Semi-Supervised Learning

Recently semi-supervised methods gained increasing attention and many novel semi-supervised learning algorithms have been proposed. These methods exploit the information contained in the usually large unlabeled data set in order to improve classification or generalization performance. Using data-dependent kernels for kernel machines one can build semi-supervised classifiers by building the kernel in such a way that feature space dot products incorporate the structure of the data set. In this paper we propose two such methods: one using specific hierarchical clustering, and another kernel for reweighting an arbitrary base kernel taking into account the cluster structure of the data

Bayesian Network Classifier for Medical Data Analysis

Bayesian networks encode causal relations between variables using probability and graph theory. They can be used both for prediction of an outcome and interpretation of predictions based on the encoded causal relations. In this paper we analyse a tree-like Bayesian network learning algorithm optimised for classification of data and we give solutions to the interpretation and analysis of predictions. The classification of logical – i.e. binary – data arises specifically in the field of medical diagnosis, where we have to predict the survival chance based on different types of medical observations or we must select the most relevant cause corresponding again to a given patient record.Surgery survival prediction was examined with the algorithm. Bypass surgery survival chance must be computed for a given patient, having a data-set of 66 medical examinations for 313 patients