Bayesian kernel projections for classification of high dimensional data

A Bayesian multi-category kernel classification method is proposed. The algorithm performs the classification of the projections of the data to the principal axes of the feature space. The advantage of this approach is that the regression coefficients are identifiable and sparse, leading to large computational savings and improved classification performance. The degree of sparsity is regulated in a novel framework based on Bayesian decision theory. The Gibbs sampler is implemented to find the posterior distributions of the parameters, thus probability distributions of prediction can be obtained for new data points, which gives a more complete picture of classification. The algorithm is aimed at high dimensional data sets where the dimension of measurements exceeds the number of observations. The applications considered in this paper are microarray, image processing and near-infrared spectroscopy data.     

SEMI-MECHANISTIC MODELLING IN NONLINEAR REGRESSION: A CASE STUDY

This paper discusses the use of highly parameterized semi‐mechanistic nonlinear models with particular reference to the PARJIB crop response model of Reid (2002) [Yield response to nutrient supply across a wide range of conditions 1. Model derivation. Field Crops Research 77, 161–171]. Compared to empirical linear approaches, such models promise improved generality of application but present considerable challenges for estimation. Some success has been achieved with a fitting approach that uses a Levenberg–Marquardt algorithm starting from initial values determined by a genetic algorithm. Attention must be paid, however, to correlations between parameter estimates and an approach is described to identify these based on large simulated datasets. This work illustrates the value for the scientist in exploring the correlation structure in mechanistic or semi‐mechanistic models. Such information might be used to reappraise the structure of the model itself, especially if the experimental evidence is not strong enough to allow estimation of a parameter free of assumptions about the values of others. Thus statistical modelling and analysis can complement mechanistic studies, making more explicit what is known and what is not known about the processes being modelled and guiding further research.