Abstract: Techniques are disclosed that implement algorithms for rapidly finding the leave-one-out (LOO) error for regularized least squares (RLS) problems over a large number of values of the regularization parameter ?. Algorithms implementing the techniques use approximately the same time and space as training a single regularized least squares classifier/regression algorithm. The techniques include a classification/regression process suitable for moderate sized datasets, based on an eigendecomposition of the unregularized kernel matrix. This process is applied to a number of benchmark datasets, to show empirically that accurate classification/regression can be performed using a Gaussian kernel with surprisingly large values of the bandwidth parameter ?. It is further demonstrated how to exploit this large ? regime to obtain a linear-time algorithm, suitable for large datasets, that computes LOO values and sweeps over ?.

Abstract: Techniques are disclosed that implement algorithms for rapidly finding the leave-one-out (LOO) error for regularized least squares (RLS) problems over a large number of values of the regularization parameter ?. Algorithms implementing the techniques use approximately the same time and space as training a single regularized least squares classifier/regression algorithm. The techniques include a classification/regression process suitable for moderate sized datasets, based on an eigendecomposition of the unregularized kernel matrix. This process is applied to a number of benchmark datasets, to show empirically that accurate classification/regression can be performed using a Gaussian kernel with surprisingly large values of the bandwidth parameter ?. It is further demonstrated how to exploit this large ? regime to obtain a linear-time algorithm, suitable for large datasets, that computes LOO values and sweeps over ?.

Abstract: The present teachings describe methods for selecting informative genetic markers including single nucleotide polymorphisms (SNPs) that may be used in the design and execution of genome wide association studies. These methods are distinguished from other methods relying on a predefined haplotype block structure and may be configured to make use of correlations that occur across neighboring haplotype blocks. The disclosed methods may further be implemented across chromosomal regions having both high and low local linkage disequilibrium. Informative genetic marker selection, as described, provides an alternative and potentially more efficient mechanism to select genetic markers such as SNPs using block-based and random approaches.