It is widely believed that both common and rare variants contribute to the risks of common diseases or complex traits and the cumulative effects of multiple rare variants can explain a significant proportion of trait variances. Advances in high-throughput DNA sequencing technologies allow us to genotype rare causal variants and investigate the effects of such rare variants on complex traits. We...

In this material, we provide the theoretical analyses to show that the trivial coefficients always correspond to the codes over errors. Lemmas 1–3 show that our errors-removing strategy will perform well when the lp-norm is enforced over the representation, where p = {1, 2,∞}. Let x 6= 0 be a data point in the union of subspaces SD that is spanned by D = [Dx D−x], where Dx and D−x consist of th...

Fisher linear discriminant analysis (FDA) and its kernel extension—kernel discriminant analysis (KDA)—are well known methods that consider dimensionality reduction and classification jointly. While widely deployed in practical problems, there are still unresolved issues surrounding their efficient implementation and their relationship with least mean squares procedures. In this paper we address...

Linear regression is an important statistical tool that models the relationship between some explanatory values and an outcome value using a linear function. In many current applications (e.g. predictive modelling in personalized healthcare), these values represent sensitive data owned by several different parties that are unwilling to share them. In this setting, training a linear regression m...

We study a decomposition-based scalable approach to performing kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an independent kernel ridge regression estimator for each subset, then averages the local solutions into a global predictor. This partitioning leads to a substantial reduction in computation ti...

Ridge regression (RR) for classification is a regularized least square method to model the linear dependency between covariate variables and labels. By applying appropriate techniques to encode the multivariate labels in face recognition as the vertices of the regular simplex which can separate points with highest degree of symmetry, RR maps the face images into a face subspace where the images...

We develop a novel preconditioning method for ridge regression, based on recent linear sketching methods. By equipping Stochastic Variance Reduced Gradient (SVRG) with this preconditioning process, we obtain a significant speed-up relative to fast stochastic methods such as SVRG, SDCA and SAG.