Abstract High‐dimensional compositional data are commonplace in the modern omics sciences, among others. Analysis of requires proper choice a log‐ratio coordinate representation, since their relative nature is not compatible with direct use standard statistical methods. Principal balances, particular class orthonormal coordinates, well suited to this context as they constructed so that first fe...

A family of regularized least squares regression models in a Reproducing Kernel Hilbert Space is extended by the kernel partial least squares (PLS) regression model. Similar to principal components regression (PCR), PLS is a method based on the projection of input (explanatory) variables to the latent variables (components). However, in contrast to PCR, PLS creates the components by modeling th...

This work provides a novel derivation based on optimization for the partial least squares (PLS) algorithm for linear regression and the kernel partial least squares (K-PLS) algorithm for nonlinear regression. This derivation makes the PLS algorithm, popularly and successfully used for chemometrics applications, more accessible to machine learning researchers. The work introduces Direct K-PLS, a...

MOTIVATION One important aspect of data-mining of microarray data is to discover the molecular variation among cancers. In microarray studies, the number n of samples is relatively small compared to the number p of genes per sample (usually in thousands). It is known that standard statistical methods in classification are efficient (i.e. in the present case, yield successful classifiers) partic...

We consider the problem of learning, from K data, a regression function in a linear space of high dimensionN using projections onto a random subspace of lower dimension M . From any algorithm minimizing the (possibly penalized) empirical risk, we provide bounds on the excess risk of the estimate computed in the projected subspace (compressed domain) in terms of the excess risk of the estimate b...