LPLS-regression: a method for prediction and classification under the influence of background information on predictor variables

A Partial Least Squares based approach is described which can utilise relevant background information on dependencies between predictor variables used for prediction or classification. Within a wide range of research areas (e.g. biomedicine, functional genomics, proteomics, chemometrics) modern measurement technology has increased the possibility to measure a very large number of variables on a given sample, whereas the number of samples usually is limited. As is well known, the large set of variables may cause many traditional statistical methods to report a high number of false positives due to collinearity and multiple testing issues. Further, most existing methods for data modelling and variable selection do not take advantage of possibly known dependencies between variables. The modified LPLS-regression method proposed here may take background knowledge on variables into account, thereby increasing the accuracy of estimates and reducing the number of false positives. The potential gain is better variable selection and prediction. The LPLSR is an extension of PLS-regression, where, in addition to response and regressor matrices, an extra data matrix is constructed which summarises the background information on the regressor variables. We illustrate the potential of the LPLSR-approach for this matter on both simulated and real data.