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Smoothed absolute loadings principal components analysis

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A crucial part of genome-wide association studies is the identification of modes of variability in genome data which do not depend on small parts of the genome. The natural statistical starting-point is principal components analysis, but in practice raw principal components produce loadings concentrated on a small number of SNPs. Therefore some sort of regularization is required.

Standard Functional Data Analysis approaches control the amount of local variability in the loadings vector, but this is not appropriate in the current case, because of the arbitrary coding of the individual SNPs. Therefore a regularization method for the absolute values of the loadings is developed and discussed. Interestingly, a promising computational approach within the method is Lamarckian genetic algorithms, thus illustrating the remark in the literature that “Lamarckism has been universally rejected as a viable theory of genetic evolution in nature but Lamarckian evolution has proven effective within computer applications”!

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