Statistics and Data Science Seminar
Yixin Fang
NYU Langone Medical Center
Penalized Linear Discriminant Analysis for Family Studies
Abstract: In family studies with multiple continuous phenotypes, we are interested
in finding linear combinations of the phenotypes with large
heritabilities, which can be considered as new phenotypes for genetic
analysis. The problem can be recast as linear discriminant analysis (LDA).
When the number of phenotypes is large, LDA is not appropriate for two
reasons: the standard estimate for the within-family covariance matrix is
singular, and it is difficult to interpret the newly defined phenotypes.
Here we propose a novel version of penalized LDA, with an $L_1^2$ penalty
in the denominator of the Rayleigh quotient. Besides overcoming the above
two problems, the proposed method has at least three advantages compared
with the existing regularization methods. First, it solves the singularity
problem and achieves the sparsity property simultaneously. Second, the
method is scale-invariant. Third, the consistency can be proved. We
evaluate the performances of the method using simulations and two family
studies.
Wednesday February 22, 2012 at 4:00 PM in SEO 636