A Conversation with Shayle R. Searle

Born in New Zealand, Shayle Robert Searle earned a bachelor's degree (1949) and a master's degree (1950) from Victoria University, Wellington, New Zealand. After working for an actuary, Searle went to Cambridge University where he earned a Diploma in mathematical statistics in 1953. Searle won a Fulbright travel award to Cornell University, where he earned a doctorate in animal breeding, with a strong minor in statistics in 1959, studying under Professor Charles Henderson. In 1962, Cornell invited Searle to work in the university's computing center, and he soon joined the faculty as an assistant professor of biological statistics. He was promoted to associate professor in 1965, and became a professor of biological statistics in 1970. Searle has also been a visiting professor at Texas A&M University, Florida State University, Universit\"{a}t Augsburg and the University of Auckland. He has published several statistics textbooks and has authored more than 165 papers. Searle is a Fellow of the American Statistical Association, the Royal Statistical Society, and he is an elected member of the International Statistical Institute. He also has received the prestigious Alexander von Humboldt U.S. Senior Scientist Award, is an Honorary Fellow of the Royal Society of New Zealand and was recently awarded the D.Sc. Honoris Causa by his alma mater, Victoria University of Wellington, New Zealand.Comment: Published in at http://dx.doi.org/10.1214/08-STS259 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Supervised Classification Using Sparse Fisher's LDA

It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications where classification is needed in the high-dimensional setting. Naive implementation of Fisher's rule in this case fails to provide good results because the sample covariance matrix is singular. Moreover, by constructing a classifier that relies on all features the interpretation of the results is challenging. Our goal is to provide robust classification that relies only on a small subset of important features and accounts for the underlying correlation structure. We apply a lasso-type penalty to the discriminant vector to ensure sparsity of the solution and use a shrinkage type estimator for the covariance matrix. The resulting optimization problem is solved using an iterative coordinate ascent algorithm. Furthermore, we analyze the effect of nonconvexity on the sparsity level of the solution and highlight the difference between the penalized and the constrained versions of the problem. The simulation results show that the proposed method performs favorably in comparison to alternatives. The method is used to classify leukemia patients based on DNA methylation features