23 Statistical Learning in Medical Data Analysis

Abstract

This article provides a tour of statistical learning regularization methods that have found application in a variety of medical data analysis problems. The uniting feature of these methods is that they involve an optimization problem which balances fidelity to the data with complexity of the model. The two settings for the optimization problems considered here are reproducing kernel Hilbert spaces (a brief tutorial is included) and ℓ 1 penalties, which involve constraints on absolute values of model coefficients. The tour begins with thin plate splines, smoothing spline ANOVA models, multicategory penalized likelihood estimates, and models for correlated Bernoulli data for regression, in these two settings. Leaving regression, the tour proceeds to the support vector machine, a modern and very popular tool for classification. Then classification based on dissimilarity information rather than direct attribute information is considered. All of the learning models discussed require dealing with the so-called bias-variance tradeoff, which means choosing the right balance between fidelity and complexity. Tuning methods for choosing the parameters governing this tradeoff are noted. The chapter ends with remarks relating empirical Bayes and Gaussian process priors to the regularization methods.