Group Lasso for Functional Logistic Regression

Abstract

Functional datasets are comprised of data that have been sampled discretely over a continuum, usually time. While the recorded data are discrete, it is assumed that there is a smooth, underlying curve describing the observations. In this thesis an attempt is made to develop a variable selection technique for the functional logistic regression model. The functional logistic regression model is the functional analog of logistic regression. In this model, the responses are binary and represent two separate classes; the predictors are functional. Due to the nature of functional data, observations at neighboring time points are correlated, leading to redundant information within each observation and each functional predictor. In a dataset with many variables, it is necessary to be able to select a smaller subset of informative variables. In this thesis, we attempt to remove the autocorrelation between neighboring observations and perform variable selection. We do this by employing a principal component analysis on binary data with multiple functional predictors. The data are then subject to a variant of the group lasso, an L1 regularization method that estimates the logistic model and selects variables simultaneously. We assess our method with a simulation study and an application to a real dataset.