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The problem of feature selection is critical in several areas of machine learning and data analysis such as, for example, cancer classification using gene expression data, text categorization, etc. In this work, we consider feature selection for supervised learning problems, where one wishes to select a small set of features that facilitate learning a good prediction model in the reduced feature space. Our interest is primarily in filter methods that select features independently of the learning algorithm to be used and are generally faster to implement compared to other types of feature selection algorithms. Many common filter methods for feature selection make use of information-theoretic criteria such as those based on mutual information to guide their search process. However, even in simple binary classification problems, mutual information based methods do not always select the best set of features in terms of the Bayes error. In this thesis, we develop a general approach for selecting a set of features that directly aims to minimize the Bayes error in the reduced feature space with respect to the loss or performance measure of interest. We show that the mutual information based criterion is a special case of our setting when the loss function of interest is the logarithmic loss for class probability estimation. We give a greedy forward algorithm for approximately optimizing this criterion and demonstrate its application to several supervised learning problems including binary classification (with 0-1 error, cost-sensitive error, and F-measure), binary class probability estimation (with logarithmic loss), bipartite ranking (with pairwise disagreement loss), and multiclass classification (with multiclass 0-1 error). Our experiments suggest that the proposed approach is competitive with several state-of-the art methods.

A suite of signal processing algorithms designed for extracting information from brain electrophysiology and movement signals, along with new insights gained by applying these tools to understanding parkinsonism, were presented in this dissertation. The approach taken does not assume any particular stimulus, underlying activity, or synchronizing event, nor does it assume any particular encoding scheme. Instead, novel signal processing applications of complex continuous wavelet transforms, cross-frequency-coupling, feature selection, and canonical correlation were developed to discover the most significant electrophysiologic changes in the basal ganglia and cortex of parkinsonian rhesus monkeys and how these changes are related to the motor signs of parkinsonism. The resulting algorithms effectively characterize the severity of parkinsonism and, when combined with motor signal decoding algorithms, allow technology-assisted multi-modal grading of the primary pathological signs. Based on these results, parallel data collection algorithms were implemented in real-time embedded software and off-the-shelf hardware to develop a new system to facilitate monitoring of the severity of Parkinson's disease signs and symptoms in human patients. Off -line analysis of data collected with the system was subsequently shown to allow discrimination between normal and simulated parkinsonian conditions. The main contributions of the work were in three areas: 1) Evidence of the importance of optimally selecting multiple, non-redundant features for understanding neural information, 2) Discovery of signi ficant correlations between certain pathological motor signs and brain electrophysiology in different brain regions, and 3) Implementation and human subject testing of multi-modal monitoring technology.