Error Control for Support Vector Machines

Error Control for Support Vector Machines by Mark A. Davenport In binary classification there are two types of errors, and in many applications these may have very different costs. We consider two learning frameworks that address this issue: minimax classification, where we seek to minimize the maximum of the false alarm and miss rates, and Neyman-Pearson (NP) classification, where we seek to minimize the miss rate while ensuring the false alarm rate is less than a specified level α. We show that our approach, based on cost-sensitive support vector machines, significantly outperforms methods typically used in practice. Our results also illustrate the importance of heuristics for improving the accuracy of error rate estimation in this setting. We then reduce anomaly detection to NP classification by considering a second class of points, allowing us to estimate minimum volume sets using algorithms for NP classification. Comparing this approach with traditional one-class methods, we find that our approach has several advantages. Acknowledgements The work presented in this thesis was accomplished with a great deal of help from Clay Scott. I greatly appreciate his assistance and insight, and especially his occasional prodding. Thanks also to my advisor, Richard Baraniuk, for his enthusiastic encouragement, and to the additional members of my committee, Don Johnson and Rudolf Riedi, for their helpful feedback. I am also deeply indebted to Ryan King and Brandon Skeen who helped provide the computational resources without which this work would not have been possible. Finally, I would like to thank all of my other friends and family for their support. Thanks especially to my parents for (perhaps unwittingly) pointing me down this road, and to Kim for her constant reassurance, optimism, and encouragement.