Kernel logistic regression using truncated Newton method

Kernel logistic regression (KLR) is a powerful nonlinear classifier. The combination of KLR and the truncated-regularized iteratively re-weighted least-squares (TR-IRLS) algorithm, has led to a powerful classification method using small-to-medium size data sets. This method (algorithm), is called truncated-regularized kernel logistic regression (TR-KLR). Compared to support vector machines (SVM) and TR-IRLS on twelve benchmark publicly available data sets, the proposed TR-KLR algorithm is as accurate as, and much faster than, SVM and more accurate than TR-IRLS. The TR-KLR algorithm also has the advantage of providing direct prediction probabilities.

[1]  Paul H. Garthwaite,et al.  Statistical Inference , 2002 .

[2]  Volker Roth,et al.  Probabilistic Discriminative Kernel Classifiers for Multi-class Problems , 2001, DAGM-Symposium.

[3]  T. Minka A comparison of numerical optimizers for logistic regression , 2004 .

[4]  David Haussler,et al.  Probabilistic kernel regression models , 1999, AISTATS.

[5]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[6]  Johan A. K. Suykens,et al.  Multi-class kernel logistic regression: a fixed-size implementation , 2007, IJCNN.

[7]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression , 2007, J. Mach. Learn. Res..

[8]  S. Sathiya Keerthi,et al.  A Fast Dual Algorithm for Kernel Logistic Regression , 2002, 2007 International Joint Conference on Neural Networks.

[9]  Vladimir Vapnik,et al.  The Nature of Statistical Learning , 1995 .

[10]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[11]  A. Asuncion,et al.  UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences , 2007 .

[12]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[13]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[14]  Nello Cristianini,et al.  Large Margin DAGs for Multiclass Classification , 1999, NIPS.

[15]  Rob Malouf,et al.  A Comparison of Algorithms for Maximum Entropy Parameter Estimation , 2002, CoNLL.

[16]  Maher Maalouf,et al.  Computational Statistics and Data Analysis Robust Weighted Kernel Logistic Regression in Imbalanced and Rare Events Data , 2022 .

[17]  Ulrich H.-G. Kreßel,et al.  Pairwise classification and support vector machines , 1999 .

[18]  Alexander J. Smola,et al.  Kernel methods and the exponential family , 2006, ESANN.

[19]  D. Hosmer,et al.  Applied Logistic Regression , 1991 .

[20]  Ji Zhu,et al.  Kernel Logistic Regression and the Import Vector Machine , 2001, NIPS.

[21]  Andrew W. Moore,et al.  Making logistic regression a core data mining tool with TR-IRLS , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[23]  Chih-Jen Lin,et al.  Trust region Newton methods for large-scale logistic regression , 2007, ICML '07.

[24]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[25]  Ryan M. Rifkin,et al.  In Defense of One-Vs-All Classification , 2004, J. Mach. Learn. Res..