Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than the commonly used quasi Newton approach for logistic regression. We also compare it with linear SVM implementations.

This paper proposes new approaches to rank individuals from their group competition results. Many real-world problems are of this type. For example, ranking players from team games is important in some sports. We propose an exponential model to solve such problems. To estimate individual rankings through the proposed model we introduce two convex minimization formulas with easy and efficient solution procedures. Experiments on real bridge records and multi-class classification demonstrate the viability of the proposed model.

The Bradley-Terry model for obtaining individual skill from paired comparisons has been popular in many areas. In machine learning, this model is related to multi-class probability estimates by coupling all pairwise classification results. Error correcting output codes (ECOC) are a general framework to decompose a multi-class problem to several binary problems. To obtain probability estimates under this framework, this paper introduces a generalized Bradley-Terry model in which paired individual comparisons are extended to paired team comparisons. We propose a simple algorithm with convergence proofs to solve the model and obtain individual skill. Experiments on synthetic and re al data demonstrate that the algorithm is useful for obtaining multi-class probability estimates. Moreover, we discuss four extensions of the proposed model: 1) weighted individual skill, 2) home-field advantage, 3) ties, and 4) comparisons with more than two teams.

The Bradley-Terry model for paired comparison has been popular in many areas. We propose a generalized version in which paired individual comparisons are extended to paired team comparisons. We introduce a simple algorithm with convergence proofs to solve the model and obtain individual skill. A useful application to multi-class probability estimates using error-correcting codes is demonstrated.

Pairwise coupling is a popular multi-class classification method that combines together all pairwise comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement. We show conceptually and experimentally that the proposed approaches are more stable than two existing popular methods: voting and [3].