Density-based logistic regression

This paper introduces a nonlinear logistic regression model for classification. The main idea is to map the data to a feature space based on kernel density estimation. A discriminative model is then learned to optimize the feature weights as well as the bandwidth of a Nadaraya-Watson kernel density estimator. We then propose a hierarchical optimization algorithm for learning the coefficients and kernel bandwidths in an integrated way. Compared to other nonlinear models such as kernel logistic regression (KLR) and SVM, our approach is far more efficient since it solves an optimization problem with a much smaller size. Two other major advantages are that it can cope with categorical attributes in a unified fashion and naturally handle multi-class problems. Moveover, our approach inherits from logistic regression good interpretability of the model, which is important for clinical applications but not offered by KLR and SVM. Extensive results on real datasets, including a clinical prediction application currently under deployment in a major hospital, show that our approach not only achieves superior classification accuracy, but also drastically reduces the computing time as compared to other leading methods.