Maximizing proportions of correct classifications in binary logistic regression
In this paper, we give simple mathematical results that allow us to get all cut-off points that maximize the overall proportion of correct classifications in any binary classification method (and, in particular, in binary logistic regression). In addition, we give results that allow us to get all cut-off points that maximize a weighted combination of specificity and sensitivity. In addition, we discuss measures of association between predicted probabilities and observed responses, and, in particular, we discuss the calculation of the overall percentages of concordant, discordant, and tied pairs of input observations with different responses. We mention that the calculation of these quantities by SAS and Minitab is sometimes incorrect. The concepts and methods of the paper are illustrated by a hypothetical example of school retention data.
Diversified retrieval and online learning are two core research areas in the design of modern information retrieval systems. In this paper, we propose the linear sub-modular bandits problem, which is an online learning setting for optimizing a general class of feature-rich submodular utility models for diversified retrieval. We present an algorithm, called LSBGREEDY, and prove that it efficiently converges to a near-optimal model. As a case study, we applied our approach to the setting of personalized news recommendation, where the system must recommend small sets of news articles selected from tens of thousands of available articles each day. In a live user study, we found that LSBGREEDY significantly outperforms existing online learning approaches.