Semi-supervised methods use unlabeled data in addition to labeled data to construct predictors. While existing semi-supervised methods have shown some promising empirical performance, their development has been based largely based on heuristics. In this paper we study semi-supervised learning from the viewpoint of minimax theory. Our first result shows that some common methods based on regulari...

Logistic regression analysis is a statistical technique to evaluate the relationship between various predictor variables (either categorical or continuous) and an outcome which is binary (dichotomous). In this article, we discuss logistic regression analysis and the limitations of this technique.

Generalized linear models (GLMs) represent a class of fixed effects regression models for several types of dependent variables (i.e., continuous, dichotomous, counts). McCullagh and Nelder [32] describe these in great detail and indicate that the term ‘generalized linear model’ is due to Nelder and Wedderburn [35] who described how a collection of seemingly disparate statistical techniques coul...

In this paper we approach the analysis of statistics algorithms from a geometric viewpoint and use techniques from computational geometry to develop new, fast algorithms for computing familiar statistical quantities. Such fundamental procedures as sorting and selection play an important role in nonparametric estimation as well as in correlation and regression and we use known results to obtain ...