Active Sampling for Class Probability Estimation and Ranking

Abstract. In many cost-sensitive environments class probability estimates are used by decision makers to evaluate the expected utility from a set of alternatives. Supervised learning can be used to build class probability estimates; however, it often is very costly to obtain training data with class labels. Active learning acquires data incrementally, at each phase identifying especially useful additional data for labeling, and can be used to economize on examples needed for learning. We outline the critical features of an active learner and present a sampling-based active learning method for estimating class probabilities and class-based rankings. BOOTSTRAP-LV identifies particularly informative new data for learning based on the variance in probability estimates, and uses weighted sampling to account for a potential example’s informative value for the rest of the input space.We show empirically that the method reduces the number of data items that must be obtained and labeled, across a wide variety of domains.We investigate the contribution of the components of the algorithm and showthat each provides valuable information to help identify informative examples.We also compare BOOTSTRAP-LV with UNCERTAINTY SAMPLING, an existing active learning method designed to maximize classification accuracy. The results show that BOOTSTRAP-LV uses fewer examples to exhibit a certain estimation accuracy and provide insights to the behavior of the algorithms. Finally, we experiment with another new active sampling algorithm drawing from both UNCERTAINTY SAMPLING and BOOTSTRAP-LV and show that it is significantly more competitive with BOOTSTRAPLV compared to UNCERTAINTY SAMPLING. The analysis suggests more general implications for improving existing active sampling algorithms for classification.NYU, Stern School of Business, IOMS Department, Center for Digital Economy Researc