Active learning for misspecified generalized linear models

Francis R. Bach

Abstract: Active learning refers to algorithmic frameworks aimed at selecting training data points in order to reduce the number of required training data points and/or im- prove the generalization performance of a learning method. In this paper, we present an asymptotic analysis of active learning for generalized linear models. Our analysis holds under the common practical situation of model misspecifica- tion, and is based on realistic assumptions regarding the nature of the sampling distributions, which are usually neither independent nor identical. We derive un- biased estimators of generalization performance, as well as estimators of expected reduction in generalization error after adding a new training data point, that allow us to optimize its sampling distribution through a convex optimization problem. Our analysis naturally leads to an algorithm for sequential active learning which is applicable for all tasks supported by generalized linear models (e.g., binary clas- sification, multi-class classification, regression) and can be applied in non-linear settings through the use of Mercer kernels.