Performance metrics are a key component of machine learning systems, and are ideally constructed to reflect real world tradeoffs. In contrast, much of the literature simply focuses on algorithms for maximizing accuracy. With the increasing integration of machine learning into real systems, it is clear that accuracy is an insufficient measure of performance for many problems of interest. Unfortunately, unlike accuracy, many real world performance metrics are non-decomposable i.e. cannot be computed as a sum of losses for each instance. Thus, known algorithms and associated analysis are not trivially extended, and direct approaches require expensive combinatorial optimization. I will outline recent results characterizing population optimal classifiers for large families of binary and multilabel classification metrics, including such nonlinear metrics as F-measure and Jaccard measure. Perhaps surprisingly, the prediction which maximizes the utility for a range of such metrics takes a simple form. This results in simple and scalable procedures for optimizing complex metrics in practice. Time permitting, I will briefly outline how the same analysis gives decision-theoretic optimal procedures for selecting point estimates from complex posterior distributions for structured objects such as graphs.
Joint work with Nagarajan Natarajan, Bowei Yan, Kai Zhong, Pradeep Ravikumar and Inderjit Dhillon.