Estimating Multi-Label Expected Accuracy Using Labelset Distributions

A multi-label classifier estimates the binary label state (relevant/irrelevant) for each of a set of concept labels, for a given instance. Probabilistic multi-label classifiers provide a distribution over all possible labelset combinations of such label states (the powerset of labels), from which we can provide the best estimate by selecting the labelset corresponding to the largest expected accuracy. Providing confidence for predictions is important for real-world application of multi-label models, which provides the practitioner with a sense of the correctness of the prediction. It has been thought that the probability of the chosen labelset is a good measure of the confidence of the prediction, but multi-label accuracy can be measured in many ways and so confidence should align with the expected accuracy of the evaluation method. In this article, we investigate the effectiveness of seven candidate functions for estimating multi-label expected accuracy conditioned on the labelset distribution and the evaluation method. We found most correlate to expected accuracy and have varying levels of robustness. Further, we found that the candidate functions provide high expected accuracy estimates for Hamming similarity, but a combination of the candidates provided an accurate estimate of expected accuracy for Jaccard index and Exact match.