F-Measure Maximization in Multi-Label Classification with Conditionally Independent Label Subsets

Abstract

We discuss a method to improve the exact F-measure maximization algorithm called GFM, proposed in [2] for multi-label classification, assuming the label set can be partitioned into conditionally independent subsets given the input features. If the labels were all independent, the estimation of only m parameters m denoting the number of labels would suffice to derive Bayes-optimal predictions in $Om^2$ operations [10]. In the general case, $m^2 + 1$ parameters are required by GFM, to solve the problem in $Om^3$ operations. In this work, we show that the number of parameters can be reduced further to $m^2/n$, in the best case, assuming the label set can be partitioned into n conditionally independent subsets. As this label partition needs to be estimated from the data beforehand, we use first the procedure proposed in [4] that finds such partition and then infer the required parameters locally in each label subset. The latter are aggregated and serve as input to GFM to form the Bayes-optimal prediction. We show on a synthetic experiment that the reduction in the number of parameters brings about significant benefits in terms of performance. The data and software related to this paper are available at https://github.com/gasse/fgfm-toy.