We discuss a method to improve the exact F-measure maximization algorithm
called GFM, proposed in (Dembczynski et al. 2011) for multi-label
classification, assuming the label set can be can 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 O(m2)
operations. In the general case, m2+1 parameters are required by GFM, to
solve the problem in O(m3) operations. In this work, we show that the number
of parameters can be reduced further to m2/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 (Gasse et al. 2015) 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