  Label distribution learning (LDL) is a general learning framework, which
assigns to an instance a distribution over a set of labels rather than a single
label or multiple labels. Current LDL methods have either restricted
assumptions on the expression form of the label distribution or limitations in
representation learning, e.g., to learn deep features in an end-to-end manner.
This paper presents label distribution learning forests (LDLFs) - a novel label
distribution learning algorithm based on differentiable decision trees, which
have several advantages: 1) Decision trees have the potential to model any
general form of label distributions by a mixture of leaf node predictions. 2)
The learning of differentiable decision trees can be combined with
representation learning. We define a distribution-based loss function for a
forest, enabling all the trees to be learned jointly, and show that an update
function for leaf node predictions, which guarantees a strict decrease of the
loss function, can be derived by variational bounding. The effectiveness of the
proposed LDLFs is verified on several LDL tasks and a computer vision
application, showing significant improvements to the state-of-the-art LDL
methods.
