  Age estimation from facial images is typically cast as a label distribution
learning or regression problem, since aging is a gradual progress. Its main
challenge is the facial feature space w.r.t. ages is inhomogeneous, due to the
large variation in facial appearance across different persons of the same age
and the non-stationary property of aging. In this paper, we propose two Deep
Differentiable Random Forests methods, Deep Label Distribution Learning Forest
(DLDLF) and Deep Regression Forest (DRF), for age estimation. Both of them
connect split nodes to the top layer of convolutional neural networks (CNNs)
and deal with inhomogeneous data by jointly learning input-dependent data
partitions at the split nodes and age distributions at the leaf nodes. This
joint learning follows an alternating strategy: (1) Fixing the leaf nodes and
optimizing the split nodes and the CNN parameters by Back-propagation; (2)
Fixing the split nodes and optimizing the leaf nodes by Variational Bounding.
Two Deterministic Annealing processes are introduced into the learning of the
split and leaf nodes, respectively, to avoid poor local optima and obtain
better estimates of tree parameters free of initial values. Experimental
results show that DLDLF and DRF achieve state-of-the-art performance on three
age estimation datasets.
