Age estimation from facial images is typically cast as a nonlinear regression problem. The main challenge of this problem is the facial feature space w.r.t. ages is heterogeneous, due to the large variation in facial appearance across different persons of the same age and the nonstationary property of aging patterns. In this paper, we propose Deep Regression Forests (DRFs), an end-to-end model, for age estimation. DRFs connect the split nodes to a fully connected layer of a convolutional neural network (CNN) and deal with heterogeneous data by jointly learning input-dependant data partitions at the split nodes and data abstractions at the leaf nodes. This joint learning follows an alternating strategy: First, by fixing the leaf nodes, the split nodes as well as the CNN parameters are optimized by Back-propagation; Then, by fixing the split nodes, the leaf nodes are optimized by iterating a step-size free and fastconverging update rule derived from Variational Bounding. We verify the proposed DRFs on three standard age estimation benchmarks and achieve state-of-the-art results on all of them.

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.

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