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Deep Regression Forests for Age Estimation
Wei Shen, Yilu Guo, Yan Wang, Kai Zhao, Bo Wang, Alan Yuille
TL;DR
Facial age regression is difficult because facial appearance is heterogeneous across people and aging patterns change with age. The paper proposes Deep Regression Forests, which jointly learn soft input-dependent partitions and leaf abstractions with CNN features through alternating optimization. DRFs achieve state-of-the-art results on three standard age-estimation benchmarks.
Problem
Precise facial age estimation requires learning a nonlinear mapping despite large same-age appearance variation and non-stationary aging patterns.
Method
Deep Regression Forests jointly learn soft input-dependent partitions at split nodes and data abstractions at leaf nodes, alternating CNN back-propagation with Variational Bounding updates.
Results
DRFs achieve state-of-the-art results on three standard age-estimation benchmarks.
Takeaways & Limitations
End-to-end learning of partitions and leaf abstractions lets DRFs model heterogeneous facial feature spaces while learning nonlinear regression to age.
Takeaways & Limitations
Leaf-node output distributions are assumed to be Gaussian because each leaf is ideally expected to represent a compact homogeneous subset.
Abstract
from arXiv · showhide
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 non-stationary 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 fast-converging 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.
1. Introduction
Precise facial age regression remains difficult because facial appearance varies substantially among people of the same age and aging patterns change across life stages. DRFs address this heterogeneity with jointly learned soft partitions and leaf abstractions integrated into an end-to-end deep model, achieving state-of-the-art results on three benchmarks.
- Precise age regression maps facial image features to chronological age, whereas age-group estimation predicts only whether age falls within a range.
- Facial age estimation is challenging because same-age people can look substantially different and facial aging changes from shape during childhood to skin texture during adulthood.
- Existing approaches use global nonlinear mappings or divide-and-conquer local regressors, but heterogeneous distributions can cause overfitting or age-based partitions that miss homogeneous subsets.
- DRFs integrate differentiable regression forests with CNNs through alternating optimization of split nodes and network parameters, followed by leaf-node updates.
- DRFs achieve state-of-the-art results on MORPH, FGNET, and CACD age-estimation benchmarks.
- DRFs jointly learn input-dependent data partitions at split nodes and data abstractions at leaf nodes to model heterogeneous facial features.
2. Related Work
Prior age-estimation work uses global nonlinear mappings, divide-and-conquer regressors, ordinal regression, label distribution learning, and deep CNNs. These approaches address parts of the problem, but heterogeneous facial data remains an open issue and differentiable forests extend tree-based learning toward regression.
- Kernel-based methods learn global nonlinear mappings or low-dimensional aging-manifold embeddings, but heterogeneous inputs can bias these mappings.
- Divide-and-conquer methods learn local regressors, while tree-based approaches traditionally make hard partitions that may not match homogeneous facial subsets.
- Ordinal regression exploits age-label order through multiple binary classifiers but is limited by its lack of scalability.
- Label distribution learning models correlations across nearby ages, reflecting that faces at close ages share related appearance information.
- Deep CNN age-estimation methods enable end-to-end learning, but handling heterogeneous facial data remains an open issue.
- Differentiable decision forests replace hard split decisions with soft partition functions, enabling joint learning with deep networks; DRFs adapt this framework to continuous regression.
3. Deep Regression Forests
Deep Regression Forests model regression with soft, learned partitions and leaf distributions, jointly optimized with CNN features. Training alternates between back-propagating split parameters and updating Gaussian leaf distributions through variational bounding.
- 3.1. Problem Formulation: A regression tree models p(y|x) using split nodes with soft routing and leaf nodes containing probability density distributions.The mapping is obtained from the conditional output distribution represented by the tree.
- 3.1. Problem Formulation: Soft split functions use CNN features, with an index function connecting split nodes to selected outputs of the feature-learning network.The CNN parameters and split-node parameters are learned through the differentiable routing functions.
- 3.2. Tree Optimization: Training alternates between fixing leaf distributions while optimizing split parameters and fixing split parameters while optimizing leaf distributions.The split parameters are updated by back-propagation, while the overall procedure repeats until convergence or a maximum iteration count.
- 3.2. Tree Optimization: Leaf distributions are modeled as Gaussians, parameterized by means and covariance matrices to represent compact homogeneous subsets.This parametric representation makes leaf-node optimization tractable.
- 3.2.2 Learning Leaf Nodes by Variational Bounding: Variational bounding updates leaf means and covariances with step-size-free, fast-converging rules that do not require manually selected learning rates.The bound is minimized iteratively while preserving non-increasing values of the original objective under the stated update construction.
- 3.2.3 Learning a Regression Forest: A regression forest averages tree losses during learning and averages individual tree predictions at test time, with independent leaf distributions for each tree.Trees may share CNN parameters while using different split-function assignments and separate leaf distributions.
4. Experiments
The experiments evaluate DRFs on three standard age-estimation benchmarks using established datasets, preprocessing, metrics, and comparison settings. Results show strong performance under heterogeneous and biased data, while visualizations and parameter studies examine the learned model.
- Benchmark setup: DRFs are evaluated against state-of-the-art methods on MORPH, FG-NET, and CACD using standard benchmark protocols.The experiments include multiple MORPH settings, leave-one-person-out validation on FG-NET, and separate CACD training and validation configurations.
- Benchmark results: 3.85 MAE is achieved on FG-NET, making DRFs the only compared method below 4.0 MAE.Evaluation uses leave-one-person-out cross-validation, which separates all images of one person for testing.
- Benchmark results: DRFs outperform DEX on CACD under both training configurations, with a larger improvement when trained on the smaller validation set.The authors attribute this pattern to DRFs directly addressing heterogeneous data when training data are limited.
- Model analysis: The learned leaf-node Gaussian mixture resembles the MORPH age histogram, while overlapping distributions reflect varied facial appearances among people of the same age.The learned distribution is denser around ages in the 20s and 40s and broader near age 60 because sample counts vary across partitions.
- Parameter discussion: Increasing the number of trees improves performance, whereas increasing tree depth initially lowers MAE before performance stabilizes.The study varies each hyper-parameter separately on MORPH Setting I while fixing the other to its default value.
5. Conclusion
The conclusion presents DRFs as an end-to-end approach for nonlinear age regression in heterogeneous facial feature spaces. Soft, learned partitions connect the forest to deep networks, while alternating optimization produces state-of-the-art results on three benchmarks.
- Contribution: DRFs learn nonlinear regression between heterogeneous facial feature spaces and chronological ages.The model is designed for precise facial age estimation.
- Learning strategy: Soft split-node partitioning enables end-to-end learning with a deep network, while leaf-node abstraction is optimized through a step-size-free update derived from Variational Bounding.Split and leaf nodes are learned through alternating optimization.
- Learning strategy: The end-to-end learning makes split partitions input-dependent and local input-output correlations at leaf nodes homogeneous.These properties are presented as consequences of jointly learning the forest components.
- Results: DRFs achieve state-of-the-art results on three age-estimation benchmarks.The conclusion summarizes the reported experimental outcome across the benchmark suite.