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.
Accurate ground truth pose is essential to the training of most existing head pose estimation algorithms. However, in many cases, the "ground truth" pose is obtained in rather subjective ways, such as asking the human subjects to stare at different markers on the wall. In such case, it is better to use soft labels rather than explicit hard labels. Therefore, this paper proposes to associate a multivariate label distribution (MLD) to each image. An MLD covers a neighborhood around the original pose. Labeling the images with MLD can not only alleviate the problem of inaccurate pose labels, but also boost the training examples associated to each pose without actually increasing the total amount of training examples. Two algorithms are proposed to learn from the MLD by minimizing the weighted Jeffrey's divergence between the predicted MLD and the ground truth MLD. Experimental results show that the MLD-based methods perform significantly better than the compared state-of-the-art head pose estimation algorithms. By observing that the faces at close ages are similar, some Label Distribution Learning (LDL) methods have been proposed to solve age estimation tasks that they treat age distributions as the training targets. However, these existent LDL methods are limited because they can hardly extract enough useful information from complex image features. In this paper, Sparsity Conditional Energy Label Distribution Learning (SCE-LDL) is proposed to solve this problem. In the proposed SCE-LDL, age distributions are used as the training targets and energy function is utilized to define the age distribution. By assigning a suitable energy function, SCE-LDL can learn distributed representations, which provides the model with strong expressiveness for capturing enough of the complexity of interest from image features. The sparsity constraints are also incorporated to ameliorate the model. Experiment results in two age datasets show remarkable advantages of the proposed SCE-LDL model over the previous proposed age estimation methods. One of the main difficulties in facial age estimation is that the learning algorithms cannot expect sufficient and complete training data. Fortunately, the faces at close ages look quite similar since aging is a slow and smooth process. Inspired by this observation, instead of considering each face image as an instance with one label (age), this paper regards each face image as an instance associated with a label distribution. The label distribution covers a certain number of class labels, representing the degree that each label describes the instance. Through this way, one face image can contribute to not only the learning of its chronological age, but also the learning of its adjacent ages. Two algorithms, named IIS-LLD and CPNN, are proposed to learn from such label distributions. Experimental results on two aging face databases show remarkable advantages of the proposed label distribution learning algorithms over the compared single-label learning algorithms, either specially designed for age estimation or for general purpose. Most existing facial expression recognition methods assume the availability of a single emotion for each expression in the training set. However, in practical applications, an expression rarely expresses pure emotion, but often a mixture of different emotions. To address this problem, this paper deals with a more common case where multiple emotions are associated to each expression. The key idea is to learn the specific description degrees of all basic emotions for each expression and the mapping from the expression images to the emotion distributions by the proposed emotion distribution learning (EDL) method.The databases used in the experiments are the s-JAFFE database and the s-BU database as they are the databases with explicit scores for each emotion on each expression image. Experimental results show that EDL can effectively deal with the emotion distribution recognition problem and perform remarkably better than the state-of-the-art multi-label learning methods. 