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.
Label Distribution Learning (LDL) is a general learning framework which includes both single label and multi-label learning as its special cases. One of the main assumptions made in traditional LDL algorithms is the derivation of the parametric model as the maximum entropy model. While it is a reasonable assumption without additional information, there is no particular evidence supporting it in the problem of LDL. Alternatively, using a general LDL model family to approximate this parametric model can avoid the potential influence of the specific model. In order to learn this general model family, this paper uses a method called Logistic Boosting Regression (LogitBoost) which can be seen as an additive weighted function regression from the statistical viewpoint. For each step, we can fit individual weighted regression function (base learner) to realize the optimization gradually. The base learners are chosen as weighted regression tree and vector tree, which constitute two algorithms named LDLogitBoost and AOSO-LDLogitBoost in this paper. Experiments on facial expression recognition, crowd opinion prediction on movies and apparent age estimation show that LDLogitBoost and AOSO-LDLogitBoost can achieve better performance than traditional LDL algorithms as well as other LogitBoost algorithms. This paper studies an interesting problem: is it possible to predict the crowd opinion about a movie before the movie is actually released? The crowd opinion is here expressed by the distribution of ratings given by a sufficient amount of people. Consequently, the pre-release crowd opinion prediction can be regarded as a Label Distribution Learning (LDL) problem. In order to solve this problem, a Label Distribution Support Vector Regressor (LDSVR) is proposed in this paper. The basic idea of LDSVR is to fit a sigmoid function to each component of the label distribution simultaneously by a multi-output support vector machine. Experimental results show that LDSVR can accurately predict peoples's rating distribution about a movie just based on the pre-release metadata of the movie. Convolutional neural networks (ConvNets) have achieved excellent recognition performance in various visual recognition tasks. A large labeled training set is one of the most important factors for its success. However, it is difficult to collect sufficient training images with precise labels in some domains, such as apparent age estimation, head pose estimation, multilabel classification, and semantic segmentation. Fortunately, there is ambiguous information among labels, which makes these tasks different from traditional classification. Based on this observation, we convert the label of each image into a discrete label distribution, and learn the label distribution by minimizing a Kullback–Leibler divergence between the predicted and ground-truth label distributions using deep ConvNets. The proposed deep label distribution learning (DLDL) method effectively utilizes the label ambiguity in both feature learning and classifier learning, which help prevent the network from overfitting even when the training set is small. Experimental results show that the proposed approach produces significantly better results than the state-of-the-art methods for age estimation and head pose estimation. At the same time, it also improves recognition performance for multi-label classification and semantic segmentation tasks.