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.
Another way to address the LDL task, is to extend existing learning algorithms to deal with label distributions. Geng and Hou @cite_7 proposed LDSVR, a LDL method by extending support vector regressor, which fit a sigmoid function to each component of the distribution simultaneously by a support vector machine. Xing @cite_26 then extended boosting to address the LDL task by additive weighted regressors. They showed that using the vector tree model as the weak regressor can lead to better performance and named this method AOSO-LDLLogitBoost. As the learning of this tree model is based on locally-optimal hard data partition functions at each split node, AOSO-LDLLogitBoost is unable to be combined with representation learning. Extending current deep learning algorithms to address the LDL task is an interesting topic. But, the existing such a method, called DLDL @cite_8 , still focuses on maximum entropy model based LDL.
@cite_26 @cite_7 @cite_8
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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. We describe distributed algorithms for two widely-used topic models, namely the Latent Dirichlet Allocation (LDA) model, and the Hierarchical Dirichet Process (HDP) model. In our distributed algorithms the data is partitioned across separate processors and inference is done in a parallel, distributed fashion. We propose two distributed algorithms for LDA. The first algorithm is a straightforward mapping of LDA to a distributed processor setting. In this algorithm processors concurrently perform Gibbs sampling over local data followed by a global update of topic counts. The algorithm is simple to implement and can be viewed as an approximation to Gibbs-sampled LDA. The second version is a model that uses a hierarchical Bayesian extension of LDA to directly account for distributed data. This model has a theoretical guarantee of convergence but is more complex to implement than the first algorithm. Our distributed algorithm for HDP takes the straightforward mapping approach, and merges newly-created topics either by matching or by topic-id. Using five real-world text corpora we show that distributed learning works well in practice. For both LDA and HDP, we show that the converged test-data log probability for distributed learning is indistinguishable from that obtained with single-processor learning. Our extensive experimental results include learning topic models for two multi-million document collections using a 1024-processor parallel computer. Although multi-label learning can deal with many problems with label ambiguity, it does not fit some real applications well where the overall distribution of the importance of the labels matters. This paper proposes a novel learning paradigm named label distribution learning (LDL) for such kind of applications. The label distribution covers a certain number of labels, representing the degree to which each label describes the instance. LDL is a more general learning framework which includes both single-label and multi-label learning as its special cases. This paper proposes six working LDL algorithms in three ways: problem transformation, algorithm adaptation, and specialized algorithm design. In order to compare the performance of the LDL algorithms, six representative and diverse evaluation measures are selected via a clustering analysis, and the first batch of label distribution datasets are collected and made publicly available. Experimental results on one artificial and 15 real-world datasets show clear advantages of the specialized algorithms, which indicates the importance of special design for the characteristics of the LDL problem. We propose a novel method called deep convolutional decision jungle (CDJ) and its learning algorithm for image classification. The CDJ maintains the structure of standard convolutional neural networks (CNNs), i.e. multiple layers of multiple response maps fully connected. Each response map-or node-in both the convolutional and fully-connected layers selectively respond to class labels s.t. each data sample travels via a specific soft route of those activated nodes. The proposed method CDJ automatically learns features, whereas decision forests and jungles require pre-defined feature sets. Compared to CNNs, the method embeds the benefits of using data-dependent discriminative functions, which better handles multi-modal heterogeneous data; further,the method offers more diverse sparse network responses, which in turn can be used for cost-effective learning classification. The network is learnt by combining conventional softmax and proposed entropy losses in each layer. The entropy loss,as used in decision tree growing, measures the purity of data activation according to the class label distribution. The back-propagation rule for the proposed loss function is derived from stochastic gradient descent (SGD) optimization of CNNs. We show that our proposed method outperforms state-of-the-art methods on three public image classification benchmarks and one face verification dataset. We also demonstrate the use of auxiliary data labels, when available, which helps our method to learn more discriminative routing and representations and leads to improved classification.