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LABEL DISTRIBUTION LEARNING AND ITS APPLICATIONS Xin Geng （耿新） Pattern Learning and Mining (PALM) Lab （模式学习与挖掘实验室, ） School of Computer Science and Engineering Southeast University, Nanjing, China （东南大学）

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Learning with Ambiguity Single-label Learning Multi-label Learning Label Ambiguity Less AmbiguityMore Ambiguity ? ?

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Label Ambiguity “What describes the instance?” cloudwaterskybuilding Multi-label Learning

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More Ambiguity? “How to describe the instance?” some cloud much water mostly sky a bit of building

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How to learn? MLL Thresholding Positive labels MLL Label Distribution Learning (LDL) Assign a real number to each label Importance Confidence Level …… Not a good choice! Keep more, learn more

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LDL – Problem Formulation A real number is assigned to the label for the instance WLOG Complete label set Description Degree Label Distribution

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LDL – Problem Formulation

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LDL – Algorithms Two Categories Conditional Probability Mass Function (Classification) Model the mapping from the instance x to the label distribution d via a conditional PMF Multivariate Support Vector Regression (Regression) Model the mapping from the instance x to the label distribution d via a multivariate support vector machine

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Conditional Probability Mass Function Learning from Label Distribution Training set: Goal: learn a conditional mass function that can generate label distributions similar to given the instance K-L divergence

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Conditional Probability Mass Function Directly minimizing the K-L divergence between predicted and real LDs MaxEnt Model

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Conditional Probability Mass Function IIS-LLD [Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]

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Conditional Probability Mass Function BFGS-LLD [Geng and Ji, ICDMW’13]

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Conditional Probability Mass Function CPNN [Geng, Yin, and Zhou, TPAMI’13] 3

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Multivariate Support Vector Regression Two issues 1. How to output a distribution composed by multiple components? Multivariate Support Vector Regression (M-SVR) [Fernandez et al., TSP’04] 2. How to constrain each component of the distribution within the range of a probability, i.e., [0, 1]? Model the regression by a sigmoid function Solve the two problems simultaneously LDSVR [Geng and Hou, submitted to IJCAI’15] Fit a sigmoid function to each component of the label distribution simultaneously by a support vector machine

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Multivariate Support Vector Regression Sigmoid model Target function of SVR Loss Function

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Multivariate Support Vector Regression The loss function Dimension by dimension Insensitive Zone Problem: Examples falling into the area ρ 1 will be penalized once while those falling into the area ρ 2 will be penalized twice.

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Multivariate Support Vector Regression The loss function Multivariate Insensitive Zone Problem: Difficult to optimize and apply the kernel trick

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Multivariate Support Vector Regression The loss function Measure the loss by calculating how far away from z i another point z′ i ∈ R c should move to get the same output with the ground truth

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Multivariate Support Vector Regression The loss function Replacing u i with u′ i /4 Insensitive Zone

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Age Estimation Aging is a slow and gradual progress The faces at close ages look quite similar Can we use the neighboring ages to relieve the ‘lack of training samples’ problem? [Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]

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Age Estimation Experiment [Geng, Yin, and Zhou, TPAMI’13] [Geng, Smith-Miles, and Zhou, AAAI’10]

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Head Pose Estimation [Geng and Xia, CVPR’14] Bivariate Label Distribution

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Head Pose Estimation Experiment [Geng and Xia, CVPR’14]

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Multilabel Ranking for Natural Scene Images Multilabel Ranking A bipartition of the relevant (positive) and irrelevant (negative) labels A proper ranking over relevant labels Multiple Rankers: Subjective Inconsistent “Ground Truth” [Geng and Luo, CVPR’14]

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Multilabel Ranking for Natural Scene Images Multilabel Ranking by Preference Distribution [Geng and Luo, CVPR’14] Virtual labels as split point between relevant and irrelevant labels

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Multilabel Ranking for Natural Scene Images Experiment [Geng and Luo, CVPR’14]

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Crowd Counting [Wang, Zhang and Geng, Neurocomputing’15]

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Pre-release Prediction of Crowd Opinion on Movies [Geng and Hou, submitted to IJCAI’15] Crowd Rating Distribution Pre-release Metadata

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Pre-release Prediction of Crowd Opinion on Movies Experiment [Geng and Hou, submitted to IJCAI’15]

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Conclusion Label distribution learning More general framework than single-label and multi-label learning Deals with different importance of labels Matches certain problems better Needs special design It is useful when There is a natural measure of description degree There are multiple labeling sources for one instance The labels are correlated to each other ……

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Interested? Download the LDL Matlab package from

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THANK YOU palm.seu.edu.cn

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