Label Distribution Learning

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 \emph{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 fifteen real-world datasets show clear advantages of the specialized algorithms, which indicates the importance of special design for the characteristics of the LDL problem

Reconstruction for the Signature of a Rough Path

Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of this uniqueness result does not contain any information on how to "see" the trajectory of a (tree-reduced) rough path from its signature, and a constructive understanding on the uniqueness result (in particular on the inverse of S) has become an interesting and important question. The aim of the present paper is to reconstruct a rough path from its signature in an explicit and universal way.Comment: 39 pages, 6 figure

Anomaly, Charge Quantization and Family

We first review the three known chiral anomalies in four dimensions and then use the anomaly free conditions to study the uniqueness of quark and lepton representations and charge quantizations in the standard model. We also extend our results to theory with an arbitrary number of color. Finally, we discuss the family problem.Comment: 7 pages, LaTex file, Proceedings of the International Workshop on Nonperturbative Methods and Lattice QCD, Guangzhou, Chin