Statistical-mechanics analysis of Gaussian labeled-unlabeled classification problems

ELC International Meeting on Inference, Computation, and Spin Glasses

Tanaka, Toshiyuki^1

Graduate School of Informatics, Kyoto University, 36-1 Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501, Japan^1

关键词: Analytical results;    Labeled and unlabeled data;    Parameter vectors;    Posterior means;    Probability modeling;    Replica symmetry;    Semi- supervised learning;    Unlabeled data;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/473/1/012001/pdf
DOI  :  10.1088/1742-6596/473/1/012001

来源: IOP

【 摘 要 】

The labeled-unlabeled classification problem in semi-supervised learning is studied via statistical-mechanics approach. We analytically investigate performance of a learner with an equal-weight mixture of two symmetrically-located Gaussians, performing posterior mean estimation of the parameter vector on the basis of a dataset consisting of labeled and unlabeled data generated from the same probability model as that assumed by the learner. Under the assumption of replica symmetry, we have analytically obtained a set of saddle-point equations, which allows us to numerically evaluate performance of the learner. On the basis of the analytical result we have observed interesting phenomena, in particular the coexistence of good and bad solutions, which may happen when the number of unlabeled data is relatively large compared with that of labeled data.