2014 Fiscal Year Annual Research Report
Empirical Bayes Kernels: Unsupervised Kernel Learning
| Project/Area Number |
25540100
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| Research Institution | Kyoto University |
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Principal Investigator |
CUTURI Marco 京都大学, 情報学研究科, 准教授 (80597344)
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| Project Period (FY) |
2013-04-01 – 2015-03-31
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| Keywords | Metric learning / Kernel learning / Aitchison geometry / Probability Simplex / Contrastive Divergence / Stochastic Optimization |
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| Outline of Annual Research Achievements |
The focus of this research was to obtain scaleable methods to define kernels and metrics on datapoints by taking advantage of large datasets of unlabeled points.
We have explored this research topic in the two recent years by considering the particular problem of defining metrics for histograms, that is metrics for vectors who have non-negative components and whose coordinates sum to 1.
Our first results focused on a particular geometry for histograms studied by Aitchison in a series of groundbreaking papers. This resulted in a publication at the Asian Conference on Machine Learning and then the Machine Learning Journal on generalized Aitchison embeddings.
We explored further that topic and showed that it was possible to learn a more advanced family of embeddings by using a technique inspired by Lebanon's work on unsupervised metric learning in the simplex.
All in all, these two contributions have proposed a viable approach to define Hilbertian metrics and therefore kernels for points in the simplex, and have therefore succeeded to provide an answer to the set of questions that were considered in defining this project.
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| Remarks |
We have released code for our previous work. We expect to release the code for our most recent contribution, about the unsupervised learning of Aitchison embeddings for histograms.
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