Bayesian inference for transductive learning of kernel matrix using the
Tanner-Wong data augmentation algorithm
Zhihua Zhang, Dit-Yan Yeung, James T. Kwok
Abstract:
In kernel methods, an interesting recent development seeks to
learn a good kernel from empirical data automatically. In this
paper, by regarding the transductive learning of the kernel matrix
as a missing data problem, we propose a Bayesian hierarchical
model for the problem and devise the Tanner-Wong data augmentation
algorithm for making inference on the model. The Tanner-Wong
algorithm is closely related to Gibbs sampling, and it also bears
a strong resemblance to the expectation-maximization (EM)
algorithm. For an efficient implementation, we propose a
simplified Bayesian hierarchical model and the corresponding
Tanner-Wong algorithm. We express the relationship between the
kernel on the input space and the kernel on the output space as a
symmetric-definite generalized eigenproblem. Based on this
eigenproblem, an efficient approach to choosing the base kernel
matrices is presented. The effectiveness of our Bayesian model
with the Tanner-Wong algorithm is demonstrated through some
classification experiments showing promising results.
Proceedings of the Twenty-First International Conference on Machine Learning
(ICML-2004), pp.935-942, Banff, Alberta, Canada, July 2004.
Pdf:
http://www.cs.ust.hk/~jamesk/papers/icml04b.pdf
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