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Kernel matrix regression

We address the problem of filling missing entries in a kernel Gram matrix, given a related full Gram matrix. We attack this problem from the viewpoint of regression, assuming that the two kernel matrices can be considered as explanatory variables and response variables, respectively. We propose a variant of the regression model based on the underlying features in the reproducing kernel Hilbert space by modifying the idea of kernel canonical correlation analysis, and we estimate the missing entries by fitting this model to the existing samples. We obtain promising experimental results on gene network inference and protein 3D structure prediction from genomic datasets. We also discuss the relationship with the em-algorithm based on information geometry.