Parametric Models for Mutual Kernel Matrix Completion

TL;DR

This paper introduces parametric models for completing multiple incomplete kernel matrices, controlling model flexibility with parameters, ensuring positive definiteness via LogDet divergence, and demonstrating improved generalization performance.

Contribution

The study proposes new parametric methods for kernel matrix completion that incorporate model restrictions and use LogDet divergence to guarantee positive definiteness, enhancing performance.

Findings

Significant improvements in generalization performance.

Effective control of model flexibility to prevent overfitting.

Guarantees positive definiteness of kernel matrices.

Abstract

Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the flexibility of the model by parameterizing the model matrix. By imposing restrictions on the model covariance, overfitting of the data is avoided. A limitation of kernel matrix estimations done via optimization of an objective function is that the positive definiteness of the result is not guaranteed. In view of this limitation, our proposed methods employ the LogDet divergence, which ensures the positive definiteness of the resulting inferred kernel matrix. We empirically show that our proposed restricted covariance models, employed with LogDet divergence, yield significant improvements in the generalization performance of previous completion methods.