Parametric Models for Mutual Kernel Matrix Completion
This work addresses a specific bottleneck in kernel-based machine learning for handling incomplete data, offering an incremental advancement with practical benefits.
The paper tackles the problem of completing multiple incomplete kernel matrices while controlling model flexibility and ensuring positive definiteness, resulting in significant improvements in generalization performance over previous methods.
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.