Differential mutual information forward search for multi-kernel discriminant-component selection with an application to privacy-preserving classification

In machine learning, feature engineering has been a pivotal stage in building a high-quality predictor. Particularly, this work explores the multiple Kernel Discriminant Component Analysis (mKDCA) feature-map and its variants. However, seeking the right subset of kernels for mKDCA feature-map can be challenging. Therefore, we consider the problem of kernel selection, and propose an algorithm based on Differential Mutual Information (DMI) and incremental forward search. DMI serves as an effective metric for selecting kernels, as is theoretically supported by mutual information and Fisher's discriminant analysis. On the other hand, incremental forward search plays a role in removing redundancy among kernels. Finally, we illustrate the potential of the method via an application in privacy-aware classification, and show on three mobile-sensing datasets that selecting an effective set of kernels for mKDCA feature-maps can enhance the utility classification performance, while successfully preserve the data privacy. Specifically, the results show that the proposed DMI forward search method can perform better than the state-of-the-art, and, with much smaller computational cost, can perform as well as the optimal, yet computationally expensive, exhaustive search.