Adaptive local kernels formulation of mutual information with application to active post-seismic building damage inference

The abundance of training data is not guaranteed in various supervised learning applications. One of these situations is the post-earthquake regional damage assessment of buildings. Querying the damage label of each building requires a thorough inspection by experts, and thus, is an expensive task. A practical approach is to sample the most informative buildings in a sequential learning scheme. Active learning methods recommend the most informative cases that are able to maximally reduce the generalization error. The information-theoretic measure of mutual information (MI), which maximizes the expected information gain over the input domain, can be used for informative sampling of a dataset in a pool-based scenario. However, the computational complexity of the standard MI algorithm prevents the utilization of this method on large datasets. A local kernels strategy was proposed to reduce the computational costs, but the adaptability of the kernels to the observed labels was not considered in the original formulation of this strategy. In this article, an adaptive local kernels methodology is developed that enables the conformability of the kernels to the observed output data while enhancing the computational complexity of the standard MI algorithm. The proposed algorithm is developed to work with a Gaussian process regression (GPR) method, where the kernel hyperparameters are updated after each label query using maximum likelihood estimation. In the sequential learning procedure, the updated hyperparameters can be used in the MI kernel matrices to improve the sample suggestion performance. The advantages of the proposed method are demonstrated in a simulation of the 2018 Anchorage, AK, earthquake. It is shown that while the proposed algorithm enables GPR to reach acceptable performance using fewer training data, the computational demand remains lower than the standard local kernels strategy.