  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) is one of the most effective
criteria to evaluate the effectiveness of the samples in a pool-based sample
selection 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 allows for 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 on a Gaussian process regression (GPR) framework, where the kernel
hyperparameters are updated after each label query using the 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 are demonstrated on a simulation of the 2018
Anchorage, AK, earthquake. It is shown that while the proposed algorithm
enables GPR to reach acceptable performance with fewer training data, the
computational demands remain lower than the standard local kernels strategy.
