Unifying Approaches in Data Subset Selection via Fisher Information and Information-Theoretic Quantities

The mutual information between predictions and model parameters -- also referred to as expected information gain or BALD in machine learning -- measures informativeness. It is a popular acquisition function in Bayesian active learning and Bayesian optimal experiment design. In data subset selection, i.e. active learning and active sampling, several recent works use Fisher information, Hessians, similarity matrices based on the gradients, or simply the gradient lengths to compute the acquisition scores that guide sample selection. Are these different approaches connected, and if so how? In this paper, we revisit the Fisher information and use it to show how several otherwise disparate methods are connected as approximations of information-theoretic quantities.