LFaB: Low fidelity as Bias for Active Learning in the chemical configuration space

Active learning promises to provide an optimal training sample selection procedure in the construction of machine learning models. It often relies on minimizing the model's variance, which is assumed to decrease the prediction error. Still, it is frequently even less efficient than pure random sampling. Motivated by the bias-variance decomposition, we propose to minimize the model's bias instead of its variance. By doing so, we are able to almost exactly match the best-case error over all possible greedy sample selection procedures for a relevant application. Our bias approximation is based on using cheap to calculate low fidelity data as known from $Δ$-ML or multifidelity machine learning. We exemplify our approach for a wider class of applications in quantum chemistry including predicting excitation energies and ab initio potential energy surfaces. Here, the proposed method reduces training data consumption by up to an order of magnitude compared to standard active learning.