  Inhomogeneities in real-world data, e.g., due to changes in the observation
noise level or variations in the structural complexity of the source function,
pose a unique set of challenges for statistical inference. Accounting for them
can greatly improve predictive power when physical resources or computation
time is limited. In this paper, we draw on recent theoretical results on the
estimation of local function complexity (LFC), derived from the domain of local
polynomial smoothing (LPS), to establish a notion of local structural
complexity, which is used to develop a model-agnostic active learning (AL)
framework. Due to its reliance on pointwise estimates, the LPS model class is
not robust and scalable concerning large input space dimensions that typically
come along with real-world problems. Here, we derive and estimate the Gaussian
process regression (GPR)-based analog of the LPS-based LFC and use it as a
substitute in the above framework to make it robust and scalable. We assess the
effectiveness of our LFC estimate in an AL application on a prototypical
low-dimensional synthetic dataset, before taking on the challenging real-world
task of reconstructing a quantum chemical force field for a small organic
molecule and demonstrating state-of-the-art performance with a significantly
reduced training demand.
