Measuring the Predictability of Recommender Systems using Structural Complexity Metrics

Recommender Systems (RS) shape the filtering and curation of online content, yet we have limited understanding of how predictable their recommendation outputs are. We propose data-driven metrics that quantify the predictability of recommendation datasets by measuring the structural complexity of the user-item interaction matrix. High complexity indicates intricate interaction patterns that are harder to predict; low complexity indicates simpler, more predictable structures. We operationalize structural complexity via data perturbations, using singular value decomposition (SVD) to assess how stable the latent structure remains under perturbations. Our hypothesis is that random perturbations minimally affect highly organized data, but cause substantial structural disruption in intrinsically complex data. By analyzing prediction errors on perturbed interactions, we derive metrics that quantify this sensitivity at both the dataset and the interaction levels, yielding a principled measure of inherent predictability. Experiments on real-world datasets show that our structural complexity metrics correlate with the performance of state-of-the-art recommendation algorithms. We also demonstrate structure-aware data selection: in low-data settings, models trained on a carefully chosen subset of interactions with low structural perturbation error consistently outperform models trained on the full dataset. Thus, structural complexity serves both as a precise diagnostic of dataset complexity and as a principled foundation for efficient, data-centric training of RS.