Escaping the Sample Trap: Fast and Accurate Epistemic Uncertainty Estimation with Pairwise-Distance Estimators

In machine learning, the ability to assess uncertainty in model predictions is crucial for decision-making, safety-critical applications, and model generalizability. This work introduces a novel approach for epistemic uncertainty estimation for ensemble models using pairwise-distance estimators (PaiDEs). These estimators utilize the pairwise-distance between model components to establish bounds on entropy, which are then used as estimates for information-based criterion. Unlike recent deep learning methods for epistemic uncertainty estimation, which rely on sample-based Monte Carlo estimators, PaiDEs are able to estimate epistemic uncertainty up to 100 times faster, over a larger input space (up to 100 times) and perform more accurately in higher dimensions. To validate our approach, we conducted a series of experiments commonly used to evaluate epistemic uncertainty estimation: 1D sinusoidal data, $\textit{Pendulum-v0}$, $\textit{Hopper-v2}$, $\textit{Ant-v2}$ and $\textit{Humanoid-v2}$. For each experimental setting, an Active Learning framework was applied to demonstrate the advantages of PaiDEs for epistemic uncertainty estimation.