The Stationarity Bias: Stratified Stress-Testing for Time-Series Imputation in Regulated Dynamical Systems

TL;DR

This paper identifies a bias in time-series imputation benchmarks caused by dominant stationary regimes and proposes a stratified stress-test approach to evaluate models across both stationary and transient regimes, with implications for regulated systems.

Contribution

It formalizes the Stationarity Bias in benchmarks and introduces a Stratified Stress-Test to evaluate models in both stationary and transient regimes, demonstrated on glucose monitoring data.

Findings

Linear interpolation excels in stationary regimes, confirming simplicity suffices there.

Deep models outperform during transients, preserving signal shape and accuracy.

Imposing realistic missingness improves model robustness for safety-critical applications.

Abstract

Time-series imputation benchmarks employ uniform random masking and shape-agnostic metrics (MSE, RMSE), implicitly weighting evaluation by regime prevalence. In systems with a dominant attractor -- homeostatic physiology, nominal industrial operation, stable network traffic -- this creates a systematic \emph{Stationarity Bias}: simple methods appear superior because the benchmark predominantly samples the easy, low-entropy regime where they trivially succeed. We formalize this bias and propose a \emph{Stratified Stress-Test} that partitions evaluation into Stationary and Transient regimes. Using Continuous Glucose Monitoring (CGM) as a testbed -- chosen for its rigorous ground-truth forcing functions (meals, insulin) that enable precise regime identification -- we establish three findings with broad implications:(i)~Stationary Efficiency: Linear interpolation achieves state-of-the-art reconstruction during stable intervals, confirming that complex architectures are computationally wasteful in low-entropy regimes.(ii)~Transient Fidelity: During critical transients (post-prandial peaks, hypoglycemic events), linear methods exhibit drastically degraded morphological fidelity (DTW), disproportionate to their RMSE -- a phenomenon we term the \emph{RMSE Mirage}, where low pointwise error masks the destruction of signal shape.(iii)~Regime-Conditional Model Selection: Deep learning models preserve both pointwise accuracy and morphological integrity during transients, making them essential for safety-critical downstream tasks. We further derive empirical missingness distributions from clinical trials and impose them on complete training data, preventing models from exploiting unrealistically clean observations and encouraging robustness under real-world missingness. This framework generalizes to any regulated system where routine stationarity dominates critical transients.