The Stationarity Bias: Stratified Stress-Testing for Time-Series Imputation in Regulated Dynamical Systems
Authors: Amirreza Dolatpour Fathkouhi, Alireza Namazi, Heman Shakeri
Organizations: Department of Computer Science Center for Diabetes Technology University of Virginia Charlottesville, Virginia, USA · School of Data Science Center for Diabetes Technology University of Virginia Charlottesville, Virginia, USA
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 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 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 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.
Figures & tables
Figure 2. Imputation performance during (a) homeostatic periods, (b) post-prandial excursions, and (c) hypoglycemia during temporal controller resets. In (a) , linear interpolation is superior due to signal stability. In contrast, for (b) and (c) , deep learning models demonstrate superior morphological fidelity.
Peaks
Model
Processed PEDAP
Raw PEDAP
Simulation
RMSE
Bias
Emp_SE
MARD
DTW
RMSE
Bias
Emp_SE
MARD
DTW
RMSE
Bias
Emp_SE
MARD
DTW
FreTS
61.64
-11.29
60.60
30.75
234.22
66.33
-27.80
60.23
28.96
251.27
59.52
-26.75
53.17
22.96
221.40
SCINet
58.26
-24.21
53.00
23.32
225.96
57.38
-11.50
56.22
28.31
246.77
60.43
-34.63
49.53
21.27
223.08
TimeMixer
138.97
-123.36
63.98
68.21
836.12
144.71
-129.48
64.63
72.18
876.02
148.70
-135.36
61.55
73.41
897.82
TSLANet
128.35
-104.38
74.69
60.32
563.02
129.09
-107.05
72.15
60.47
593.91
135.68
-115.80
70.71
63.20
612.62
TEFN
67.48
-26.41
62.10
31.42
382.07
67.53
-26.74
62.01
31.33
381.20
83.56
-53.06
64.56
33.23
451.91
Table 1. Performance in Scenario B. Bold indicates best; underline indicates second best.
Model
RMSE
Bias
Emp_SE
MARD
DTW
FreTS
58.41
52.63
25.35
72.46
203.35
SCINet
32.44
27.18
17.71
39.52
101.07
TimeMixer
43.81
-38.92
20.10
43.93
179.61
TSLANet
44.43
-23.50
37.71
44.28
165.33
TEFN
57.25
51.49
25.03
71.89
227.88
TOTEM
41.65
-37.98
17.11
44.01
125.45
Table 2. Performance on the TCR simulation dataset (Scenario C). Bold indicates best, underline indicates second best.
Figure 3. Distributional calibration analysis. Each panel shows the conditional density of imputed values (shaded) against the ground-truth density (dashed black) during transient regimes. Vertical lines indicate distribution means.
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4. Hourly probability of a missingness gap beginning during the day.
Figure 5. Empirical cumulative distribution function (CDF) of missingness durations. Comparison between day and night regimes.
Figure 6. Tail Density of Missingness Durations. Empirical tails overlaid with the fitted mixture model (Eq. 8 ).
Figure 7. Cross-scenario performance comparison. Each panel displays the average performance of the models (Lerp, FreTS, SCINet, SAITS) in terms of (a) DTW, (b) MARD, and (c) RMSE. Lower values indicate better performance.
Figure 9
Figure 9. Scenario A: Impact of missing data ratio and gap duration on model performance. Results are presented for three datasets (Raw PEDAP, Processed PEDAP, Simulation). Gold stars indicate the best-performing model for each condition.
Figure 10. Scenario B: Impact of gap duration on post-prandial peak reconstruction. Performance comparison across three datasets with masked meal peaks of varying durations. Gold stars denote the best-performing model at each duration.
Figure 11. Scenario B: Impact of post-prandial severity on model performance. Performance comparison across three datasets with an increasing number of masked meal peaks across different gap durations. Shaded regions denote ±1 standard deviation; gold stars mark the best-performing model.
Figure 12. Scenario C: Hypoglycemia stress test (TCR dataset). Impact of hypoglycemic event duration (30–120 min) on model performance. Gold stars denote the best-performing model at each duration.
Ratio
Model
Processed PEDAP
Raw PEDAP
Simulation
RMSE
Bias
Emp_SE
MARD
DTW
RMSE
Bias
Emp_SE
MARD
DTW
RMSE
Bias
Emp_SE
MARD
DTW
FreTS
23.18
15.59
17.15
18.18
48.61
19.15
10.71
15.88
14.68
39.26
12.24
6.76
10.20
9.35
23.65
SCINet
13.46
7.65
11.07
10.29
26.62
29.91
26.82
13.23
25.66
67.06
5.43
3.07
4.48
4.12
8.92
TimeMixer
65.56
-63.51
16.27
56.83
156.67
71.25
-69.35
16.34
62.25
170.99
67.20
-65.44
15.29
58.91
157.89
TSLANet
59.98
-44.12
40.63
48.66
143.04
59.12
-47.24
35.55
47.92
140.35
61.42
-49.05
36.98
50.64
143.34
TEFN
36.54
28.63
22.71
29.85
74.00
36.08
28.17
22.54
29.44
73.00
30.89
22.31
21.36
25.06
58.60
Appendix
Table 3. Performance in Scenario A. Bold indicates best; underline indicates second best.
Figure 13. Imputation examples for Scenario A. Rows correspond to masking ratios of 0.1, 0.2, and 0.3, while columns represent datasets.
Figure 14. Scenario B imputation examples. Rows indicate 1, 2, and 3 masked peaks; columns correspond to datasets.
Figure 15. Scenario C imputation examples on the TCR simulation dataset.
Imputing physiological time series (arterial blood pressure, blood glucose, etc.) is essential for addressing the missingness that pervades clinical data. Yet modern imputation methods perform poorly in this domain: a recent benchmark found that simple linear interpolation outperformed every learned imputer on real-world clinical signals with realistic gaps. We show that this reflects two properties of physiological missingness that generic imputers ignore: gaps may occur when the signal is clinically extreme rather than typical, and gap lengths can easily span orders of magnitude. To this end, we introduce Curriculum-Aware Interpolate-then-Refine (CAIR), a two-stage framework for physiological time-series imputation. Our key motivation is to learn a coarse base curve and then repeatedly correct it toward physiological realism, rather than predict a gap in a single pass. Consequently, CAIR couples a bidirectional-GRU interpolator with a Transformer refiner that corrects its own estimate over three successive passes, trained jointly under a broad, signal-agnostic random-gap curriculum. We evaluate imputers stratified by gap length and missingness mechanism (MCAR, MAR, NMAR) rather than by a single average, and CAIR is the most accurate under every mechanism on continuous glucose monitoring (AI-READI) and arterial pressure in intensive care (MIMIC-III). Its margin over the strongest baseline grows with difficulty, from 9% under MCAR to 19% under value-dependent dropout, where generic learned imputers are weakest. We further show low reconstruction error alone does not recover the burden metrics clinicians act on: interpolants matching CAIR's error fail to preserve those metrics, imputers that recover them are far less accurate, and CAIR alone ranks among the best on both axes.
Yu-Chao Huang, Haochen Zhang, Nicholas Konz +1
UNITES Lab, University of North Carolina at Chapel Hill
Clinical care often relies on key laboratory indicators, yet real-world patient visits are sparse and tests are ordered irregularly, leading to pervasive missingness. While many imputation methods improve average accuracy, they provide limited guidance on which imputed values are reliable enough for high-stakes downstream use. In this work, we study reliable clinical imputation, aiming to produce accurate imputations while selectively releasing the reliable results, with statistical control over clinically unacceptable errors. To achieve this goal, we propose SafeImpute, a reliable imputation framework for irregular and sparse clinical longitudinal records. SafeImpute constructs an event graph that captures both intra-patient temporal trajectories and inter-patient clinical similarity, and learns imputations with a two-relation GNN and adaptive fusion, regularized by an auxiliary masked reconstruction objective. For reliability guarantees, SafeImpute converts a proxy risk score into conformal p-values and applies the Benjamini--Hochberg procedure to control the false discovery rate (FDR) of unacceptable errors among released imputations at a user-specified tolerance. Experiments on our Mayo Clinic data, the public MIMIC-III and MIMIC-IV datasets show that SafeImpute achieves strong imputation accuracy while providing reliable error control, outperforming diverse baselines in both standard imputation evaluation and FDR-controlled selective-release evaluation.
Xinrui He, Mengting Ai, Junting Wang +2
University of Illinois Urbana-Champaign Champaign, IL, USA · Mayo Clinic Scottsdale, AZ, USA
Wearable device data enables continuous health monitoring, but suffers from structured missingness: features sharing a physical sensor drop out together. Deep imputation methods such as BRITS and SAITS have seen limited evaluation on multimodal physiological data under realistic missingness, and existing benchmarks use random-point holdout protocols that incorrectly assume missingness is independent across features and time. Using data from a person with epilepsy recorded on a Garmin smartwatch, we develop an evaluation protocol that mines contiguous missing-run templates from training data, stratifies them by per-feature gap-length quantiles, and injects them as block masks with preserved co-missingness structure. A matched training protocol exposing models to the same missingness distribution reduces BRITS's severe-gap MAE by 43%, demonstrating the potential benefit of the proposed evaluation and training protocol within this single-participant dataset. We further extend BRITS with time-of-day encoding and a circadian harmonic channel. No single model dominates: linear interpolation is optimal for slow-moving features over short gaps; extended BRITS achieves lower MAE on dynamic cardiac features in moderate and severe gaps; and SAITS better preserves the ground-truth distribution by Jensen-Shannon distance despite higher MAE. Ultimately, model rankings strongly depend on evaluation designs. By exposing how traditional evaluation methods obscure true model capabilities, our transferable protocol establishes critical steps towards developing better imputation strategies for future multi-sensor wearable datasets.
School of Engineering Mathematics and Technology, University of Bristol, UK · Centre for AI Fundamentals, University of Manchester, UK · Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, UK