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Curriculum-Aware Interpolate-then-Refine: Learned Physiological Time-Series Imputation under Realistic Missingness
Yu-Chao Huang, Haochen Zhang, Nicholas Konz, Tianlong Chen
TL;DR
Physiological imputation must handle clinically informative missingness and gaps spanning very different lengths, yet linear interpolation can outperform learned imputers under realistic conditions. CAIR learns a base curve and iteratively refines it under a broad gap curriculum, achieving the best reconstruction accuracy across mechanisms and domains while also ranking highly on clinical-metric fidelity.
Problem
Realistic physiological gaps can be clinically extreme and span orders of magnitude, while generic learned imputers and standard evaluations often ignore these properties.
Method
CAIR jointly trains a bidirectional-GRU interpolator and a Transformer refiner that performs three successive corrections under a broad, signal-agnostic random-gap curriculum.
Results
CAIR is most accurate under every missingness mechanism on glucose and arterial pressure, with its margin over the strongest baseline increasing from 9% under MCAR to 19% under NMAR.
Takeaways & Limitations
Reconstruction accuracy and clinical-metric fidelity are distinct axes, and CAIR is among the best on both.
Takeaways & Limitations
The evaluation targets contiguous gaps of 15–60 minutes because gaps beyond roughly one hour are not considered a realistic clinical imputation target.
Abstract
from arXiv · showhide
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.
1 Introduction
Physiological signals are frequently incomplete, while realistic gaps can be mechanism-driven, clinically extreme, and highly variable in length. CAIR addresses these properties by learning a base interpolation and refining it iteratively, then evaluates performance across mechanisms and clinical domains.
- Physiological-signal imputation affects downstream clinical metrics and risk models because missing values propagate into clinical conclusions.
- Real-world benchmarks found linear interpolation outperformed every learned imputer on clinical signals with realistic gaps.
- MCAR, MAR, and NMAR missingness differ in whether dropout depends on data, observed covariates, or the missing value itself.
- Physiological gaps span isolated samples to multi-hour holes, so a single average score can obscure short-gap performance.
- CAIR learns a coarse base curve with a bidirectional GRU and repeatedly refines it with a Transformer over three successive passes.
- CAIR is evaluated under realistic missingness mechanisms and achieves the lowest reconstruction error across two clinical domains, with margins increasing from 9% under MCAR to 19% under NMAR.
2 Related Work
Prior work spans deterministic, statistical, recurrent, attention-based, and generative imputers, but realistic clinical missingness remains underrepresented in standard evaluation. CAIR builds on learned interpolation and iterative refinement while targeting mechanism- and gap-length-aware evaluation.
- Clinical pipelines still commonly use deterministic interpolants because they require no fitting and remain accurate on short gaps.
- Learned imputers model informative missingness with recurrent, attention-based, and generative architectures.
- CAIR differs from SAITS by using an information-restricted recurrent interpolator followed by a tied-weight iteratively unrolled refiner.
- Standard imputation benchmarks usually delete values completely at random, although recent studies show clinically plausible patterns can change method rankings.
3 Method
CAIR combines a learned bidirectional-GRU base curve with a Transformer that refines the estimate using observed data, masks, context, and previous predictions. Joint curriculum training, repeated refinement, and direct Stage-1 supervision define the method.
- The imputation task reconstructs missing positions in a uniformly sampled physiological trace using an observation mask and optional auxiliary channels.
- Stage 1: Learned interpolator: Stage 1 uses a bidirectional GRU to read the masked signal and mask and predict a base value at every position.
- Stage 2: Transformer refiner: The Transformer receives the base curve both as per-position conditioning and as an additive residual base.
- Stage 2: Transformer refiner: The GRU supplies a smooth base curve, while the Transformer adds physiological shapes such as postprandial rises, nocturnal dips, and pressure excursions.
- Training: Training uses a signal-agnostic curriculum mixing scattered points and contiguous blocks, with about 20% of observed samples held out.
- Training: The refiner runs for three passes with increasing pass weights, and an auxiliary loss directly supervises Stage 1 to preserve a smooth base.
- Inference: At inference, CAIR processes full traces with overlapping 576-step windows, cosine-window averaging, three refinement passes, and unchanged observed positions.
4 Experiments
The experiments test CAIR across realistic missingness mechanisms, gap lengths, clinical signals, physiological strategies, burden metrics, and component ablations. CAIR consistently performs strongly, with its advantages largest for difficult, clinically meaningful gaps, while reconstruction accuracy and downstream burden recovery remain distinct objectives.
- Main Results: CAIR attains the lowest RMSE under MCAR, MAR, and NMAR, with its margin over linear interpolation increasing from 9% to 19% as difficulty rises.The strongest baseline is linear interpolation, and NMAR is described as the hardest and most clinically loaded regime.
- Main Results: Generic neural baselines M-RNN and GP-VAE fall below every non-constant baseline across all three missingness mechanisms.The comparison attributes CAIR’s advantage to broad training-gap coverage rather than neural capacity alone.
- Physiological Strategies: CAIR improves the strongest classical baseline by 1.33 mg/dL on the physiological five-strategy average, with the largest gain on long sleep blocks.For sleep blocks, CAIR costs 24.9 mg/dL versus 29.3 mg/dL for the strongest classical baseline.
- Cross-Modal Conditioning: Multivariate conditioning reverses univariate CAIR’s disadvantage on heart rate and respiration, while adding the same channels leaves CGM accuracy essentially unchanged.The CGM average changes from 13.11 to 12.98 mg/dL, within seed noise; heart-rate and respiration gains over the strongest classical baseline are 20–34% and 15–28%.
- Cross-Domain Transfer: On arterial pressure CAIR is most accurate under every mechanism, whereas heart rate is a boundary case where linear interpolation wins under MCAR and NMAR.The arterial-pressure comparison against linear interpolation is significant under all three mechanisms; the MAR and NMAR heart-rate differences are ties.
- Curriculum Analysis: Broad signal-agnostic random-gap training outperforms physiology-specific masking, showing that the training gap distribution materially affects transfer across signals.The identical ABP architecture is worse than linear under glucose-tailored masks but better under the broad curriculum.
- Clinical Metrics: CAIR is the only method among the best on both reconstruction error and burden recovery: it reaches 11.4 mmHg RMSE and 0.64 burden recovery.Interpolants matching CAIR’s RMSE fail on burden, while methods matching its burden recovery have 10–60% higher RMSE.
5 Conclusion
CAIR addresses realistic physiological missingness with a curriculum-aware, two-stage interpolate-then-refine design. Across clinical domains, its advantage over generic learned imputers is attributed to training on realistic gap distributions rather than greater neural capacity.
- CAIR replaces deterministic interpolation with a jointly trained learned interpolator followed by an iteratively unrolled Transformer refiner.The design targets mechanism-driven gaps and gap lengths spanning orders of magnitude.
- 19% is CAIR’s margin over the strongest baseline under value-dependent dropout, with the margin increasing as missingness becomes harder.CAIR is reported as most accurate under every missingness mechanism on glucose and arterial pressure.
- CAIR’s reconstruction accuracy and clinical-metric fidelity are distinct axes, and it alone ranks among the best on both.
- Classical interpolants remain accurate on short gaps, while cubic splines can overshoot across long gaps and physiological smoothers assume stationarity violated across meals and sleep.
- Generic learned imputers remain below non-constant baselines because their training gap distributions differ from CAIR’s, not because they lack neural capacity.Changing only the gap distribution removes the advantage over linear interpolation.
B.1 Data preparation
The experiments use participant- or subject-disjoint clinical datasets, mechanism-specific masks, a detailed CAIR architecture, and matched baseline evaluation. External-cohort pretraining does not improve physiological-protocol accuracy.
- AI-READI provides uniformly resampled CGM, heart-rate, and respiration traces with participant-disjoint train, validation, and test splits.The evaluation target is day two within a 24-hour window.
- MIMIC-III contributes 22,156 subject-disjoint 24-hour windows on a 5-minute grid, retaining observed sensor masks.Targets include mean arterial blood pressure and heart rate.
- MCAR deletes positions independently, whereas MAR and NMAR use contiguous windows triggered by observed covariates or the target value, respectively.Each mechanism is evaluated at six missingness rates with five seeded masks per rate.
- CAIR uses a four-layer bidirectional GRU for Stage 1 and an eight-layer bidirectional Transformer encoder for Stage 2.The refiner reads the Stage-1 prediction as a learned base curve through the interpolant interface.
- The refiner is unrolled for three passes, while training uses a broad random-gap curriculum mixing scattered points and contiguous blocks.
- External-cohort pretraining does not improve accuracy: every external cell is within 0.2 mg/dL of control and none improves on it.
B.6 Metrics
The paper reports held-out-position RMSE in native units and uses metric-recovery ratio to quantify preservation of selected clinical metrics relative to mean-fill.
- RMSE is computed over held-out positions only and reported in native units.
- MRR compares a method’s clinical-metric error with mean-fill error, where 1 is exact recovery, 0 matches mean-fill, and negative values are worse.The reported clinical metrics include time-in-range, MAGE, coefficient of variation, and arterial-pressure band occupancy.
C External-Cohort Pretraining Does Not Improve Accuracy
External CGM pretraining does not improve target-domain accuracy, while the training recipe and checkpoint-selection objective materially affect reported performance.
- Accuracy results: Pretraining on three external CGM pools leaves the physiological average within 0.2 mg/dL of an AI-READI-only model and never improves it.The pools span type-1 and type-2 physiology.
- Experimental setup: The external-data procedure standardizes datasets, adds dataset-specific Transformer embeddings, pretrains jointly, and fine-tunes on AI-READI with the zero embedding frozen.Inference is bit-identical to a model that never saw external data after fine-tuning.
- Accuracy results: 7.73 mg/dL versus 7.99 mg/dL on the short-gap mean shows a negligible pretraining delta relative to the main model’s 5.69 mg/dL.This comparison uses the Shanghai-pretrained checkpoint and its control.
- Interpretation: 13.79 mg/dL versus 14.61 mg/dL reflects different two-stage recipes, with the lower average dominated by multi-hour sleep blocks and associated over-smoothing of short gaps.The selected recipe is over 2 mg/dL worse at every main-paper gap length, including 7.99 versus 5.69 mg/dL on short gaps.
- Conditioning analysis: Adding up to ten co-recorded modalities changes the physiological average only from 13.11 to 12.98 mg/dL, with no rung distinguishable from control at five seeds.The average change is non-monotone.
D.3 Complete MIMIC-III baselines, both signals
Complete MIMIC-III baselines confirm CAIR’s advantage on arterial pressure, while heart rate remains a smooth-signal boundary case where linear interpolation is competitive.
- Arterial pressure: Both CAIR variants are more accurate than every baseline on arterial pressure under every missingness mechanism.The complete arterial-pressure table reports RMSE in mmHg averaged over six missingness rates.
- Interpretation: The heart-rate result is consistent with scattered single-sample deletion on a smooth signal, where CAIR and linear interpolation are separated by at most 0.22 bpm.This makes heart rate a boundary case rather than a uniform CAIR win.
- Statistical comparisons: All three arterial-pressure paired tests favor CAIR, while heart-rate significance favors linear interpolation under MCAR and leaves MAR and NMAR differences unresolved.The arterial-pressure tests use paired window-rate comparisons; the heart-rate pattern is mixed.
- Two-axis evaluation: Only CAIR ranks among the best on reconstruction RMSE and clinical-burden recovery; interpolants match its RMSE but fail on burden, while tabular and neural methods recover burden at higher RMSE.kNN and hot-deck match CAIR’s burden recovery at approximately 11% higher RMSE.
- Heart rate: CAIR is most accurate for heart rate under MAR, whereas linear interpolation is best under MCAR and NMAR, with separations of at most 0.22 bpm.MissForest is within 0.15 bpm of linear interpolation.
D.6 Single-vital outcome prediction
Single-vital mortality prediction does not track reconstruction fidelity: smoothing can outperform the recorded trace, whereas burden recovery remains a distinct evaluation axis.
- Interpretation: No mortality-prediction column follows reconstruction accuracy, so hard outcomes are insensitive to reconstruction fidelity in this experiment.The completed trace is the classifier’s only input, preventing compensation by co-recorded vitals.
- Outcome prediction: Four of five fills exceed the recorded-trace oracle under MCAR, and all five do under NMAR, because interpolation denoises the vital.The experiment predicts in-hospital mortality from arterial pressure alone using a 1D-CNN.
- Outcome prediction: Under MCAR, linear interpolation and PCHIP score 0.692 versus 0.679 for the oracle, despite the oracle containing the recorded trace.The outcome experiment was run under MCAR and NMAR only.
- Burden recovery: Under NMAR, CAIR achieves lower RMSE and higher time-in-range recovery than linear interpolation in all four AI-READI diabetes study groups.The advantage is largest in the insulin-dependent group, where deleted excursions are most frequent.
- Gap difficulty: For AI-READI NMAR at 30%, increasing difficulty from easiest to hardest causes every method to miss whole excursions, but each fails differently.GP-VAE and M-RNN remain near-constant, linear follows endpoint chords, and CAIR bends toward physiological structure.