Evaluating Deep Multivariate Imputation Models on Wearable Device Data

Skye Goodman; Roussel Desmond Nzoyem; Leandro Junges; Peter Kissack; Yasser Qureshi; Amberly Brigden; Jeff Clark; Nawid Keshtmand

cs.LGAug 25, 2026

Evaluating Deep Multivariate Imputation Models on Wearable Device Data

Authors: Skye Goodman, Roussel Desmond Nzoyem, Leandro Junges, Peter Kissack, Yasser Qureshi, Amberly Brigden, Jeff Clark, Nawid Keshtmand

Organizations: 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

Abstract

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.

Figures & tables

Feature	Description	#Runs	$\bm{P_{50}}$	$\bm{P_{75}}$	$\bm{P_{90}}$	Max
steps	Cumulative daily step count	37	56.0	105.0	212.4	236
steps_rate	Interval-level step rate	38	53.0	101.25	209.8	236
bodyBattery	Garmin Body Battery score (5–100)	83	35.0	98.0	207.8	1484
hr	Heart rate (bpm)	162	25.0	63.75	154.7	1492
ibi	Inter-beat interval (ms)	212	18.5	39.25	120.1	1491
sleep	Sleep stage (0–4)	107	16.0	39.0	185.0	1333

Table 1: Contiguous missing-run length statistics per feature, computed on the training set. A “missing run” is defined as one or more consecutive missing timestamps for a given feature. Run length is measured as the number of consecutive missing timestamps in the run. #Runs reports the total number of missing episodes in the training data.

P_{50}

P_{75}

and

P_{90}

denote the 50th, 75th and 90th percentiles of run length

L

, and Max denotes the longest observed run in the training set.

Figure 1: Conditional missingness matrix for the wearable features, where each cell reports $P(Y\ \mathrm{missing}\mid X\ \mathrm{missing})$ . The heatmap highlights sensor-coupled co-missingness, including close to global feature dropouts when the accelerometer channels are missing, and a strongly coupled PPG-derived cluster of variables.

Figure 2: Wearable-realistic training protocol used for BRITS and SAITS. Contiguous missing-run templates are extracted from training data and stored in a severity-bucketed library. During training, a template is sampled and injected into each window. Loss is computed on both naturally observed entries (reconstruction) and artificially held-out entries (masked imputation).

Typical ( $L\leq P_{50}$ )
Feature	BRITS	BRITS-ext	SAITS	SAITS-ext
hr	0.386 $\pm$ 0.017 / 5.93%	0.366 $\pm$ 0.016 / 5.64%	0.377 $\pm$ 0.015 / 5.84%	0.385 $\pm$ 0.016 / 5.92%
ibi	0.280 $\pm$ 0.017 / 5.12%	0.276 $\pm$ 0.014 / 5.06%	0.296 $\pm$ 0.019 / 5.39%	0.298 $\pm$ 0.016 / 5.44%
device_stress	0.268 $\pm$ 0.019 / 17.47%	0.254 $\pm$ 0.017 / 17.77%	0.309 $\pm$ 0.022 / 20.01%	0.292 $\pm$ 0.018 / 19.23%
pulseOx	0.163 $\pm$ 0.021 / 0.45%	0.173 $\pm$ 0.020 / 0.47%	0.247 $\pm$ 0.023 / 0.68%	0.231 $\pm$ 0.028 / 0.63%
steps	0.085 $\pm$ 0.008 / 69.7%	0.106 $\pm$ 0.011 / 68.6%	0.068 $\pm$ 0.006 / 68.9%	0.095 $\pm$ 0.009 / 71.3%

Table 2: Effect of the temporal context extension on BRITS and SAITS under wearable-realistic block masking for the core nine features, and extended with time-of-day and circadian auxiliary channels appended. Each cell reports test MAE (mean

\pm

std) and sMAPE (%) per target feature and gap severity bucket over 10 seeded evaluation trials sharing identical sampled mask templates. Bold entries indicate the better variant within each model and row.

Typical ( $L\leq P_{50}$ )
Feature	LOCF	LI	BRITS-ext	SAITS
hr	0.527 $\pm$ 0.021 / 8.10%	0.394 $\pm$ 0.021 / 6.14%	0.366 $\pm$ 0.016 / 5.64%	0.377 $\pm$ 0.015 / 5.84%
ibi	0.415 $\pm$ 0.028 / 7.50%	0.324 $\pm$ 0.019 / 5.85%	0.276 $\pm$ 0.014 / 5.06%	0.296 $\pm$ 0.019 / 5.39%
device_stress	0.409 $\pm$ 0.028 / 24.95%	0.336 $\pm$ 0.024 / 20.89%	0.254 $\pm$ 0.017 / 17.77%	0.309 $\pm$ 0.022 / 20.01%
pulseOx	0.148 $\pm$ 0.017 / 0.41%	0.129 $\pm$ 0.015 / 0.35%	0.173 $\pm$ 0.020 / 0.47%	0.247 $\pm$ 0.023 / 0.68%
steps	0.042 $\pm$ 0.012 / 15.56%	0.021 $\pm$ 0.006 / 10.44%	0.106 $\pm$ 0.011 / 68.6%	0.068 $\pm$ 0.006 / 68.9%

Table 3: Comparison of BRITS-ext and SAITS against univariate classical baselines (LOCF - last observation carried forward, LI - linear interpolation) under wearable-realistic block masking. Each cell reports MAE (mean

\pm

std) / sMAPE (%). Bold indicates the lowest MAE in each row.

Figure 3: Average bucket MAE for BRITS-ext and SAITS under the original training schedule (grey) versus the modified wearable-realistic block training schedule (green). Both variants are evaluated on the same masks, at the same positions, across the same 10 seeded trials. The only variable is the training objective. BRITS sees substantial gains across every bucket; SAITS gains more selectively, in the moderate and severe regimes.

	Typical		Moderate		Severe
Feature	BRITS-ext	SAITS	BRITS-ext	SAITS	BRITS-ext	SAITS
hr	0.169 $\pm$ 0.023	0.152 $\pm$ 0.015	0.163 $\pm$ 0.009	0.142 $\pm$ 0.014	0.250 $\pm$ 0.014	0.231 $\pm$ 0.008
ibi	0.174 $\pm$ 0.016	0.178 $\pm$ 0.016	0.157 $\pm$ 0.013	0.143 $\pm$ 0.009	0.240 $\pm$ 0.013	0.222 $\pm$ 0.016
pulseOx	0.601 $\pm$ 0.058	0.689 $\pm$ 0.031	0.601 $\pm$ 0.058	0.689 $\pm$ 0.031	0.662 $\pm$ 0.033	0.693 $\pm$ 0.039
steps	0.244 $\pm$ 0.025	0.219 $\pm$ 0.028	0.202 $\pm$ 0.011	0.176 $\pm$ 0.010	0.192 $\pm$ 0.009	0.148 $\pm$ 0.011
steps_rate	0.212 $\pm$ 0.011	0.205 $\pm$ 0.011	0.181 $\pm$ 0.007	0.181 $\pm$ 0.006	0.169 $\pm$ 0.003	0.169 $\pm$ 0.003

Table 4: Jensen–Shannon distance (10-seed mean

\pm

std) between imputed and ground-truth distributions, computed per feature and gap-severity bucket. Lower is better. Bold indicates the better-performing model for each feature and bucket.

Figure 4: Kernel density estimates of imputed values against ground-truth distributions at evaluation-mask positions, pooled across all three gap-severity buckets.

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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

UNITES Lab, University of North Carolina at Chapel Hill

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Open paper AskPDF arXiv

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.

Abstract

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