Filling in the Blanks: Applying Data Imputation in incomplete Water Metering Data

Dimitrios Amaxilatis; Georgios Mylonas; Ioannis Chatzigiannakis; Themistoklis Sarantakos

REVIEW 4 major objections 4 minor 16 references

Filling in the Blanks: Applying Data Imputation in incomplete Water Metering Data

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A model trained on water-meter data pooled from 22 buildings fills hidden hourly readings with mean absolute error as low as 0.13, outperforming per-building models.

desk verdict Useful real-world imputation benchmark, but the headline MAE applies only to isolated single-hour gaps, not the dataset's actual bursty missingness. read the letter →

arxiv 2506.08882 v1 pith:2EG7JOB6 submitted 2025-06-10 cs.LG

Dimitrios Amaxilatis , Themistoklis Sarantakos , Ioannis Chatzigiannakis , Georgios Mylonas This is my paper

classification cs.LG

keywords dataimputationsmartwatermetersmissingtimeseriesTransformerk-nearestneighborsIoTmeanabsoluteerror

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether machine-learning imputation can fill gaps in hourly smart water meter readings from a real IoT deployment. The authors show that when a single hourly value is artificially hidden per day, several imputation methods recover it with mean absolute error around 0.13–0.16 in the reported consumption units. Their finding is that a single model trained on data pooled from all 22 buildings beats models trained separately for each building. This matters because water utilities need complete series for leak detection and maintenance scheduling, and a shared model is cheaper to deploy and update than 22 bespoke models.

What carries the argument

The unit of analysis is the 24-hour vector of hourly readings: each day is one data entry with 24 features, and imputation targets missing hours within that vector. Training uses only days with all 24 values present; evaluation hides a single random hour in 20 percent of the validation days, a procedure applied identically across all models and both training regimes. The comparison covers seven algorithms (kNN, MissForest, SAITS, Transformer, TimesNet, USGAN, MRNN) with grid-searched hyperparameters, scored by mean absolute error.

What would settle it

Re-run the same models on held-out periods where genuine consecutive-hour gaps exist, comparing imputed hourly values against the building's cumulative water register totals, which are unaffected by the communication losses; if the MAE on those real gaps is much higher than 0.13–0.16, the single-blank simulation does not transfer.

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Extended reading notes

Core claim

The central claim is that data imputation methods, particularly a Transformer and k-nearest neighbors, can fill missing hourly water-consumption readings with low error, and that training one common model on all buildings' data generalizes better than training dedicated models per building. In the authors' evaluation, the common Transformer reaches an average MAE of 0.13 and the common kNN reaches 0.16, while the best dedicated models are roughly twice as inaccurate (0.30 and 0.31). The conclusion is that a shared model exploits cross-building consumption patterns, including irregular out-of-profile days, to produce better estimates than a model that only sees one building's history.

Load-bearing premise

The results depend on the assumption that hiding one random hourly value per day mimics the real missing-data patterns, even though the actual gaps include long stretches and whole days.

Editorial extensions

If this is right

Utilities could deploy one shared imputation model across many buildings instead of training and maintaining separate models per site.
Hourly imputation error around 0.13–0.16 in the reported consumption units is small enough to keep downstream analyses such as consumption profiling and anomaly detection usable.
The same pooling benefit likely applies to other sensor networks with heterogeneous but related time-series profiles, such as electricity or gas smart meters.
Deployments with very sparse data on some buildings may still benefit from shared training, though the paper's building 8 result shows that all methods struggle when data are extremely sparse.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The single-blank evaluation leaves open whether imputation accuracy survives realistic bursty gaps; a natural extension is to train with masks of consecutive missing hours and compare against actual gaps reconstructed from meter registers.
If missingness is driven by the same failures that cause leaks or communication outages, the missing-at-random assumption is violated; models that use missingness indicators as features could be tested against this dataset.
The paper's claim that imputation enhances leak detection and predictive maintenance is asserted without an experiment; a direct test would feed imputed series into a leak-detection algorithm and measure detection latency and false positives against complete data.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First, the thing to know: this is a competent, honest benchmark of seven off-the-shelf imputation methods on a real 22-building smart water metering dataset. The main empirical finding—a common model trained on pooled data beats per-building models (Transformer MAE 0.13, kNN 0.16)—is plausible and internally consistent. Second: those numbers come from the easiest missingness pattern. They hide one hour in an otherwise complete 24-hour vector, train only on fully observed days, and never test on the multi-hour or whole-day gaps that the paper itself says dominate the deployment (Section III.B; Table I shows 20–79% missing per building). So the abstract's '0.16 MAE' does not transfer to the real data's failure mode.

What's genuinely useful: the Tethys dataset is real, spans three years with hourly aggregates across 22 buildings, and the dedicated-versus-common model comparison answers a real deployment question—should you train per meter or pool data? The result that pooling helps is exactly the kind of practical guidance utilities need. The paper doesn't oversell the algorithms; it explicitly uses established methods and describes the evaluation clearly.

Soft spots, in order. First and load-bearing: the missingness mechanism mismatch. Training on complete days and imputing a single blank per vector ignores the bursty, correlated gaps that actually occur. A Transformer or kNN relying on surrounding hours will behave differently when the entire neighborhood is missing. Without experiments on multi-hour or whole-day gaps, the reported MAEs are not a prediction of field performance. The paper is transparent about this (Section IV.C says 'we focus on imputing a single blank value'), but the conclusion overreaches. Second: no trivial baseline. Last-observation-carried-forward or a day-of-week median would anchor the MAE numbers; right now '0.16' is uninterpretable without knowing the scale of hourly consumption. Third: a single random mask, no seeds, no error bars. Fourth: leak detection and maintenance benefits are asserted but never tested.

None of this suggests fabrication. The numbers are internally consistent and the method is standard, but the central claim is narrower than advertised.

This paper is for practitioners building imputation pipelines for smart meter data and for researchers who want a realistic public benchmark. It is not a methodological contribution. A serious referee should see it because the dataset and the dedicated-vs-common result are worth reporting, but the review will need to push for evaluation on realistic missingness patterns, baselines, and error bars. I'd accept it for peer review with major revision expected.

Referee Report

4 major / 4 minor

Summary. The paper evaluates seven data imputation methods (kNN, MissForest, SAITS, Transformer, TimesNet, USGAN, MRNN) on hourly aggregated smart water meter readings from 22 buildings in the Tethys deployment. The pipeline forms 24-hour day vectors, trains on days with all 24 values present, and evaluates by hiding one measurement in held-out complete day vectors. Models are trained per building and as a shared model across buildings, with performance measured by MAE. The main reported result is that shared models outperform dedicated models, with the common Transformer reaching MAE 0.13 and kNN 0.16. The authors conclude that these imputation techniques fill missing values with low error and support applications such as leak detection and predictive maintenance.

Significance. If the central result were robust, the paper would provide a useful empirical benchmark for imputation in smart water metering: a real multi-year dataset, 22 buildings, seven methods, and a clear finding that pooling data across buildings improves MAE. The held-out masking design is standard and the Table II values are internally consistent. The main weaknesses are that the evaluation covers only single-point random missingness on complete days, whereas the deployment has 20-79% missing data including consecutive hours and whole days; only one random mask is used; and no trivial baseline is included. These issues currently prevent the paper's quantitative claims from supporting the deployment-level conclusion.

major comments (4)

[§III.B, §IV.A, §IV.C, §V.A] The evaluation protocol does not match the missingness mechanism described for the deployment. Section III.B states that blanks can be "single measurements over a week-long recording period or even whole days," and Table I reports 20-79% missing hours per building; if missingness were limited to one hour per day, the rate would be at most about 4%, so the observed rates imply consecutive multi-hour or whole-day gaps. Yet Section IV.A trains only on days with all 24 hourly values present, and Sections IV.C and V.A/V.B restrict evaluation to hiding a single measurement in each validation vector. The reported MAE values in Table II are therefore conditional on a single-point, missing-at-random mechanism and are not a valid estimate of performance on the actual incomplete dataset. The manuscript should add experiments with multi-hour and whole-day gaps (or evaluation on the native missing timestamps) and report MAE separately for those patterns.
[§V.A, §V.B, Table II] The results rest on a single random masking of the validation data. The text in Section V.A says "we randomly replaced one measurement" and does not describe repetition over seeds or multiple masks. The MAE differences between the best common models are small (Transformer 0.13 vs kNN 0.16 in Table II), so a single mask cannot establish which method is best or how stable the averages are. Report the mean over several independent masks with standard deviations or confidence intervals.
[§VI, Table II] The conclusion states that the imputation "resulted in filling in the blanks in the original dataset with low deviations from the actual values and a mean absolute error as low as 0.16," but Table II reports a common-model Transformer MAE of 0.13, which is lower than 0.16. The quantitative summary in the conclusion is inconsistent with the results table and should be corrected to cite the actual best value (0.13) with the model and setting.
[§V] No trivial baseline is included in the evaluation. The paper's central claim is that the imputation techniques produce "low deviations" and "fill in the blanks" effectively, but without comparisons to simple approaches such as mean imputation, last-observation-carried-forward, or linear interpolation, the absolute MAE values in Table II cannot be interpreted as low, and the added value of the neural and statistical models is not demonstrated. Add such baselines to the comparison.

minor comments (4)

[Abstract, §VI] The abstract and conclusions claim benefits for leak detection and predictive maintenance, but no experiment evaluates those applications; please soften these claims or add supporting evidence.
[§V, Figures 1 and 4, Table II] The MAE values are reported without units; state the units (e.g., m³/h) so that values like 0.13 can be interpreted by readers.
[§IV.B] The hyperparameter values are listed, but the grid search procedure is not described in terms of search space, selection criterion, or whether the validation split was used for model selection, which limits reproducibility.
[Table I] The column header "Data Hourly" is unclear, and the phrase "Data Without Data" should be reworded to "Hours Missing" or similar.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MAE results are genuine out-of-sample evaluations of external imputation methods, and the only self-citations concern dataset provenance rather than load-bearing claims.

full rationale

The paper's derivation chain is: collect real smart-meter data from the Tethys deployment; train standard external imputation models (kNN, MissForest, SAITS, Transformer, TimesNet, USGAN, MRNN) on 80% of complete 24-hour vectors; hold out 20% of such vectors; randomly replace one observed hourly value per held-out vector with NaN; impute and compare against the true held-out value using MAE. This is a genuine out-of-sample evaluation: the values used to compute MAE in Table II (kNN 0.16, Transformer 0.13) are never seen during training, and the reported errors are measured predictions, not fitted parameters renamed as predictions. The methods themselves are imported from the external literature ([6]-[14]), so no ansatz is smuggled in via self-citation. The only self-citations are [15] and [16], which describe the Tethys deployment and prior COVID-era analysis of the same data; these establish dataset provenance rather than supplying a load-bearing theorem, uniqueness claim, or fitted value. The mismatch between the simulated single-missing-hour evaluation (Section IV.C, V.A) and the real bursty or whole-day gaps described in Section III.B is a threat to external validity, not circularity: it does not make the reported MAE equal to an input by construction, nor does it mean the held-out values were used in training. No equation reduces to its own input, and no fitted quantity is relabeled as a prediction. Therefore no significant circularity is present.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new conceptual entities, forces, or fundamental parameters; its methods and even its dataset (Tethys, references [15] and [16]) come from prior work. The quantities the conclusion rides on are the MAE benchmarks, and those depend on the masking design (20 percent of days, one hidden hour), the training-on-complete-days rule, and the grid-searched hyperparameters. None of these is a fitted physical constant; they are experimental design choices, and the single-point masking choice is the most consequential because it does not match the bursty real missingness.

free parameters (4)

KNN number of neighbors = k = 3
Selected by grid search on the Tethys data (Section IV.B), purportedly with validation on the same 20 percent split used to report final MAE.
MissForest tree configuration = 4 estimators, max depth 10, bootstrap with 50 percent sample cap
Picked as the configuration 'that we found to work better in our use case' (Section IV.B); specific to this dataset.
Deep model hyperparameters (SAITS, Transformer, TimesNet, USGAN, MRNN) = hidden sizes 128 to 512, 4 attention heads, dropout 0.1 to 0.5, learning rate 0.001, 100 epochs
Chosen via grid search (Section IV.B); because the search appears to use the same validation set as the final report, the headline MAE is mildly optimistically selected.
Masking design = 20 percent of validation days, one hidden hour per day
Chosen by the authors (Section V); the 20 percent rate and the single-point pattern define the simulation that all conclusions depend on.

assumptions (3)

domain assumption Hourly aggregation of the cumulative meter counters faithfully represents true consumption with no metering or aggregation error.
Section III.B transforms raw readings at varying reporting intervals into hourly totals; any aggregation artifacts are treated as ground truth.
ad hoc to paper Single-point random missingness is representative of the deployment's real missing data.
Section IV.C evaluates only one missing value per 24-hour vector, while Section III.B reports real gaps covering weeks and whole days; this assumption is the bridge from simulation to deployment.
domain assumption Training on fully observed days transfers to partial days.
Section IV.A discards all days with any missing value from training, so the models never see a partial-day input during training; the evaluation then applies them to partial-day inputs anyway.

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Cite this review

Pith. "Pith review of Filling in the Blanks: Applying Data Imputation in incomplete Water Metering Data." pith.science (2026). https://pith.science/paper/2EG7JOB6

@misc{pith2026250608882,
  author       = {Pith},
  title        = {Pith review of: Filling in the Blanks: Applying Data Imputation in incomplete Water Metering Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2EG7JOB6}},
  note         = {Machine review of arXiv:2506.08882}
}

read the original abstract

In this work, we explore the application of recent data imputation techniques to enhance monitoring and management of water distribution networks using smart water meters, based on data derived from a real-world IoT water grid monitoring deployment. Despite the detailed data produced by such meters, data gaps due to technical issues can significantly impact operational decisions and efficiency. Our results, by comparing various imputation methods, such as k-Nearest Neighbors, MissForest, Transformers, and Recurrent Neural Networks, indicate that effective data imputation can substantially enhance the quality of the insights derived from water consumption data as we study their effect on accuracy and reliability of water metering data to provide solutions in applications like leak detection and predictive maintenance scheduling.

Figures

Figures reproduced from arXiv: 2506.08882 by the authors.

**Figure 3.** Actual & Imputed data using the dedicated Transformer model [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 1.** MAE for each dedicated model for all 22 buildings of our dataset. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: MAE for the common model for all 22 buildings of our dataset. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Actual and Imputed values using the common kNN model. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

A solution for water management and leakage detection problems using iots based approach,

A. S. Ali, M. N. Abdelmoez, M. Heshmat, and K. Ibrahim, “A solution for water management and leakage detection problems using iots based approach,”Internet of Things, vol. 18, p. 100504, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2542660522000105

work page 2022

[2] [2]

Precise water leak detection using machine learning and real-time sensor data,

J. Alves Coelho, A. Gl ´oria, and P. Sebasti ˜ao, “Precise water leak detection using machine learning and real-time sensor data,” IoT, vol. 1, no. 2, pp. 474–493, 2020. [Online]. Available: https://www.mdpi.com/2624-831X/1/2/26 Model MAE dedicated MAE common kNN 0.31 0.16 MissForest 0.35 0.17 SAITS 0.35 0.23 Transformer 0.30 0.13 TimesNet 0.42 0.21 USGAN...

work page 2020

[3] [3]

Leakage detection via edge processing in lorawan-based smart water distribution networks,

D. Garlisi, G. Restuccia, I. Tinnirello, F. Cuomo, and I. Chatzigian- nakis, “Leakage detection via edge processing in lorawan-based smart water distribution networks,” in2022 18th International Conference on Mobility, Sensing and Networking (MSN), 2022, pp. 223–230

work page 2022

[4] [4]

Real-time leakage zone detection in water distribution networks: A machine learning-based stream processing algorithm,

——, “Real-time leakage zone detection in water distribution networks: A machine learning-based stream processing algorithm,” inAlgorithmic Aspects of Cloud Computing, I. Chatzigiannakis and I. Karydis, Eds. Cham: Springer Nature Switzerland, 2024, pp. 86–99

work page 2024

[5] [5]

Advanced strategies for monitoring water consumption patterns in households based on iot and machine learning,

D. Arsene, A. Predescu, B. Pahont ,u, C. G. Chiru, E.-S. Apostol, and C.-O. Truic ˘a, “Advanced strategies for monitoring water consumption patterns in households based on iot and machine learning,”Water, vol. 14, no. 14, 2022. [Online]. Available: https://www.mdpi.com/2073- 4441/14/14/2187

work page 2022

[6] [6]

A survey on data imputation techniques: Water distribution system as a use case,

M. S. Osman, A. M. Abu-Mahfouz, and P. R. Page, “A survey on data imputation techniques: Water distribution system as a use case,”IEEE Access, vol. 6, pp. 63 279–63 291, 2018

work page 2018

[7] [7]

Data imputation for multivariate time series sensor data with large gaps of missing data,

R. Wu, S. D. Hamshaw, L. Yang, D. W. Kincaid, R. Etheridge, and A. Ghasemkhani, “Data imputation for multivariate time series sensor data with large gaps of missing data,”IEEE Sensors Journal, vol. 22, no. 11, pp. 10 671–10 683, 2022

work page 2022

[8] [8]

K-nearest neighbor (k-nn) based missing data imputation,

D. M. P. Murti, U. Pujianto, A. P. Wibawa, and M. I. Akbar, “K-nearest neighbor (k-nn) based missing data imputation,” in2019 5th Interna- tional Conference on Science in Information Technology (ICSITech), 2019, pp. 83–88

work page 2019