Beyond Accuracy: An Empirical Study of Uncertainty Estimation in Imputation

Mostafa Milani; Zarin Tahia Hossain

REVIEW 4 major objections 5 minor 1 cited by

Beyond Accuracy: An Empirical Study of Uncertainty Estimation in Imputation

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper claims that accuracy and uncertainty calibration are often misaligned in imputation, and that method choice should weigh calibration quality, not just reconstruction error.

desk verdict A useful but over-sold benchmark: the accuracy-calibration misalignment is real within some methods, but the cross-method comparison partly reflects different ways of extracting uncertainty. read the letter →

arxiv 2511.21607 v1 pith:C2TOCYQD submitted 2025-11-26 cs.DB cs.LG

Zarin Tahia Hossain , Mostafa Milani This is my paper · ORCID

classification cs.DBcs.LG

keywords dataimputationuncertaintycalibrationexpectederrormissingnessmechanismsmultipledeepgenerativemodelspredictivedistributioncurve

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 tries to establish that, in missing-data imputation, point accuracy and uncertainty calibration are separate properties: a method can be very accurate on average while its stated confidence is systematically wrong, and a less accurate method can be the one whose confidence is trustworthy. It compares six imputation families (MICE, SoftImpute, OT-Impute, GAIN, MIWAE, TabCSDI) across five numerical datasets, three missingness mechanisms (MCAR, MAR, MNAR), and three routes for extracting per-cell uncertainty (repeated runs, conditional sampling, predictive-distribution output), scoring calibration with calibration curves and Expected Calibration Error (ECE). The observed pattern is that MICE is often the best-calibrated despite lower accuracy, SoftImpute is accurate but the least calibrated, and MIWAE offers a favorable accuracy-calibration balance at high computational cost. The authors argue that imputation method choice should depend on whether the downstream task needs reliable uncertainty (risk-sensitive decisions, human-in-the-loop review) or primarily fast, accurate fills. The evaluation covers only numerical tabular data, and TabCSDI was too costly to run on all datasets—both left as future work.

What carries the argument

The mechanism that carries the argument is a three-route uncertainty-extraction protocol coupled with a common scoring metric. For each imputer, uncertainty is obtained either from the spread across repeated independent runs, from sampling a trained generative model, or from model output that directly predicts a distribution (mean and variance); all are then evaluated with the same calibration curve and the Expected Calibration Error (ECE), which measures how often the claimed coverage intervals actually contain the true values. This standardization makes it possible to compare per-cell uncertainty across very different model families—from deterministic matrix completion (SoftImpute, whose r

What would settle it

A concrete test: pick a dataset where SoftImpute has low MAE but high ECE, and recompute its uncertainty by bootstrapping the observed rows (or wrapping it in a conformal predictor) instead of using randomized-SVD pseudo-uncertainty. If ECE drops substantially while MAE is unchanged, the misalignment for SoftImpute is largely an artifact of the chosen uncertainty route; if ECE stays high, the misalignment is real for that method.

Watch

Extended reading notes

Core claim

The central discovery is that accuracy and calibration are not redundant properties of an imputer. Across datasets and missingness regimes, methods with the lowest MAE (e.g., SoftImpute, MIWAE) do not systematically have low ECE, while methods with high ECE reliability (e.g., MICE) are often not the most accurate. This is demonstrated by standardizing how uncertainty is obtained—via multi-run variability, conditional sampling from a trained model, or direct predictive-distribution output—and then measuring empirical coverage against the nominal confidence level. The practical content of the result is that 'accurate' and 'trustworthy' are different axes, and a practitioner who picks an impute

Load-bearing premise

The central comparison assumes that the three uncertainty-extraction routes—multi-run variability, conditional sampling, and predictive-distribution output—produce commensurable per-cell uncertainties that can be scored by the same ECE metric, even though SoftImpute's uncertainty is explicitly 'pseudo-uncertainty' from randomized SVD (Section IV-A) and MICE's spread reflects residual sampling; if these routes measure different mixtures of aleatory and epistemic uncertainty, t

Editorial extensions

If this is right

Imputation benchmarks should report calibration metrics such as ECE alongside MAE, since a method can win on accuracy yet mislead on confidence.
In risk-sensitive or human-in-the-loop settings, a well-calibrated imputer with moderate accuracy (e.g., MICE) should be preferred over a highly accurate but miscalibrated one (e.g., SoftImpute).
A poorly calibrated but accurate imputer needs a separate calibration step (or a different uncertainty route) before its confidence values are usable, suggesting that accuracy and uncertainty can be engineered independently.
The finding that calibration stabilizes after roughly five runs, twenty conditional samples, or fifty diffusion trajectories gives concrete deployment guidance for uncertainty-aware imputation.
Calibration degrades consistently from MCAR to MAR to MNAR, so missingness mechanism should be a factor in method selection, not just in accuracy analysis.

Reading between the lines

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

The study's 'pseudo-uncertainty' route for SoftImpute may explain part of its poor calibration; if SoftImpute were given a fairer uncertainty mechanism (e.g., bootstrap resampling or conformal intervals), its ECE might improve without changing its MAE, which would test whether the misalignment is a property of the method or of the extraction route.
If accuracy and calibration are truly separable, then post-hoc recalibration of high-accuracy imputers (e.g., temperature scaling or isotonic regression on held-out missing cells) could produce the best of both worlds, making the practical recommendation 'high-accuracy imputer + recalibrated confidence' rather than a natively well-calibrated imputer.
The MCAR-to-MNAR degradation suggests that explicitly modeling the missingness mechanism (e.g., MNAR-aware imputers) should narrow the calibration gap; this is a testable extension of the paper's framework.
All experiments are on numerical tabular data; the claimed trade-offs may not transfer to categorical or mixed-type data, where uncertainty representation and calibration metrics differ.

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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

Short version: this is the first systematic calibration comparison across statistical, OT, and deep-generative imputers, and it is honestly reported. But the headline finding—accuracy and calibration are often misaligned—is stronger than the evidence supports, because the three uncertainty routes are not commensurable.

What is new: they standardize three routes (multi-run, sampling, predictive distribution) and evaluate MAE and ECE on five datasets across MCAR, MAR, and MNAR. The observation that MIWAE gives both good accuracy and calibration, while MICE calibrates well but is less accurate, is concrete and useful. The calibration curves and tables are consistent with the qualitative claims. They are transparent about SoftImpute's pseudo-uncertainty and about TabCSDI being incomplete.

Soft spots: the central claim rests on comparing SoftImpute and OT-Impute, whose uncertainties are not predictive distributions, with MICE and MIWAE, whose are. A deterministic method with an ad hoc variance proxy will look miscalibrated; that is partly manufactured. The paper does not restrict the headline accordingly. Also, n-runs and n-samples are chosen by watching ECE plateaus on the same datasets, which is not fatal circularity but should be disclosed as tuning on the evaluation set. ECE is shown as curves for selected conditions; the paper would be stronger with a full ECE table with error bars. TabCSDI is missing on several datasets for cost; the conclusion treats it as representative, so that should be flagged.

None of these are fatal. The empirical work is reproducible (code repo) and the results are internally consistent. The fix is analytic: report ECE per route, add a sensitivity analysis that applies the same uncertainty route to all methods (e.g., multi-run for everyone), and soften the abstract.

Recommendation: worth a serious referee. It will be useful to the data-cleaning and missing-data community. I would not cite the headline claim as established; I would cite the benchmark and the MIWAE/MICE comparison.

Referee Report

4 major / 5 minor

Summary. This paper presents an empirical study of uncertainty calibration for six imputation methods (MICE, SoftImpute, OT-Impute, GAIN, MIWAE, TabCSDI) across five small tabular datasets and three missingness mechanisms (MCAR, MAR, MNAR). Uncertainty is extracted through three routes: repeated model runs, conditional sampling from trained generative models, and direct predictive-distribution outputs. Accuracy is measured by MAE and calibration by calibration curves and Expected Calibration Error (ECE). The main reported finding is that accuracy and calibration are often misaligned: high-accuracy methods such as SoftImpute and OT-Impute are poorly calibrated, MICE is well calibrated but only moderately accurate, and MIWAE offers a favorable accuracy-calibration trade-off at higher computational cost. The paper also reports runtimes, analyzes missingness-rate trends, and gives practical guidelines for choosing imputers when uncertainty matters.

Significance. If the central claim is robust, the paper fills a real gap: imputation research overwhelmingly focuses on point accuracy, while uncertainty calibration is rarely evaluated across method families and missingness mechanisms. The paper's strengths include its transparent semi-synthetic evaluation protocol, the breadth of methods compared, and the public code repository. A well-executed version of this study could give practitioners concrete guidance. However, the current manuscript does not yet provide the quantitative evidence needed to establish the headline claim: the comparison uses fundamentally different uncertainty routes for different methods, ECE values are not tabulated with variability across the full experimental grid, and key hyperparameters are tuned on the evaluation data. These issues are fixable but require substantial additional analysis.

major comments (4)

[Section IV-A and Section V-D] The central 'misalignment' claim rests on comparing uncertainties that are not commensurable. Section IV-A explicitly states that SoftImpute is 'deterministic by design' and that its uncertainty is 'treated as pseudo-uncertainty' from randomized SVD; OT-Impute's uncertainty comes from 'repeated optimization with different initializations or minibatch orders.' Neither is a predictive distribution for a missing cell. Section V-D then uses their flat, over-narrow calibration curves to conclude that high-accuracy methods are poorly calibrated. This is close to circular: any deterministic method assigned an ad hoc variance proxy will appear miscalibrated. The paper should either restrict the headline claim to the chosen uncertainty-extraction routes, or add a control experiment that gives all methods a common uncertainty wrapper (e.g., bootstrap resampling or conformal prediction) to test whe
[Section IV-C and Section V-D] No ECE table is provided and no error bars are reported for ECE. The text makes quantitative-sounding claims ('MICE achieves the lowest ECE', 'SoftImpute is the least calibrated', 'MIWAE is generally well-calibrated') but the supporting evidence is only selected calibration curves (Figures 6, 8-11) for a few datasets at 30% MCAR. Given the paper's stated goal of a systematic study across five datasets and three mechanisms, the full ECE matrix (mean and standard deviation across seeds) for every method, variant, dataset, and mechanism should be tabulated. This is essential to assess whether the reported rankings are consistent or driven by a few configurations.
[Section V-A] The hyperparameters n-runs and n-samples are selected by observing ECE plateaus on the same datasets (Figures 1-2) and then used in the reported ECE comparisons. Tuning on the evaluation data can bias the calibration comparisons in favor of the tuned methods. The paper should either use a separate validation split for this tuning or report ECE as a function of n-runs/n-samples for the main comparisons, demonstrating that the qualitative conclusions are insensitive to the chosen values.
[Section IV-A and Tables II-III] The 'standardized' uncertainty-extraction framework is not actually standardized across methods: MICE only supports multi-run, TabCSDI has no predictive-distribution variant, and SoftImpute/OT-Impute have no native uncertainty at all, while GAIN-U and MIWAE-U use direct variance outputs. This is not a flaw per se, but it means that the paper compares the best available uncertainty proxy for each method rather than a common protocol. The abstract and introduction should be revised to state this explicitly, and the guidelines in Section VI should be framed as conditional on the uncertainty route used, not as intrinsic properties of the imputation algorithms.

minor comments (5)

[Section IV-B] The missingness protocol is under-specified. The text says 'we fixed a target missingness rate (e.g., 10–15%)' but the results are consistently reported at 30% missingness, and Figure 7 implies multiple rates without stating them. Please specify the exact target rates for each experiment and whether rates refer to total cells or per-feature.
[Section IV-C] The ECE definition uses a grid q∈{0,0.1,...,1.0} and a CDF-based approach, but the paper does not specify the binning scheme or interval construction for continuous targets. In particular, it is unclear how zero-width or degenerate predictive distributions (as can occur for deterministic methods) are handled. Please provide the exact interval construction and any binning used.
[Section V-B (Figure 3 caption)] Runtime comparisons mix 'total time' for classical methods and 'train+single imputation' for deep models. This makes the runtime comparisons hard to interpret. It would be clearer to report training time, inference time, and total time separately for all methods.
[Section III.B, SoftImpute paragraph] The sentence 'Although newer deep generative and diffusion-based methods often achieve higher accuracy and better uncertainty calibration' is not supported by the paper's own results (e.g., TabCSDI has higher MAE than SoftImpute on most datasets). Please rephrase to avoid an unsubstantiated background claim.
[General] There are several typographical and rendering issues (e.g., 'MIW AE', 'a approache', garbled axis labels in Figures 6 and 8). Please ensure the final PDF renders all symbols and legends correctly.

Circularity Check

1 steps flagged · score 2.0 of 10

Essentially an independent empirical benchmark; mild circularity only in selecting n-runs/n-samples from the same ECE curves that are later reported.

fitted input called prediction [Section V-A (Tuning and Default Parameter Setting), Figs 1–2; applied in Section V-D (Calibration Curves and ECE)]
"Figure 1 shows that ECE steadily improves with increasing n-runs, but the gains plateau around five runs. Accordingly, we set n-runs=5 as the default for all multi-run experiments. For sampling-based variants (Figure 2), both MIWAE-S and GAIN-S reach stable calibration by n-samples≈20, while TabCSDI-S exhibits its best calibration performance between 50 to 70 samples. We therefore adopt n-samples=20 for MIWAE-S and GAIN-S, and n-samples=50 for TabCSDI-S."

The hyperparameters n-runs and n-samples are chosen by observing ECE at 30% MCAR on the same datasets (wine, energy) that later generate the reported ECE comparisons. For TabCSDI-S, the selected interval is explicitly the one with 'best calibration performance', so the reported calibration for that variant is an in-sample optimum rather than a prediction on held-out settings. This is a selection-on-the-evaluation-metric form of circularity. It is mild because the choice is justified by a plateau (so nearby values give similar ECE) and the main accuracy/calibration misalignment is corroborated by several methods and datasets.

full rationale

The paper is an empirical benchmark against external, complete datasets with synthetically injected missingness; it does not derive a formal result from its inputs, and no step equates a fitted parameter with the quantity it claims to predict. The central claim — that point accuracy and calibration are often misaligned — is a summary of direct measurements across six methods, five datasets, and three missingness mechanisms, so it is not forced by a self-citation chain or by definition. The pseudo-uncertainty assigned to deterministic SoftImpute (Section IV-A: 'any minor stochasticity from randomized SVD is treated as pseudo-uncertainty') is an acknowledged construct-validity limitation, not a hidden circular step, because the paper transparently labels it and does not present it as a native predictive distribution. Self-citations [40]–[43], [46] are related work or a reproducibility repository and are not load-bearing. The only circularity-adjacent practice is the in-sample selection of n-runs and n-samples from the same ECE curves later reported; this mildly biases the calibration numbers for the tuned variants but does not reduce the headline result to its inputs.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The central empirical claims rest on standard imputation assumptions (MAR, low-rank, OT distribution matching), plus experimental-design choices (synthetic missingness, z-scoring, hyperparameter fixing). No new theoretical constants or entities are introduced; the GAIN-U variant is a model variant without external evidence.

free parameters (7)

n_runs (multi-run uncertainty) = 5
Chosen as the plateau point of ECE vs. number of runs in Figure 1 (wine/energy, 30% MCAR), then used as default for all multi-run evaluations.
n_samples (sampling variants) = 20 (MIWAE-S, GAIN-S), 50 (TabCSDI-S)
Chosen from ECE-vs-samples curves in Figure 2 (wine/energy, 30% MCAR) as the point where ECE stabilizes; TabCSDI-S needs more samples to reach best calibration.
SoftImpute shrinkage lambda = selected via CV on observed entries (log grid, grid_len 15-25)
Tuned per dataset to balance accuracy/runtime (Section V-A); regularization strength affects imputation and thus calibration.
MIWAE importance samples K = 10
Hyperparameter fixed to 10; more samples tighten the likelihood bound but increase cost.
GAIN/MIWAE epochs = 1500-2500
Training iterations chosen per dataset size; affects convergence and calibration.
TabCSDI epochs/num_steps = wine: 500/600; energy: 400/1000
Capped for computational cost; not evaluated on larger datasets.
Missingness rates = 30% (main tables), also 10-20% (Figure 7)
Target missingness rates set by experiment design; MAR/MNAR rates probabilistic so actual rates differ slightly.

assumptions (5)

domain assumption Rubin's MCAR/MAR/MNAR taxonomy and Eq. (1)-(2) posterior factorization under row i.i.d. with shared parameter theta
The paper assumes missingness mechanisms are correctly described by P_phi(M|X) and that the imputation target is the posterior predictive P(X_mis|X_obs, M). This is standard in imputation (Sec. III-A).
domain assumption MICE and MIWAE assume MAR (and MNAR handled only by inclusion of mechanism in data generation)
Sec. III-B states MICE 'assumes data are MAR' and MIWAE performs variational inference 'under the MAR assumption'; evaluations under MNAR therefore test methods outside their stated assumptions.
domain assumption SoftImpute low-rank/nuclear-norm prior on the complete matrix
Sec. III-B.2 assumes the complete data is well-approximated by low rank; if false, both accuracy and pseudo-uncertainty collapse.
domain assumption OT-Impute assumes random subsets of the dataset share the same distribution
Sec. III-B.3: minibatch distributional alignment via Sinkhorn divergence; this is the model's inductive bias.
domain assumption Z-scored Gaussian predictive distributions and CDF-based calibration are appropriate for all methods
Features are z-scored; calibration uses CDF-based approach for continuous targets (Sec. IV-C). For multi-run/sampling, per-cell uncertainty is presumably summarized as a Gaussian or empirical quantiles, but the paper does not fully specify the interval construction.

invented entities (1)

GAIN-U (heteroscedastic GAIN variant)
purpose: Adds a variance head to the GAIN generator, replacing MSE with Gaussian NLL on observed coordinates, to yield per-cell predictive variances.
Introduced in this paper (Sec. III-B.4) and used in the evaluation; no external validation or pre-registered prediction. It is a model variant, not a new physical entity, but it is new to this paper.

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Cite this review

Pith. "Pith review of Beyond Accuracy: An Empirical Study of Uncertainty Estimation in Imputation." pith.science (2026). https://pith.science/paper/C2TOCYQD

@misc{pith2026251121607,
  author       = {Pith},
  title        = {Pith review of: Beyond Accuracy: An Empirical Study of Uncertainty Estimation in Imputation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C2TOCYQD}},
  note         = {Machine review of arXiv:2511.21607}
}

read the original abstract

Handling missing data is a central challenge in data-driven analysis. Modern imputation methods not only aim for accurate reconstruction but also differ in how they represent and quantify uncertainty. Yet, the reliability and calibration of these uncertainty estimates remain poorly understood. This paper presents a systematic empirical study of uncertainty in imputation, comparing representative methods from three major families: statistical (MICE, SoftImpute), distribution alignment (OT-Impute), and deep generative (GAIN, MIWAE, TabCSDI). Experiments span multiple datasets, missingness mechanisms (MCAR, MAR, MNAR), and missingness rates. Uncertainty is estimated through three complementary routes: multi-run variability, conditional sampling, and predictive-distribution modeling, and evaluated using calibration curves and the Expected Calibration Error (ECE). Results show that accuracy and calibration are often misaligned: models with high reconstruction accuracy do not necessarily yield reliable uncertainty. We analyze method-specific trade-offs among accuracy, calibration, and runtime, identify stable configurations, and offer guidelines for selecting uncertainty-aware imputers in data cleaning and downstream machine learning pipelines.

Figures

Figures reproduced from arXiv: 2511.21607 by the authors.

**Figure 1.** ECE vs. n-runs at 30% MCAR. the calibration curve: perfect calibration lies on y = x, while deviations indicate over- or under-confidence. We measure miscalibration with the expected calibration error ECE = 1 |Q| X q∈Q [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 4.** Runtime vs. n-samples at 30% MCAR in wine. Sinkhorn computations over many pairs and iterations, which can be moderately costly, yet it remains faster than deep learning and diffusion models since it avoids lengthy neuralnetwork training and sampling. Its runtime also appears nearly constant across datasets because a fixed batch size and iteration count are used. SoftImpute is slower than MICE and can even be slowe… view at source ↗

**Figure 3.** Time per run at 30% missingness vs Classical methods [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: Runtime vs. n-samples at 30% MCAR on wine for TabCSDI-S. 0.0 0.2 0.4 0.6 0.8 1.0 Expected Confidence Level 0.0 0.2 0.4 0.6 0.8 1.0 Empirical Frequency Imputation Methods Perfect calibration OT-Impute (ECE=0.148) MICE (ECE=0.014) SoftImpute (ECE=0.227) MIWAE (ECE=0.094)…

**Figure 8.** Figure 8: Calibration curves for 30% MCAR. D. Calibration Curves and ECE Figures 6 and 8 present calibration curves across imputation methods and datasets at a 30% MCAR. Overall, MICE achieves the most reliable calibration, producing curves near the ideal diagonal and the lowes…

**Figure 7.** Figure 7: MAE vs. missing rate for MCAR. biodegradation the OT-Impute performs best due to its effective distribution-matching. SoftImpute often ranks second best overall, where its nuclear-norm regularization effectively captures latent structure. 0.0 0.2 0.4 0.6 0.8 1.0 Expect…

**Figure 9.** Figure 9: Calibration curves for GAIN family in 30% MCAR. [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 10.** Figure 10: Calibration curves for MIWAE family in 30% MCAR. [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Reviewed August 3, 2026 · model on record in the stance chip above.

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