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ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read ImputeINR claims that time series imputation, even with 90% of values missing, is best done by learning a continuous implicit neural function of time rather than imputing discrete points.

desk verdict Reasonable INR-imputation extension with a plausible grouped-MLP design, but the SOTA claim rests on an under-specified preprocessing protocol and missing closest baselines. read the letter →

arxiv 2505.10856 v1 pith:EC7WNCMK submitted 2025-05-16 cs.LG cs.AI

Mengxuan Li , Ke Liu , Jialong Guo , Jiajun Bu , Hongwei Wang , Haishuai Wang This is my paper · ORCID
classification cs.LGcs.AI
keywords timeseriesimputationimplicitneuralrepresentationsmissingdatadiseasediagnosiscontinuousfunctionmodelingvariableclusteringhealthcare
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

ImputeINR is built on a simple bet: a time series is a continuous signal, so the right way to impute it is to learn a continuous function of time, not to fill discrete slots. The paper proposes an implicit neural representation (INR), a network that maps any timestamp to the values of all recorded variables, whose parameters are predicted by a transformer from the few observed points. On eight benchmark datasets with 10% to 90% of values randomly masked, the authors report the best or second-best MSE or MAE in most settings, with an average MSE reduction of 62.0% against the second-best method and 68.2% at the 90% mask rate. Because real healthcare records are extremely incomplete, with MIMIC-III at 63.15% missing and the PhysioNet ICU challenges around 79.67%, the claim matters for downstream diagnosis, where using ImputeINR-imputed data raises AUROC on three clinical benchmarks.

What carries the argument

The load-bearing object is the INR continuous function $f$ that maps a timestamp $t$ to the variable vector $X(t)$, an MLP queryable at any moment rather than only on the original sampling grid. It is decomposed into a polynomial trend, a Fourier seasonal component, and an adaptive group-based residual MLP, so the network can fit both smooth long-term motion and periodic structure. Its parameters are supplied by a transformer encoder that ingests multi-scale convolutional features of the reordered masked data and outputs the INR tokens serving as weights, which avoids a per-series optimization loop. Variable clustering, using agglomerative clustering with no preset number of clusters, fixes the grouping used by the residual layers, and the claimed benefit is that variables with similar distributions share capacity while cross-variable correlations are still handled by global layers.

What would settle it

Re-run the eight-dataset comparison with variable clustering and standardization fit on training windows only and frozen before any test window is processed. If ImputeINR's average MSE advantage over the second-best method drops from the reported 62.0%, or from 68.2% at 90% masking, to a small or negative margin, the claim that continuous INR imputation is intrinsically superior at high missing rates would be falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that treating a multivariate time series as a continuous signal makes imputation robust to extreme missingness. ImputeINR learns a function $f(t)$ that returns all variables at timestamp $t$, written as a polynomial trend $f_{tre}(t)$, a Fourier seasonal term $f_{sea}(t)$, and a residual term $f_{res}(t)$ computed by an MLP whose layers are partly global and partly grouped by variable cluster. The network weights are not optimized per series; a transformer encoder predicts them, producing the 'INR tokens', from the observed masked data after variable clustering and multi-scale convolutional feature extraction. The authors report that this design achieves the best or second-best imputation error in most of the forty dataset-mask-rate conditions, and that the imputed values improve disease-diagnosis AUROC on PhysioNet 2012, PhysioNet 2019, and MIMIC-III over all compared imputation baselines.

Load-bearing premise

The reported gains assume the variable clustering and standardization are computed from the training split only; the paper never states this, and its Algorithm 2 runs clustering on the data being imputed, so if test windows shape the variable groups, part of the measured advantage could come from test-set information.

Editorial extensions

If this is right

  • At 90% masked values, ImputeINR's average MSE is 68.2% lower than the second-best baseline, so extreme sparsity stops being a hard barrier for imputation.
  • Imputed healthcare data from ImputeINR improves disease-diagnosis AUROC on PhysioNet 2012, PhysioNet 2019, and MIMIC-III compared with data imputed by all nine baselines and by zero or mean imputation.
  • Ablations attribute the gain to the combination of multi-scale features, variable clustering, and the adaptive group MLP; using clustering plus the group MLP gives the largest paired improvement, so the continuous representation alone is not sufficient.
  • Because $f$ can be queried at arbitrary timestamps, the same trained model can impute at off-grid or irregularly spaced times without retraining, a capability grid-based imputers lack.
  • The runtime-versus-MSE analysis places ImputeINR near the bottom-left corner with a small parameter count, indicating the accuracy gain is not bought by a large model or slow inference.

Reading between the lines

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

  • If clustering were restricted to training data, the reported numbers might shrink; the paper's Algorithm 2 applies clustering to the input data being imputed, so the exact 62% figure should be read as an upper bound until the protocol is clarified.
  • The trend, seasonal, and residual decomposition suggests ImputeINR should transfer to irregularly sampled and super-resolution time series, where querying off-grid is the point; neither setting is tested in the paper.
  • A direct test of which component matters is to compare against the same architecture without the Fourier seasonal term on nonstationary clinical signals; the seasonal term may contribute little there, isolating the residual group MLP as the driver.
  • In deployment, missingness is present in the very data used to cluster variables, so the grouping must be inferred from incomplete observations; the paper does not test whether clustering remains stable under missingness.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes ImputeINR, a time series imputation method based on implicit neural representations (INR). The model learns a continuous function from timestamps to multivariate values, using a transformer encoder to predict INR parameters from observed data. A variable clustering step groups variables with similar distributions, and an adaptive group-based MLP with trend, seasonal, and residual components forms the INR function. Multi-scale convolutional feature extraction is added. Experiments on eight datasets with mask rates from 10% to 90% are reported, claiming state-of-the-art MSE/MAE in most conditions, and downstream disease diagnosis on Phy2012, Phy2019, and MIMIC3 shows improved AUROC compared with other imputation baselines. The paper includes ablation studies, efficiency analysis, and robustness checks.

Significance. If the results hold, ImputeINR would be a useful contribution for imputing time series at high missing ratios, which is practically relevant for healthcare data. The architectural idea of combining variable clustering with a group-based INR is interesting, and the ablation studies support the contribution of each module. The authors state that code is available, which aids reproducibility. However, the empirical support for the central claim is weakened by an ambiguous preprocessing protocol, the omission of the closest INR-based baselines, and the absence of error bars and significance tests. These issues need to be addressed before the state-of-the-art claim can be accepted.

major comments (3)
  1. [Section 4.1, Algorithm 2] The experimental protocol never states whether variable clustering and standardization are computed on the training set only or on the full dataset including test windows. Algorithm 2 takes 'Time series data X with missing values' as input and performs feature clustering on X (line 3) before reordering and standardizing; in the evaluation setup X is the masked test set. If clustering and normalization moments are derived from test-set statistics, the adaptive group-based INR architecture is tailored to the test distribution, which is not neutral preprocessing and could inflate ImputeINR's advantage over baselines that use fixed architectures and training-only normalization. Please specify that clustering and standardization are fit on the training set only, or rerun the experiments with train-only preprocessing and report the resulting differences.
  2. [Section 2.3, Table 1] The related work identifies HyperTime and TimeFlow as the closest INR-based imputation methods and criticizes their limitations, but neither appears in the experimental comparison in Table 1. Since the paper's central novelty is an INR-based imputation architecture, omitting these two baselines leaves the state-of-the-art claim incomplete. Please include them in the comparison under the same masking and preprocessing protocol, or provide a specific justification for their exclusion.
  3. [Table 1, Section 4.2] The main results report a single run per condition with no standard deviations or statistical significance tests. Several per-condition differences are very small (e.g., Weather 90% MSE 0.065 vs 0.066; Phy2019 10% MSE 0.071 vs 0.072), and the headline '62.0% average MSE reduction' is presented without confidence intervals. Without repeated-seed variability or significance testing, the claim of state-of-the-art performance is not robustly established. Please report means and standard deviations over multiple seeds and, where feasible, paired significance tests for the main comparisons.
minor comments (5)
  1. [Appendix A.2, Algorithm 1] Algorithm 1 can loop forever: if the closest pair distance d(C_i,C_j) is not less than epsilon, no merge occurs but the while condition |C|>1 remains true. Please revise the termination condition, e.g., break when the minimum distance is >= epsilon.
  2. [Section 4.1, Methodology] Several free parameters are not reported: the trend polynomial degree m in Eq. (10), the clustering stopping criterion epsilon in Algorithm 1, the similarity metric used in Eq. (3), and the handling of missing values when computing the similarity matrix from partially observed data. Please specify these choices for reproducibility.
  3. [Table 1] The 'Average' row should state how the average is computed (over all dataset-mask-rate conditions) and which method is considered second-best for each metric; currently the comparison baseline for the 62.0% reduction claim is ambiguous.
  4. [Section 4.3] Please specify whether the LSTM classifier is trained on the imputed training set and evaluated on the imputed test set, and whether it is retrained separately for each imputation method; otherwise the downstream diagnosis comparison is not fully reproducible.
  5. [Section 4.4, Figure 4] The efficiency analysis reports running time and model size only as a bubble chart; please provide numeric values or a table so that readers can verify the efficiency comparison quantitatively.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: ImputeINR's SOTA claim is an external benchmark comparison; the only self-citations are architectural adoptions, not load-bearing evidence.

full rationale

ImputeINR's derivation is self-contained in the relevant sense. The imputation loss (Eq. 1) is the standard masked reconstruction error, and the INR continuous function (Eqs. 8-16) is a feed-forward architecture whose parameters are predicted from the observed values; neither reduces to the evaluation metric by construction. The claimed superiority is an empirical result against nine baselines on eight standard benchmarks with fixed masking rates, so the central claim does not depend on a fitted parameter being renamed as a prediction. The trend/seasonal/residual decomposition is adopted from prior work, including the authors' TSINR (Li et al., 2024), but this is an architectural choice made explicit by "Following the previous work" rather than a uniqueness theorem or a derived result, and the benchmarks do not reduce to it. The variable-clustering and standardization steps are a potential evaluation-validity concern: Algorithm 2 runs feature clustering on the input X, and the paper never states whether that X is the training windows only or includes test windows. If test windows are included, the group structure is tailored to the test distribution, which could inflate the reported gains; but that is a leakage/correctness issue, not a circularity, because the model's output is not defined in terms of the target metric. No self-citation is load-bearing: the cited prior INR works are used for general background and architecture components, while the SOTA claim is checked against external benchmarks and baselines. Therefore no circular step can be exhibited with the paper's own equations.

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

The central claim depends on a set of user-chosen hyperparameters and modeling assumptions. The most consequential unknowns are the clustering threshold and similarity metric, which determine the group architecture, and the unspecified handling of standardization, which affects all downstream comparisons. No new physical or algorithmic entities are introduced beyond the learned INR function, which is a standard modeling tool.

free parameters (4)
  • m (trend polynomial degree) = not reported
    Equation 10 defines the trend as a polynomial of degree m, but m is never specified in the experiments; it affects the expressiveness of the continuous function.
  • epsilon (clustering stopping criterion) = not reported
    Algorithm 1 uses a distance threshold epsilon to decide when to stop merging clusters; the value is not given, so the number of groups K is not reproducible.
  • number of groups K = data-dependent
    K is determined by agglomerative clustering with an unreported threshold, making the group architecture adaptive but under-specified.
  • variable similarity metric and handling of missing values = not specified
    The similarity matrix S in Equation 3 is central to clustering, but the paper does not state which similarity measure is used or how missing values are treated when computing it.
assumptions (4)
  • domain assumption Missing values are missing completely at random (MCAR).
    The evaluation uses random masking to create missingness, so the method is only validated under MCAR, not under the informative missingness common in healthcare.
  • domain assumption Time series can be decomposed into trend, seasonal, and residual components as in Equation 9.
    The INR function is defined as a sum of polynomial, Fourier, and MLP residual terms; this decomposition is taken from prior INR works and is not tested against alternatives.
  • domain assumption Variables with similar distributions share useful representation when placed in the same group.
    The group architecture is motivated by a synthetic experiment (Figure 3) and is assumed to hold for real datasets.
  • ad hoc to paper The similarity matrix and clustering can be computed reliably from partially observed data.
    No method is given for computing pairwise similarity with missing entries; this is an unstated assumption specific to the proposed pipeline.

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Cite this review

Pith. "Pith review of ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data." pith.science (2026). https://pith.science/paper/EC7WNCMK

@misc{pith2026250510856,
  author       = {Pith},
  title        = {Pith review of: ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EC7WNCMK}},
  note         = {Machine review of arXiv:2505.10856}
}
read the original abstract

Healthcare data frequently contain a substantial proportion of missing values, necessitating effective time series imputation to support downstream disease diagnosis tasks. However, existing imputation methods focus on discrete data points and are unable to effectively model sparse data, resulting in particularly poor performance for imputing substantial missing values. In this paper, we propose a novel approach, ImputeINR, for time series imputation by employing implicit neural representations (INR) to learn continuous functions for time series. ImputeINR leverages the merits of INR in that the continuous functions are not coupled to sampling frequency and have infinite sampling frequency, allowing ImputeINR to generate fine-grained imputations even on extremely sparse observed values. Extensive experiments conducted on eight datasets with five ratios of masked values show the superior imputation performance of ImputeINR, especially for high missing ratios in time series data. Furthermore, we validate that applying ImputeINR to impute missing values in healthcare data enhances the performance of downstream disease diagnosis tasks. Codes are available.

Figures

Figures reproduced from arXiv: 2505.10856 by the authors.

Figure 1
Figure 1. The illustration of INR applied to time series data. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The overall workflow of the proposed method. The input data with missing values is imputed using the ImputeINR model, and the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The four architectures we test to evaluate the representation capability of the INR continuous function for the synthetic time series [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: A bubble chart reporting running time vs. imputation per [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Robustness analysis for mask rates and the number of variables. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.