Title: Meta Guidance: Incorporating Inductive Biases into Deep Time Series Imputers
Venue: NeurIPS 2025
Accepted: yes
Keywords: data imputation; time series; inductive bias; non-stationarity; periodicity
Abstract: Missing values, frequently encountered in time series data, can significantly impair the effectiveness of analytical methods. While deep imputation models have emerged as the predominant approach due to their superior performance, explicitly incorporating inductive biases aligned with time-series characteristics offers substantial improvement potential. Taking advantage of non-stationarity and periodicity in time series, two domain-specific inductive biases are designed: (1) Non-Stationary Guidance, which operationalizes the proximity principle to address highly non-stationary series by emphasizing temporal neighbors, and (2) Periodic Guidance, which exploits periodicity patterns through learnable weight allocation across historical periods. Building upon these complementary mechanisms, the overall module, named Meta Guidance, dynamically fuses both guidances through data-adaptive weights learned from the specific input sample. Experiments on nine benchmark datasets demonstrate that integrating Meta Guidance into existing deep imputation architectures achieves an average 27.39\% reduction in imputation error compared to state-of-the-art baselines.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents a novel plugin module called Meta Guidance for multivariate time series with missing values. Meta Guidance dynamically fuses NSG and PG via a learnable meta-weighting mechanism, allowing models to adaptively focus on temporal dynamics based on data characteristics. MG can be seamlessly integrated into popular deep imputation models (Transformers, CSDI, SAITS, TimesNet, etc.), yielding an average 27.39% improvement over state-of-the-art methods on nine real-world datasets.\n\nSTRENGTHS AND WEAKNESSES:\nPros:\n1. The paper is well-structured and easy to follow.\n2. The proposed method is plug-and-play with strong adaptability, and brings effective performance improvements across a variety of models.\n3. The paper provides thorough experiments, including comparison with several backbones on 9 datasets and under different missing mechanisms.\n\nCons:\n1. Periodicity detection relies on FFT, assuming stable periodic patterns. This may not generalize well to irregular periodicities. \n2. Some baselines are absent. PatchTST[1] has been proven to be an effective and efficient on time series tasks, the paper should further investigate its effectiveness when applied to methods employing patch trick (This trick is widely used for time series models). Also, the non-stationary transformer[2] also consider the non-stationary factor. It should be included as a baseline.\n[1] A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. ICLR 2023.\n[2] Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting, NeurIPS 2022.\n\nQUESTIONS:\n1. Why NSG and PG are designed in Channel-independent style? In my opinion, different channels may exhibits different non-stationary levels and different periodicities. \n2. In Eq. 7, for each previous period, the PG only consider the exact one time point. So for periodic data with high noise levels or even anomalies, could this affect the model's robustness to noise? Would additionally considering the neighboring points of each periodic point be a more robust approach?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors introduce a novel method that enhances deep learning for time-series imputation. It achieves this by integrating inductive biases for both non-stationary and periodic characteristics, dynamically weighted by a Meta Guidance mechanism. This approach is highly adaptable, designed to augment existing imputation methods, and is shown to improve their performance across diverse real-world time-series datasets with various missing data types (MAR, MNAR, MCAR) and rates.\n\nSTRENGTHS AND WEAKNESSES:\nStrength: \n- The proposed method is compatible with existing time-series imputation techniques and offers a promising avenue for performance enhancement through augmentation. \n- The MG mechanism is highly adaptive and can be applied to other existing imputation methods.\n- The performance improvements are both consistent and significant across various experiments.\n- This work offers a meaningful departure by providing compatibility with existing time-series imputation techniques (which have primarily concentrated on developing novel architectures and objective functions, often incorporating diverse inductive biases, frequency and trend-seasonality decomposition) and offering a promising avenue for performance enhancement through augmenting high-level information of the given time-series.\n\nWeakness:\n- While the authors mentioned that the current time-series imputation methods do not concurrently consider the characteristics of non-stationarity and periodicity in time series, many recent related works use inductive bias to put localized influence [A, B] or both trend and seasonality [C] for time-series imputation.\n- The proposed framework is highly adaptive. But, its adaptability to multiple imputation methods (such as [A, B, C] and many more) is missing. \n\n\nReferences: \n\n[A] M. Choi and C. Lee, \"Conditional Information Bottleneck Approach for Time Series Imputation,\" ICLR 2024.\n\n[B] V. Fortuin et al, \"GP-VAE: Deep Probabilistic Time Series Imputation.\" AISTATS 2020.\n\n[C] X. Yang et al., \"Frequency-aware Generative Models for Multivariate Time Series Imputation,\" NeurIPS 2024.\n\nQUESTIONS:\n- The construction of the non-stationary guidance, periodicity guidance, and meta-guidance vectors remains unclear. Visualizing these guidance vectors would greatly enhance understanding of when and why the imputation process prioritizes non-stationary or periodic signals. Can the authors elaborate on this?\n\n- A concern arises regarding potential overfitting of the gamma parameters in Equations (3) and (8) to the training set. How do the authors address this and demonstrate that the parameters are well chosen in augmented imputation methods?\n\n\n- While the authors have provided an extensive ablation study, they primarily focused on showing the effect of including or excluding certain components. The authors do not adequately explain when and why non-stationary guidance and periodic guidance are beneficial, nor do they connect these benefits to specific characteristics of the evaluated time-series datasets. A plot illustrating the method's performance against key time-series statistics would significantly strengthen this aspect.\n\n-  The authors demonstrate the method's effectiveness across multiple real-world time-series datasets and various missingness scenarios (e.g., MAR, MNAR, MCAR) and missing rates. However, these static missingness patterns fail to capture the dynamic nature of real-world missing data, where missingness is often influenced by temporal dependencies. This raises questions about why augmenting the proposed method helps and when it is most effective. Hence, a more thorough investigation of its behavior under dynamic temporal variations is recommended. Specifically, the authors could explore: \n(i) How the meta-guidance mechanism responds to changing temporal characteristics.\n(ii) How the method performs when missingness is generated based on temporal dependencies, rather than static patterns.\n\n- While the authors highlight contributions in non-stationary/periodic modeling and meta guidance, the related work section fails to adequately position their approach. The discussion of stationary imputation and general time-series characteristics is too broad, hindering a clear understanding of the proposed method's novelty.\n\n- As mentioned in the Weakness, important multiple imputation methods for time-series data are missing.\n\n- It would be valuable to incorporate experiments illustrating that the imputed values produced by the proposed method maintain high predictive and/or discriminative power.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-27"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper addresses the imputation task for time series that exhibit non-stationarity and periodicity behavior. In particular, the authors propose two modules, namely Non-Stationary Guidance (NSG) and Periodic Guidance (PG), to extend existing deep learning (DL) models in handling the aforementioned challenges and leveraging the non-stationarity and periodicity characteristics of the time series. Finally, a Meta Guidance (MG) module is introduced. The MG module learns to balance the matrix representations learned by NSG and PG, and to appropriately weight the time series within the deep learning architectures.\n\nIn the experiments, the authors integrate the MG module into 5 state-of-the-art models, they evaluate them on 9 real-world datasets. The models+MG show improved performance across all scenarios. The authors also present various ablation studies.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The idea is novel, and the performance of the MG module are quite interesting.\n- The paper is well written and easy to follow, although some details could be improved or explained more  (see below).\n\nWeaknesses:\nMajor:\n- There is no comparison againsts other approaches handling non stationarity and periodicity. Like simple pre-processing approaches, or deep learning solutions.  \n- In the modules,  \"ψ(i) is the probability density of standard normal distribution N(0,1)\" , centered at the current time step and used to compute the guidance matrices; and the hyperparameter \"r\" controls the neighborhood points. I wonder whether this hyperparameter could instead be learned, or better, whether the model could learn the most appropriate distribution (e.g., the standard deviation of N(0, sigma2)) for each channel, rather than relying on hyperparameters. The authors provide some ablation studies, but further exploration would be useful.\n- All the proposed modules are channel-independent. While the deep learning architecture may still capture inter-channel dependencies, I believe that the embeddings produced by the MG module could mislead the imputation process (of the DL models) for some multivariate datasets. I would like to see more discussion of this potential limitation.\n- Some well-known datasets with missing data are not included. For example, the Air Quality (PM2.5) dataset (which may have periodicity behavior); and PhysioNet. Both are used benchmarks in CSDI. \n\nMinor and Typos:\n- The repository link is expired; it would be helpful to provide an active one.\n- Figure 1 could be improved in quality. The meaning of the yellow dots and pink squares is not explained, their interpretation is left to the reader. Also, the figure style is quite different from the others in the paper.\n- Although basic, it would be useful to define the MAE and RMSE acronyms, and briefly justify why these metrics. For example, why not use the Continuous Ranked Probability Score (CRPS)?\n- The use of bold metrics in Table 11 is unclear. \n- Table 8, which includes standard deviations, is confusing to me. Which experiments are the values referring to?\n\nQUESTIONS:\n1) What is exactly the MLP loss used in the different modules? Is it a reconstruction loss wrt the vanilla imputation? If so, can the authors motivate better this strategy, and alternatives.\n2) The results are averaged over three independent runs. Does it mean the models are trained 3 times? Or the imputation is done three times, using different random seeds / initialisation? \n3) I understand the added computation time for the MG module is reasonable, for a single epoch. However, we have additional embeddings, does a model requires more epochs to converge / achieve the optimal performance? Are the base models and models+MG trained the same number of epochs/ amount of time?\n4) What if we apply a simple pre-processing (like de-trending or differentiation) instead of meta guidance? What about the performance in this case?\n\nLIMITATIONS:\nYes. However, the authors could extend the limitation section.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this submission, authors introduce Meta Guidance (MG), a novel technique designed to enhance multivariate time series imputation tasks. The authors present three key contributions that constitute MG: first, a guidance mechanism for non-stationarity that utilizes measurements from timesteps close to the missing data point; second, a guidance mechanism for periodicity that employs measurements from timesteps N periods away from the missing point; and third, a method to combine both guidance approaches by determining which to favor based on dataset characteristics, as controlled by a parameter lambda. Notably, this proposal is channel-independent and can be applied to various existing architectures such as Transformers or Diffusion models. \n\nThe effectiveness of MG has been evaluated across nine common multivariate time series datasets against multiple baselines.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n * Presents a well-designed and clearly understandable architecture\n * Conducts extensive experimentation across multiple datasets and scenarios\n * Offers an interesting proposal that has strong potential to become an important baseline in the field\n * Demonstrates compatibility with various existing architectures (Transformers, Diffusion models)\n\n### Weaknesses\n * Focuses primarily on individual missing data points, which may not fully represent real-world scenarios with consecutive or patterned missing data\n * Uses datasets that may not be best suited for studying the impact of hyperparameters, potentially limiting the insights gained\n * Lacks sufficient analysis of lambda's impact in the ablation study, which is crucial for understanding the method's behavior\n * Git repository is not available, hindering verification and reproduction of results\n * Without prior knowledge of existing baselines, it can be challenging to fully appreciate the contributions (though page limitations make exhaustive comparisons difficult)\n * Would benefit from evaluation on synthetic datasets with controlled trends and frequencies\n * Lacks component-wise comparisons with simpler baselines\n * Could provide more detailed analysis of how different parameter settings affect performance across various dataset characteristics\n\nQUESTIONS:\n### Similarity to Existing Solutions\nThe PeriodGuidance (PG) approach appears similar to existing solutions where deep learning imputation methods typically leverage learned patterns in the dataset. While I understand the proposal of PG is different, I would appreciate confirmation on how it distinctly differs from current methods.\n\n### Performance Analysis\nThe paper should provide more intuition or explanation regarding why Meta Guidance (MG) shows limited benefit for TimesNet/CSDI models. The performance difference is relatively small (~0.00X) compared to other models across most datasets, which warrants further discussion.\n\n### Hyperparameter Investigation\nRegarding the hyperparameter $r$, it might be more appropriate to have separate investigations for Non-Stationary Guidance (NSG) and Periodic Guidance (PG). The assumption that the same $r$ value should be used for both guidances is not immediately obvious and could benefit from justification or separate analysis.\n\n### Clarification Needed\nThe sentence on line 275 (\"Notably, both our method and other recent advances substantially outperform earlier baselines on the HD dataset, demonstrating MG's effectiveness in mitigating non-stationarity\") seems contradictory to line 271. I believe this refers to Table 10 with additional baselines, but this should be clarified to avoid confusion. (how other advances demonstrate MG effectiveness?)\n\n### Ablation Study Improvements\nFor the ablation study in Table 3, the last row should include checkmarks for both $G^{NS}$ and $G^{Per}$. The $G^{Meta}$ column could be removed since it represents $\\lambda \\times G^{NS} + (1 - \\lambda) \\times G^{Per}$. \nActually, it would be more suitable to replace column $G^{Meta}$ with a $\\lambda$ column. The first row of the ablation study would include only $G^{NS}$, the second only $G^{Per}$, a third one will sum them without using $\\lambda$ and the last one would sum them using $\\lambda$ (all items checked to showcase $G^{Meta}$). This would emphasize the impact of $G^{Meta}$ as a whole and better demonstrate the impact of $\\lambda$ compare to the section on the lambda ratio with detailed lambda value (which could be  moved to the appendix if necessary).\n\n### Suggested Improvements regarding Parameter Impact Analysis\nThe impact of $k$ for selecting top frequencies should be evaluated on highly cyclical datasets like weather or traffic, rather than ETTh1. Figure 6 suggests that weather dataset use more $G^{Per}$ (lambda < 0.5), making it more suitable for this analysis. But to avoid overgeneralization, it would be preferable to test $k$ on multiple datasets with varying seasonality, including highly seasonal datasets (weather, traffic) and less seasonal ones (ETTh1 or others).\n\nSimilarly, the impact of $r$ for proximity selection should be analyzed on highly non-stationary datasets like HD to better understand its effect. This analysis should also include less non-stationary datasets (ETTh1 or others) to provide a comprehensive view.\nAnd if $r$ is investigated for both guidance, the chosen dataset should reflect each guidance.\n\n### Clarity Enhancements\n * The double bar notation (1) should be explicitly identified as the indicator function for clarity. \n * Figure 2 would benefit from adding $X'_{:,c}$ notation. Besides, the pink and yellow blocks in this figure should be replaced with their respective notations ($g^{NS}$, $g^{Per,l}$, $g^{Per}$) to avoid confusion (reader might see the block as a place where additional operations are being performed).\n * The acronym MCAR on line 255 should be introduced with its full form (\"Missing Completely At Random\") and potentially include a reference for readers unfamiliar with the term.\n * Figure 8 should clearly identify the missing points to better illustrate the impact of imputation.\n\n### Proofreading\nThe text on line 208 requires revision for clarity and correctness.\n\nLIMITATIONS:\n### Limitations and Suggestions for Improvement\nThe submission would significantly benefit from incorporating a synthetic dataset where trend and frequency components are controlled. This addition would provide a clearer demonstration of MetaGuidance's benefits, particularly in visualizing the shifts in lambda values under different conditions. While this might not be feasible for the camera-ready version, it's important to acknowledge this point and suggest it as future work.\n\nA more comprehensive evaluation using controlled missingness with various missing data ratios and patterns would strengthen the study. The current focus on a maximum missing ratio of 40% and primarily Missing Completely At Random (MCAR) patterns may not sufficiently demonstrate the method's robustness. In large datasets with MCAR, consecutive missing data points might be rare, potentially making linear interpolation methods appear more effective than they would be in more challenging scenarios.\n\nTo provide a more thorough analysis, the authors should consider adding baseline comparisons and testing higher missing ratios. Specifically, comparing MetaGuidance components with established imputation methods would help validate the claims:\n * Comparing Non-Stationary Guidance (NSG) against linear interpolation or k-nearest neighbors (kNN) imputation\n * Comparing Periodic Guidance (PG) against seasonal historical averages\nThese comparisons would better illustrate how the proposed methods provide more informative data for imputation and validate claims about handling complex temporal dependencies.\n\nThe evaluation would also benefit from incorporating more diverse missing data patterns beyond MCAR. As noted by Niu et al. [https://epubs.siam.org/doi/pdf/10.1137/1.9781611977653.ch37], controlled environments with clearly defined missing patterns enable better interpretation of results and clearer understanding of when a proposal performs well or poorly. The analysis should consider not just individual missing data points but also consecutive missing timesteps, both synchronized and unsynchronized across different channels (which close to reality). For multivariate time series datasets, it's particularly important to examine how imputation can leverage relationships learned between channels.\n\n### Reproducibility Concerns\nReproducibility is currently limited due to several factors:\n * The Git repository is not available (expired), preventing verification of the implementation. \n * Crucial experimental details are missing, including:\n     * The number of diffusion steps used for CSDI\n     * Sequence and prediction lengths employed\n     * Specific prediction configurations (M2M, M2U)\n\nFor the latter, while default parameters might have been used, explicitly stating this would eliminate any ambiguity and enhance reproducibility.\n\n### Conclusion\nGiven the current state of the submission, I have selected a borderline accept. However, I would be inclined to increase the score to accept if several of the points mentioned in the questions and limitations sections are adequately addressed during the rebuttal and reflected in an updated version of the paper. I understand that not all suggestions can be implemented immediately, particularly those regarding different missing data patterns or tests on controlled datasets. Nevertheless, many other points can be discussed or incorporated to strengthen the submission.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}