Pith. sign in

REVIEW 4 major objections 7 minor 74 references

FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation

T0 review · 4 major / 7 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A diffusion imputer that learns a Fourier bias projection in the frequency domain consistently outperforms prior state-of-the-art multivariate time series imputation methods across benchmarks and missing rates.

desk verdict The SOTA claim in this paper is not pinned to a reproducible model: the main tables never specify which FADTI variant produced the numbers, and the paper's own ablation gives better results for a different variant. read the letter →

arxiv 2512.15116 v2 pith:HHUYZFKE submitted 2025-12-17 cs.LG cs.AI

Runze Li , Hanchen Wang , Wenjie Zhang , Binghao Li , Yu Zhang , Xuemin Lin , Ying Zhang This is my paper
classification cs.LGcs.AI
keywords multivariatetimeseriesimputationdiffusionmodelsFourierbiasprojectionfrequency-domainlearningself-attentiongatedconvolutionmissingdatasingle-cell
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 a diffusion model for multivariate time series imputation can be made consistently more accurate by injecting an explicit frequency-domain inductive bias through a learnable Fourier Bias Projection (FBP) module. The author's claim is that FADTI, which combines FBP with self-attention and gated convolution inside the denoising network, outperforms state-of-the-art imputation methods on most benchmark settings, with the largest gains at high missingness. A sympathetic reader should care because missing data is pervasive in healthcare, traffic, and biological monitoring, and the paper argues that periodic and trend structure—which time-domain-only models miss—is what carries the improvement. The paper also introduces a new biological benchmark (Yeast) and reports that the frequency module, not the temporal backbone, drives the gains.

What carries the argument

The Fourier Bias Projection (FBP) module: a frequency-aware normalization layer maps input features to a spectral representation; the real and imaginary parts are projected onto fixed orthogonal cosine and sine bases to form a bias-enhanced frequency representation; and a learnable linear layer maps this to the feature dimension. FBP can be instantiated with DFT, STFT, or Fourier Synchrosqueezed Transform, and its low-frequency parameterization acts as a smooth global trend prior during denoising. Around it, the architecture stacks residual blocks with temporal self-attention, feature-level attention, and a gated TCN, trained with a masked denoising objective.

What would settle it

Rerun the ETT point-0.5 experiment with the DFT-Attn variant from Table VII using the same seeds and report the MAE; if it reproduces 0.283 (Table III) rather than 0.221 (Table VII), the claim that the paper's described FADTI is the best configuration fails.

Watch

Extended reading notes

Core claim

In the paper's own terms, FADTI is a conditional diffusion imputer whose denoising blocks receive a frequency-informed feature modulation: each residual block decomposes the input into trend and residual, projects both through fixed cosine and sine Fourier bases with learnable linear weights, and feeds the result alongside self-attention over time or features and a gated temporal convolution. The central claim is that this design yields state-of-the-art imputation accuracy: best MAE in 10 of 12 dataset-pattern-rate settings, best or top-3 CRPS, and top-3 RMSE in 10 of 12 settings, with ablated no-frequency variants always worse. The ablation identifies the Fourier module as the main driver,

Load-bearing premise

The headline accuracy claim depends on the reported FADTI results being produced by a single, fully specified configuration and evaluation protocol that matches the best-performing ablated variant, so that the comparison against baselines is fair and reproducible.

Editorial extensions

If this is right

  • FADTI sets a new state of the art for point-wise and time-wise missingness up to 50% on ETT, Weather, and METR-LA, and on the new Yeast benchmark.
  • The frequency-domain inductive bias, not the temporal backbone, is the main driver of imputation accuracy according to the ablation study.
  • STFT- and FrSST-based instantiations of FBP are viable for multivariate imputation, extending time-frequency analysis into generative imputation.
  • The model is sample-efficient: with fewer reverse diffusion steps it matches or beats baselines that use many more steps.
  • The new Yeast single-cell dataset provides a non-periodic, noisy biological benchmark for future imputation research.

Reading between the lines

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

  • FBP is a generic module: the same bias-projection idea could be dropped into any diffusion or even non-generative imputer, since it only adds a learnable linear layer over fixed spectral bases.
  • The assumption of smooth or periodic trend structure means FADTI's advantage should be smallest on event-driven or bursty series; the paper itself concedes this, and a direct test on such a dataset would bound the scope.
  • The reported best ablated variant (DFT-Attn) outperforming the headline FADTI numbers suggests the paper has not pinned down which instantiation is canonical; a reader should treat the architecture as a family rather than a single model.
  • The Yeast dataset's introduction may be as valuable as the method itself for benchmarking robustness in non-stationary biological signals.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 7 minor

Summary. The paper proposes FADTI, a conditional diffusion framework for multivariate time series imputation. Its main novelty is a Fourier Bias Projection (FBP) module that injects frequency-domain inductive biases into the denoising process, with instantiations based on DFT, STFT, and FrSST, combined with self-attention or gated-convolution temporal backbones. The method is evaluated on ETT, Weather, METR-LA, and a newly introduced Yeast dataset under point- and time-wise missingness at 10% and 50% rates. The central claim is that FADTI consistently outperforms state-of-the-art imputation methods, particularly at high missing rates, and that the frequency module is the main driver of the gains, supported by an eight-variant ablation.

Significance. If the stated results hold, the paper makes a useful contribution: it demonstrates a principled way to combine spectral inductive biases with diffusion-based imputation, provides the first application of STFT/FrSST-based modules to MTSI, contributes a new biological time-series benchmark, and ships code. The ablation design is clear and the comparison set is representative. However, the headline SOTA claim is currently not attached to a fully specified model configuration, and several internal inconsistencies in the experimental reporting prevent the reader from verifying that the claimed gains are real rather than artifacts of protocol differences.

major comments (4)
  1. [§IV, Tables III and VII] The exact FADTI configuration used for Tables III–VI is never specified. Section IV describes a modular architecture with three FBP instantiations (DFT/STFT/FrSST) and two temporal backbones (attention/convolution), but none of the main tables state which variant is 'FADTI'. This is not merely a presentation gap: Table VII, run on the same datasets, patterns, and rates, reports variants that beat the main-table FADTI numbers. For example, DFT-Attn achieves ETT point-0.5 MAE 0.221 versus FADTI's 0.283, and Weather point-0.1 MAE 4.182 versus FADTI's 6.946. Since FADTI should be one of the eight ablated variants, the main-table results are either produced by a different protocol or by a deliberately suboptimal configuration. The central claim 'consistently outperforms state-of-the-art methods' therefore cannot be attributed to a well-defined model as written.
  2. [Table V, Weather point-0.1] The Weather point-0.1 RMSE for FADTI is 165.712, whereas CSDI's is 92.844 and MTSCI's is 93.834, despite nearly equal MAE (FADTI 6.946 vs CSDI 6.347). This is a large, unexplained outlier that contradicts the paper's claim (Section V.C.2) that FADTI is 'among the top three' in 10 of 12 RMSE settings and its broader robustness narrative. A single extreme error or a normalization/evaluation inconsistency is plausible; the paper should explain this entry or correct it, and report per-seed behavior to show it is not a fluke.
  3. [§V.C.1 and Table IV] CRPS is reported for deterministic baselines (BRITS, SAITS, TimesNet, TimeMixer, TimeMixer++) without any stated distributional procedure. CRPS is only defined for a predictive distribution; deterministic models require an explicit assumption such as a Dirac delta, a Gaussian with fixed predictive variance, or an empirical noise distribution. No such procedure is given, so Table IV's probabilistic comparison is not reproducible and may not be comparable across methods. Since the paper claims 'calibrated and sharper predictive distributions', this is a load-bearing missing detail.
  4. [§V.A.4 and Tables III–VI] All accuracy results are averages over five random seeds with different missing masks, but no standard deviations, confidence intervals, or per-seed results are reported. The headline margins over the strongest diffusion baselines are small (typically 0.02–0.04 MAE, e.g., ETT point-0.1 0.197 vs CSDI 0.240 and MTSCI 0.248), and without variance information the reader cannot judge whether these differences are consistent across seeds and masks. The paper should report variances or per-seed numbers, and ideally a simple significance test, for the main tables.
minor comments (7)
  1. [§V.C.1] The sentence 'Our model achieves the lowest CRPS in most cases and is consistently among the top three elsewhere' is repeated verbatim in the same paragraph.
  2. [§IV.F.1] The sentence defining \bar{\alpha}_s and the noise schedule appears twice in consecutive lines.
  3. [Table VII] The heading 'Metr LA' is inconsistent with 'METR-LA' used elsewhere.
  4. [Figures 5 and 6] In Figure 5 the x-axis is labeled 'inference time (seconds)' while the text discusses n_sample; Figure 6 uses n_sample on the x-axis. Please unify the notation and axes.
  5. [Table VI] In the TimesNet row, the Yeast time-wise MAPE entries appear as '88.964167.337', likely two concatenated numbers; please fix the formatting.
  6. [Algorithm 3 and Eq. (24)] Algorithm 3 declares the output shape as B×D×C×T, while Eq. (24) defines the projected representation as B×D×C×F×L. Clarify how the flattening/Linear layer maps between these shapes.
  7. [§IV and abstract] The acronym FrSST is spelled inconsistently: 'Fourier Synchro-squeezed Transform' in the introduction and 'Fourier-based Synchrosqueezing Transform' in Section IV. Please use one name.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: FBP is a fixed-basis learnable projection and the headline claims rest on empirical comparisons to external baselines.

full rationale

The paper contains no load-bearing step in which a prediction is equivalent to its own input by construction. The Fourier Bias Projection is explicitly defined with fixed orthogonal cosine/sine bases and non-trainable spectral operators, with learnable parameters confined to linear projection layers (Eqs. 23-24, Algorithm 3, Section IV-C). There is no fitted parameter that is later renamed as a prediction; the training objective (Eq. 31) is the standard masked epsilon-prediction loss against injected Gaussian noise, not against the reported MAE/CRPS metrics. The claimed performance improvements are empirical comparisons against external baselines (CSDI, MTSCI, BRITS, SAITS, TimesNet, TimeMixer++), not deductions from a self-citation or from an assumed uniqueness theorem. No load-bearing result is imported solely from the authors' prior work; references to Fourier/STFT/FrSST tools are standard signal-processing citations. The observed inconsistency between the main-table FADTI row and the Table VII ablation variants, and the unspecified exact FBP/temporal instantiation used for the headline SOTA claim, are reproducibility and protocol-specification concerns rather than circular-reasoning defects. They do not show that any claimed result is true by definition or forced by a self-citation chain. Therefore the appropriate circularity finding is a clean non-finding.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The method rests on standard DDPM machinery, the domain belief that smooth/periodic structure helps imputation (acknowledged by the authors as a limitation in V.H), and an evaluation protocol whose distributional details (CRPS for point models, seed variance) are unstated. No invented entities are postulated; FBP is a learnable module, not a new physical quantity.

free parameters (6)
  • Diffusion schedule endpoints and step count = beta_start=1e-4, beta_end=0.5, S=50
    Fixed by hand following DDPM practice (§IV.F.1); affects the noise corruption and sampling dynamics, not derived in the paper.
  • Decomposition kernel size K_d = not reported per dataset
    Hyperparameter controlling trend smoothing in FBP (§IV.C.1, Algorithm 2); no values or sensitivity analysis are given.
  • STFT window length K_f = K_f = 2T/3
    Hand-chosen window length for STFT/FrSST (§IV.B.2); no sensitivity analysis reported.
  • Number of frequency bins F = not reported
    Selects spectral resolution in Eq. (11); unspecified in the experiments, and the projection quality depends on it.
  • Aggregation sample count K = not reported
    Number of reverse-diffusion trajectories averaged in Eq. (34); directly affects MAE and CRPS, yet no value is stated.
  • Network hyperparameters (layers, dims, heads, lr, batch) = not reported
    Architecture details for the residual blocks, attention, and gated TCN are not specified; required to reproduce the headline results.
assumptions (5)
  • standard math DDPM forward/reverse Gaussian process with a fixed noise schedule (Eqs. 2-8)
    Lifted from Ho et al. [66] and Sohl-Dickstein et al. [65] without re-derivation (§III.B).
  • domain assumption Time series imputation benefits from a smoothness/periodicity inductive bias
    Core premise of FBP; the paper itself states the advantage 'may shrink on highly irregular, event-driven series' (§V.H).
  • standard math Fixed cosine/sine bases in Eq. (23) are orthogonal Fourier bases and the projection preserves magnitude and phase
    Standard Fourier basis; no free parameters (§IV.C.2).
  • domain assumption CRPS is a meaningful comparison across deterministic and probabilistic models under an unstated distributional assumption for the former
    Deterministic baselines output point estimates; the paper does not say how their predictive distributions are formed (§V.C.1, Table IV).
  • domain assumption Applying identical masks across methods and averaging over five seeds yields a fair comparison
    Stated in §V.A.2 and §V.A.4; seed-level variance is not reported.

how reviews work

0 comments
Cite this review

Pith. "Pith review of FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation." pith.science (2026). https://pith.science/paper/HHUYZFKE

@misc{pith2026251215116,
  author       = {Pith},
  title        = {Pith review of: FADTI: Fourier and Attention Driven Diffusion for Multivariate Time Series Imputation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HHUYZFKE}},
  note         = {Machine review of arXiv:2512.15116}
}
read the original abstract

Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. However, existing Transformer- and diffusion-based models lack explicit inductive biases and frequency awareness, limiting their generalization under structured missing patterns and distribution shifts. We propose FADTI, a diffusion-based framework that injects frequency-informed feature modulation via a learnable Fourier Bias Projection (FBP) module and combines it with temporal modeling through self-attention and gated convolution. FBP supports multiple spectral bases, enabling adaptive encoding of both stationary and non-stationary patterns. This design injects frequency-domain inductive bias into the generative imputation process. Experiments on multiple benchmarks, including a newly introduced biological time series dataset, show that FADTI consistently outperforms state-of-the-art methods, particularly under high missing rates. Code is available at https://anonymous.4open.science/r/TimeSeriesImputation-52BF

Figures

Figures reproduced from arXiv: 2512.15116 by the authors.

Figure 1
Figure 1. Distortion of frequency-domain representations under missing [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of the FADTI framework. The model performs denoising-based imputation via conditional feature extraction, temporal–frequency modeling, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Architecture of the temporal module. It consists of a FBP block for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Structure of the Fourier Bias Projection module. It consists of three operations: (1) a frequency-aware normalization layer that maps input features to [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: MAE and CRPS of FADTI, CSDI, and MTSCI on the ETT dataset [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 7
Figure 7. Figure 7: Performance comparison on the METR-LA dataset (point-wise, 10% [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Noise sensitivity analysis. (a) RMSE under Gaussian, Laplace, and [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

74 extracted references · 3 linked inside Pith

  1. [1]

    Recurrent neural networks for multivariate time series with missing values,

    Z. Che, S. Purushotham, K. Cho, D. A. Sontag, and Y . Liu, “Recurrent neural networks for multivariate time series with missing values,”Sci. Rep., vol. 8, no. 1, p. 6085, 2018

    2018

  2. [2]

    Temporal belief memory: Imputing missing data during RNN training,

    Y . Kim and M. Chi, “Temporal belief memory: Imputing missing data during RNN training,” inProc. Int. Joint Conf. Artif. Intell. (IJCAI), 2018, pp. 2326–2332

    2018

  3. [3]

    Predicting in-hospital mortality of icu patients: The physionet/computing in car- diology challenge 2012,

    I. Silva, G. Moody, D. J. Scott, L. A. Celi, and R. G. Mark, “Predicting in-hospital mortality of icu patients: The physionet/computing in car- diology challenge 2012,” inComput. Cardiol. Conf. (CinC), 2012, pp. 245–248

    2012

  4. [4]

    Forecasting economic time series using targeted predictors,

    J. Bai and S. Ng, “Forecasting economic time series using targeted predictors,”J. Econometrics, vol. 146, no. 2, pp. 304–317, 2008

    2008

  5. [5]

    Data imputation for sparse radio maps in indoor positioning,

    X. Li, H. Li, H. K. Chan, H. Lu, and C. S. Jensen, “Data imputation for sparse radio maps in indoor positioning,” inIEEE Int. Conf. Data Eng. (ICDE), 2023, pp. 2235–2248

    2023

  6. [6]

    Missing value imputation for multi-view urban statistical data via spatial correlation learning,

    Y . Gong, Z. Li, J. Zhang, W. Liu, Y . Yin, and Y . Zheng, “Missing value imputation for multi-view urban statistical data via spatial correlation learning,”IEEE Trans. Knowl. Data Eng., vol. 35, no. 1, pp. 686–698, 2023

    2023

  7. [7]

    Missing data in clinical studies: issues and methods,

    J. G. Ibrahim, H. Chu, and M.-H. Chen, “Missing data in clinical studies: issues and methods,”J. Clin. Oncol., vol. 30, no. 26, pp. 3297–3303, 2012. 14

    2012

  8. [8]

    Real-valued (medical) time series generation with recurrent conditional gans,

    C. Esteban, S. L. Hyland, and G. R ¨atsch, “Real-valued (medical) time series generation with recurrent conditional gans,”CoRR, vol. abs/1706.02633, 2017

    arXiv 2017

Show all 74 references
  1. [9]

    How deep is your guess? A fresh perspective on deep learning for medical time-series imputation,

    L. Qian, T. Wang, J. Wang, H. L. Ellis, R. Mitra, R. J. B. Dobson, and Z. M. Ibrahim, “How deep is your guess? A fresh perspective on deep learning for medical time-series imputation,”IEEE J. Biomed. Health Inform., 2025

    2025

  2. [10]

    SAITS: self-attention-based imputation for time series,

    W. Du, D. C ˆot´e, and Y . Liu, “SAITS: self-attention-based imputation for time series,”Expert Syst. Appl., vol. 219, p. 119619, 2023

    2023

  3. [11]

    Cross-modal missing time-series imputation using dense spatio-temporal transformer nets,

    X. Qian, T. Zhang, M. Miao, G. Xu, X. Zhang, W. Yu, and D. Chen, “Cross-modal missing time-series imputation using dense spatio-temporal transformer nets,”Math. Biosci. Eng., vol. 21, no. 4, pp. 4989–5006, 2024

    2024

  4. [12]

    Timer: Generative pre-trained transformers are large time series models,

    Y . Liu, H. Zhang, C. Li, X. Huang, J. Wang, and M. Long, “Timer: Generative pre-trained transformers are large time series models,” in Proc. Int. Conf. Mach. Learn. (ICML), 2024

    2024

  5. [13]

    Heterogeneous multivariate time series imputation by transformer model with missing position encoding,

    C. Liu, Z. Zhu, W. Hao, and G. Sun, “Heterogeneous multivariate time series imputation by transformer model with missing position encoding,” Expert Syst. Appl., vol. 271, p. 126435, 2025

    2025

  6. [14]

    Timesnet: Temporal 2d-variation modeling for general time series analysis,

    H. Wu, T. Hu, Y . Liu, H. Zhou, J. Wang, and M. Long, “Timesnet: Temporal 2d-variation modeling for general time series analysis,” in Int. Conf. Learn. Represent. (ICLR), 2023

    2023

  7. [15]

    LSCD: lomb-scargle conditioned diffusion for time series imputation,

    E. Fons, A. Sztrajman, Y . El-Laham, L. Ferrer, S. Vyetrenko, and M. Veloso, “LSCD: lomb-scargle conditioned diffusion for time series imputation,”CoRR, vol. abs/2506.17039, 2025

    2025 arXiv

  8. [16]

    Conditional time series diffusion model for high-speed train multi-sensor signals imputation,

    Z. Yang, H. Dong, H. Zhang, and R. Wang, “Conditional time series diffusion model for high-speed train multi-sensor signals imputation,” IEEE Trans. Intell. Transp. Syst., 2025

    2025

  9. [17]

    A diffusion model for traffic data imputation,

    B. Lu, Q. Miao, Y . Liu, T. S. Tamir, H. Zhao, X. Zhang, Y . Lv, and F. Wang, “A diffusion model for traffic data imputation,”IEEE CAA J. Autom. Sinica, vol. 12, no. 3, pp. 606–617, 2025

    2025

  10. [18]

    Conditional information bottleneck approach for time series imputation,

    M. Choi and C. Lee, “Conditional information bottleneck approach for time series imputation,” inInt. Conf. Learn. Represent. (ICLR), 2024

    2024

  11. [19]

    CSDI: conditional score- based diffusion models for probabilistic time series imputation,

    Y . Tashiro, J. Song, Y . Song, and S. Ermon, “CSDI: conditional score- based diffusion models for probabilistic time series imputation,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2021, pp. 24 804–24 816

    2021

  12. [20]

    MTSCI: A conditional diffusion model for multivariate time series consistent imputation,

    J. Zhou, J. Li, G. Zheng, X. Wang, and C. Zhou, “MTSCI: A conditional diffusion model for multivariate time series consistent imputation,” in Proc. ACM Int. Conf. Inf. Knowl. Manag. (CIKM), 2024, pp. 3474–3483

    2024

  13. [21]

    Provably convergent schr ¨odinger bridge with applications to probabilistic time series imputation,

    Y . Chen, W. Deng, S. Fang, F. Li, N. T. Yang, Y . Zhang, K. Rasul, S. Zhe, A. Schneider, and Y . Nevmyvaka, “Provably convergent schr ¨odinger bridge with applications to probabilistic time series imputation,” inProc. Int. Conf. Mach. Learn. (ICML), vol. 202, 2023, pp. 4485–4513

    2023

  14. [22]

    Frequency-aware generative models for multivariate time series imputation,

    X. Yang, Y . Sun, X. Yuan, and X. Chen, “Frequency-aware generative models for multivariate time series imputation,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2024

    2024

  15. [23]

    Optimal transport for time series imputation,

    H. Wang, H. Li, X. Chen, M. Gong, Z. Chenet al., “Optimal transport for time series imputation,” inInt. Conf. Learn. Represent. (ICLR), 2025

    2025

  16. [24]

    Tslanet: Rethinking transformers for time series representation learning,

    E. Eldele, M. Ragab, Z. Chen, M. Wu, and X. Li, “Tslanet: Rethinking transformers for time series representation learning,” inProc. Int. Conf. Mach. Learn. (ICML), 2024

    2024

  17. [25]

    Rethinking fourier transform from A basis functions perspective for long-term time series forecasting,

    R. Yang, L. Cao, J. Yang, and J. Li, “Rethinking fourier transform from A basis functions perspective for long-term time series forecasting,” in Adv. Neural Inf. Process. Syst. (NeurIPS), 2024

    2024

  18. [26]

    An algorithm for the machine calculation of complex fourier series,

    J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex fourier series,”Math. Comput., vol. 19, pp. 297–301, 1965

    1965

  19. [27]

    Depthwise spatio-temporal STFT convolutional neural networks for human action recognition,

    S. Kumawat, M. Verma, Y . Nakashima, and S. Raman, “Depthwise spatio-temporal STFT convolutional neural networks for human action recognition,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 44, no. 9, pp. 4839–4851, 2022

    2022

  20. [28]

    Synchrosqueezing-based short-time fractional fourier transform,

    Z. Zhao and G. Li, “Synchrosqueezing-based short-time fractional fourier transform,”IEEE Trans. Signal Process., vol. 71, pp. 279–294, 2023

    2023

  21. [29]

    Time series analysis: Forecasting and control,

    G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, “Time series analysis: Forecasting and control,”The Statistician, vol. 27, pp. 265–265, 1978

    1978

  22. [30]

    Improving artificial neural networks’ performance in seasonal time series forecasting,

    C. Hamzac ¸ebi, “Improving artificial neural networks’ performance in seasonal time series forecasting,”Inf. Sci., vol. 178, no. 23, pp. 4550– 4559, 2008

    2008

  23. [31]

    Mice: Multivariate imputation by chained equations in r,

    S. van Buuren and K. G. M. Groothuis-Oudshoorn, “Mice: Multivariate imputation by chained equations in r,”J. Stat. Softw., vol. 45, pp. 1–67, 2011

    2011

  24. [32]

    A novel purity-based k nearest neighbors imputation method and its application in financial distress prediction,

    C. Cheng, C. Chan, and Y . Sheu, “A novel purity-based k nearest neighbors imputation method and its application in financial distress prediction,”Eng. Appl. Artif. Intell., vol. 81, pp. 283–299, 2019

    2019

  25. [33]

    A hybrid method for imputation of missing values using optimized fuzzy c-means with support vector regression and a genetic algorithm,

    I. B. Aydilek and A. Arslan, “A hybrid method for imputation of missing values using optimized fuzzy c-means with support vector regression and a genetic algorithm,”Inf. Sci., vol. 233, pp. 25–35, 2013

    2013

  26. [34]

    Missforest - non-parametric missing value imputation for mixed-type data,

    D. J. Stekhoven and P. B ¨uhlmann, “Missforest - non-parametric missing value imputation for mixed-type data,”Bioinform., vol. 28, no. 1, pp. 112–118, 2012

    2012

  27. [35]

    Deep learning for multivariate time series imputation: A survey,

    J. Wang, W. Du, W. Cao, K. Zhang, W. Wang, Y . Liang, and Q. Wen, “Deep learning for multivariate time series imputation: A survey,”CoRR, vol. abs/2402.04059, 2024

    2024 arXiv

  28. [36]

    Estimating missing data in temporal data streams using multi-directional recurrent neural networks,

    J. Yoon, W. R. Zame, and M. van der Schaar, “Estimating missing data in temporal data streams using multi-directional recurrent neural networks,” IEEE Trans. Biomed. Eng., vol. 66, no. 5, pp. 1477–1490, 2019

    2019

  29. [37]

    BRITS: bidirectional recurrent imputation for time series,

    W. Cao, D. Wang, J. Li, H. Zhou, L. Li, and Y . Li, “BRITS: bidirectional recurrent imputation for time series,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2018, pp. 6776–6786

    2018

  30. [38]

    Multivariate time series imputation with generative adversarial networks,

    Y . Luo, X. Cai, Y . Zhang, J. Xu, and X. Yuan, “Multivariate time series imputation with generative adversarial networks,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2018, pp. 1603–1614

    2018

  31. [39]

    Mind the gap: An experimental evaluation of imputation of missing values techniques in time series,

    M. Khayati, A. Lerner, Z. Tymchenko, and P. Cudr ´e-Mauroux, “Mind the gap: An experimental evaluation of imputation of missing values techniques in time series,”Proc. VLDB Endow., vol. 13, no. 5, pp. 768– 782, 2020

    2020

  32. [40]

    GP-V AE: deep probabilistic time series imputation,

    V . Fortuin, D. Baranchuk, G. R ¨atsch, and S. Mandt, “GP-V AE: deep probabilistic time series imputation,” inInt. Conf. Artif. Intell. Stat. (AISTATS), vol. 108, 2020, pp. 1651–1661

    2020

  33. [41]

    Graph wavenet for deep spatial-temporal graph modeling,

    Z. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang, “Graph wavenet for deep spatial-temporal graph modeling,” inProc. Int. Joint Conf. Artif. Intell. (IJCAI), 2019, pp. 1907–1913

    2019

  34. [42]

    Missing value imputation on multidimensional time series,

    P. Bansal, P. Deshpande, and S. Sarawagi, “Missing value imputation on multidimensional time series,”Proc. VLDB Endow., vol. 14, no. 11, pp. 2533–2545, 2021

    2021

  35. [43]

    Filling the g ap s: Multivariate time series imputation by graph neural networks,

    A. Cini, I. Marisca, and C. Alippi, “Filling the g ap s: Multivariate time series imputation by graph neural networks,” inInt. Conf. Learn. Represent. (ICLR), 2022

    2022

  36. [44]

    Learning to reconstruct missing data from spatiotemporal graphs with sparse observations,

    I. Marisca, A. Cini, and C. Alippi, “Learning to reconstruct missing data from spatiotemporal graphs with sparse observations,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2022

    2022

  37. [45]

    Attention is all you need,

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, “Attention is all you need,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2017, pp. 5998–6008

    2017

  38. [46]

    Transformers in time series: A survey,

    Q. Wen, T. Zhou, C. Zhang, W. Chen, Z. Ma, J. Yan, and L. Sun, “Transformers in time series: A survey,” inProc. Int. Joint Conf. Artif. Intell. (IJCAI), 2023, pp. 6778–6786

    2023

  39. [47]

    Multivariate time-series imputation with disentangled temporal representations,

    S. Liu, X. Li, G. Cong, Y . Chen, and Y . Jiang, “Multivariate time-series imputation with disentangled temporal representations,” inInt. Conf. Learn. Represent. (ICLR), 2023

    2023

  40. [48]

    Imputeformer: Low rankness-induced transformers for generalizable spatiotemporal impu- tation,

    T. Nie, G. Qin, W. Ma, Y . Mei, and J. Sun, “Imputeformer: Low rankness-induced transformers for generalizable spatiotemporal impu- tation,” inProc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. (KDD), 2024, pp. 2260–2271

    2024

  41. [49]

    Causality-aware spatiotemporal graph neural networks for spatiotemporal time series imputation,

    B. Jing, D. Zhou, K. Ren, and C. Yang, “Causality-aware spatiotemporal graph neural networks for spatiotemporal time series imputation,” in Proc. ACM Int. Conf. Inf. Knowl. Manag. (CIKM), 2024, pp. 1027– 1037

    2024

  42. [50]

    Higher-order spatio- temporal physics-incorporated graph neural network for multivariate time series imputation,

    G. Liang, P. Tiwari, S. Nowaczyk, and S. Byttner, “Higher-order spatio- temporal physics-incorporated graph neural network for multivariate time series imputation,” inProc. ACM Int. Conf. Inf. Knowl. Manag. (CIKM), 2024, pp. 1356–1366

    2024

  43. [51]

    An observed value consistent diffusion model for imputing missing values in multivariate time series,

    X. Wang, H. Zhang, P. Wang, Y . Zhang, B. Wang, Z. Zhou, and Y . Wang, “An observed value consistent diffusion model for imputing missing values in multivariate time series,” inProc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. (KDD), 2023, pp. 2409–2418

    2023

  44. [52]

    Diffusion-ts: Interpretable diffusion for general time series generation,

    X. Yuan and Y . Qiao, “Diffusion-ts: Interpretable diffusion for general time series generation,” inInt. Conf. Learn. Represent. (ICLR), 2024

    2024

  45. [53]

    Pristi: A conditional diffusion framework for spatiotemporal imputation,

    M. Liu, H. Huang, H. Feng, L. Sun, B. Du, and Y . Fu, “Pristi: A conditional diffusion framework for spatiotemporal imputation,” inIEEE Int. Conf. Data Eng. (ICDE), 2023, pp. 1927–1939

    2023

  46. [54]

    Uncertainty-aware variational- recurrent imputation network for clinical time series,

    A. W. Mulyadi, E. Jun, and H. Suk, “Uncertainty-aware variational- recurrent imputation network for clinical time series,”IEEE Trans. Cybern., vol. 52, no. 9, pp. 9684–9694, 2022

    2022

  47. [55]

    Probabilistic imputation for time-series classification with missing data,

    S. Kim, H. Kim, E. Yun, H. Lee, J. Lee, and J. Lee, “Probabilistic imputation for time-series classification with missing data,” inProc. Int. Conf. Mach. Learn. (ICML), vol. 202, 2023, pp. 16 654–16 667

    2023

  48. [56]

    NAOMI: non- autoregressive multiresolution sequence imputation,

    Y . Liu, R. Yu, S. Zheng, E. Zhan, and Y . Yue, “NAOMI: non- autoregressive multiresolution sequence imputation,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2019, pp. 11 236–11 246. 15

    2019

  49. [57]

    Generative semi- supervised learning for multivariate time series imputation,

    X. Miao, Y . Wu, J. Wang, Y . Gao, X. Mao, and J. Yin, “Generative semi- supervised learning for multivariate time series imputation,” inAAAI Conf. Artif. Intell. (AAAI), 2021, pp. 8983–8991

    2021

  50. [58]

    A survey on diffusion models for time series and spatio-temporal data,

    Y . Yang, M. Jin, H. Wen, C. Zhang, Y . Liang, L. Ma, Y . Wang, C. Liu, B. Yang, Z. Xu, J. Bian, S. Pan, and Q. Wen, “A survey on diffusion models for time series and spatio-temporal data,”CoRR, vol. abs/2404.18886, 2024

    2024

  51. [59]

    Diffusion-based time series impu- tation and forecasting with structured state space models,

    J. M. L. Alcaraz and N. Strodthoff, “Diffusion-based time series impu- tation and forecasting with structured state space models,”Trans. Mach. Learn. Res., vol. 2023, 2023

    2023

  52. [60]

    SADI: similarity-aware diffusion model-based imputation for incomplete temporal EHR data,

    Z. Dai, E. J. Getzen, and Q. Long, “SADI: similarity-aware diffusion model-based imputation for incomplete temporal EHR data,” inInt. Conf. Artif. Intell. Stat. (AISTATS), vol. 238, 2024, pp. 4195–4203

    2024

  53. [61]

    A unified approach to short-time fourier analysis and synthesis,

    J. B. Allen and L. R. Rabiner, “A unified approach to short-time fourier analysis and synthesis,”Proc. IEEE, vol. 65, no. 11, pp. 1558–1564, 1977

    1977

  54. [62]

    Novel short-time fractional fourier transform: Theory, implementation, and applications,

    J. Shi, J. Zheng, X. Liu, W. Xiang, and Q. Zhang, “Novel short-time fractional fourier transform: Theory, implementation, and applications,” IEEE Trans. Signal Process., vol. 68, pp. 3280–3295, 2020

    2020

  55. [63]

    The fractional order fourier transform and its application to quantum mechanics,

    V . Namias, “The fractional order fourier transform and its application to quantum mechanics,”IMA J. Appl. Math., vol. 25, no. 3, pp. 241–265, 1980

    1980

  56. [64]

    Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool,

    I. Daubechies, J. Lu, and H. Wu, “Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool,”Appl. Comput. Harmon. Anal., vol. 30, no. 2, pp. 243–261, 2011

    2011

  57. [65]

    Deep unsupervised learning using nonequilibrium thermodynamics,

    J. Sohl-Dickstein, E. A. Weiss, N. Maheswaranathan, and S. Ganguli, “Deep unsupervised learning using nonequilibrium thermodynamics,” in Proc. Int. Conf. Mach. Learn. (ICML), vol. 37, 2015, pp. 2256–2265

    2015

  58. [66]

    Denoising diffusion probabilistic models,

    J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” inAdv. Neural Inf. Process. Syst. (NeurIPS), 2020

    2020

  59. [67]

    Informer: Beyond efficient transformer for long sequence time-series forecasting,

    H. Zhou, S. Zhang, J. Peng, S. Zhang, J. Li, H. Xiong, and W. Zhang, “Informer: Beyond efficient transformer for long sequence time-series forecasting,” inAAAI Conf. Artif. Intell. (AAAI), 2021, pp. 11 106– 11 115

    2021

  60. [68]

    Diffusion convolutional recurrent neural network: Data-driven traffic forecasting,

    Y . Li, R. Yu, C. Shahabi, and Y . Liu, “Diffusion convolutional recurrent neural network: Data-driven traffic forecasting,” inInt. Conf. Learn. Represent. (ICLR), 2018

    2018

  61. [69]

    Deep model predictive control of gene expression in thousands of single cells,

    J.-B. Lugagne, C. M. Blassick, and M. J. Dunlop, “Deep model predictive control of gene expression in thousands of single cells,”Nat. Commun., vol. 15, no. 1, p. 2148, 2024

    2024

  62. [70]

    Another look at measures of forecast accuracy,

    R. J. Hyndman and A. B. Koehler, “Another look at measures of forecast accuracy,”Int. J. Forecast., vol. 22, no. 4, pp. 679–688, 2006

    2006

  63. [71]

    Accuracy measures: theoretical and practical concerns,

    S. Makridakis, “Accuracy measures: theoretical and practical concerns,” Int. J. Forecast., vol. 9, no. 4, pp. 527–529, 1993

    1993

  64. [72]

    Strictly proper scoring rules, prediction, and estimation,

    T. Gneiting and A. E. Raftery, “Strictly proper scoring rules, prediction, and estimation,”J. Am. Stat. Assoc., vol. 102, no. 477, pp. 359–378, 2007

    2007

  65. [73]

    Timemixer: Decomposable multiscale mixing for time series forecasting,

    S. Wang, H. Wu, X. Shi, T. Hu, H. Luo, L. Ma, J. Y . Zhang, and J. Zhou, “Timemixer: Decomposable multiscale mixing for time series forecasting,” inInt. Conf. Learn. Represent. (ICLR), 2024

    2024

  66. [74]

    Timemixer++: A general time series pattern machine for universal predictive analysis,

    S. Wang, J. Li, X. Shi, Z. Ye, B. Mo, W. Lin, S. Ju, Z. Chu, and M. Jin, “Timemixer++: A general time series pattern machine for universal predictive analysis,” inInt. Conf. Learn. Represent. (ICLR), 2025

    2025

Pith tools

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