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REVIEW 4 major objections 5 minor 69 references

Load Forecasting on A Highly Sparse Electrical Load Dataset Using Gaussian Interpolation

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Gaussian imputation lets a 62%-sparse load record train a usable LSTM forecaster.

desk verdict Circular evaluation sinks the paper: the BUET test 'actuals' are Gaussian samples from the same per-hour distributions used for training, so the reported MAPE measures fit to the imputation rule, not forecasting skill. read the letter →

arxiv 2508.14069 v1 pith:WZQS4O5J submitted 2025-08-12 cs.LG eess.SP

Chinmoy Biswas , Nafis Faisal , Vivek Chowdhury , Abrar Al-Shadid Abir , Sabir Mahmud , Mithon Rahman , Shaikh Anowarul Fattah , Hafiz Imtiaz This is my paper · ORCID
classification cs.LGeess.SP
keywords loadforecastingsparsityGaussianinterpolationLSTMBiTransformerwide-sensestationarymissingdataimputation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether a real hourly electrical load record with about 62% of entries missing can still be used for load forecasting. The answer it defends is yes: if the series is treated as wide-sense stationary at the hourly scale, each hour's missing values can be imputed by sampling from a Gaussian whose mean and variance are estimated from the values that were observed. After that imputation, an LSTM network forecasts the completed series with roughly 10.7% mean absolute percentage error, better than nine alternative forecasting models. The authors conclude that Gaussian interpolation is a workable option for sparse, mildly non-stationary load data.

What carries the argument

The load-bearing mechanism is hourly Gaussian imputation: for each hour of the day at which the plant operates, estimate $\mu$ and $\sigma$ from the existing load values for that hour, then fill every missing entry by drawing $X = \mu + \sigma Z$ with $Z \sim \mathcal{N}(0,1)$, clipping samples above the plant's generating capacity to that capacity and negative samples to zero. This single rule produces the complete series on which all ten forecasters are trained and scored, so the reported accuracy numbers are accuracy on the imputed record, not on the original sparse record.

What would settle it

Hold out a random subset of originally observed hours before imputation, train the LSTM exactly as in the paper, and score it only on those held-out observed hours; if the MAPE on genuinely observed load departs substantially from 10.67%, the published figure is an artifact of the Gaussian imputation. A second check is to refit the same pipeline on a complete real load record from the same plant and ask whether forecasts of true future hours reach comparable error.

Watch

Extended reading notes

Core claim

The paper's central claim is that per-hour Gaussian imputation converts a record that is roughly 62% empty into a series on which standard load forecasters train successfully, provided one accepts the data as wide-sense stationary within each hour. The empirical core is a model comparison on the interpolated series: LSTM reaches 10.67% MAPE, ahead of Transformer (11.02%), BiLSTM and DLinear (13.13%), Random Forest (14.56%), Prophet (17.73%), XGBoost (18.11%), and SARIMA (20.40%). The same LSTM on a dense public hourly load benchmark yields 1.55% MAPE, which the authors read as confirming that the interpolation, rather than the model choice, dominates the error on the sparse campus data.

Load-bearing premise

The load-bearing premise is that each missing load value can be modeled as an independent draw from a per-hour Gaussian whose mean and variance come from the observed hours, with those synthetic draws then treated as ground truth for training and scoring forecasters; the paper's own stationarity test rejects stationarity and its chi-squared test rejects Gaussianity, so if missing periods follow different dynamics or retain temporal autocorrelation, the reported errors measure fit to the imputation rule rather than fit to real load.

Editorial extensions

If this is right

  • A roughly 62%-sparse hourly load record can be made trainable for short-horizon forecasting by per-hour Gaussian imputation, with no strict stationarity required.
  • On the imputed series, recurrent architectures, especially LSTM, outperform classical statistical, tree, and shallow-linear baselines, so sequence structure carries most of the predictive signal.
  • The large gap between the sparse-campus error (10.67% MAPE) and the dense-benchmark error (1.55% MAPE) implies that interpolation quality, not model family, dominates the forecasting error.
  • The completed series shows high autocorrelation over long lags, so the forecasting models learn from smooth, synthetic structure rather than from a naturally dense record.

Reading between the lines

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

  • Editorial inference: the method would be tested more honestly by holding out originally observed hours and ignoring imputed entries when computing error; the current protocol cannot separate skill at forecasting real load from skill at reproducing Gaussian draws.
  • Editorial inference: the approach transfers naturally to other sparse infrastructure time series such as water, gas, or traffic demand, where gaps are also non-random and the same synthetic-fit risk would appear.
  • Editorial inference: when imputation is misspecified, comparing models on the imputed series ranks their ability to track the imputation rule rather than their ability to track true load, so model rankings should be re-verified on dense data.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a Gaussian-interpolation approach for an hourly electrical load dataset of the BUET campus that is approximately 62% missing. Missing values are imputed by fitting a per-hour Gaussian distribution to the observed values and sampling from it, with samples clipped to [0, 2000] kW. The completed series is used to train and evaluate LSTM, BiLSTM, CNN-LSTM, CNN-BiLSTM, Transformer, Prophet, DLinear, SARIMA, XGBoost, and Random Forest models, with LSTM reported as best at 10.67% MAPE. The authors also train the LSTM on the complete Dayton dataset and report 1.55% MAPE, and conclude that Gaussian interpolation is suitable for load forecasting on sparse data.

Significance. If the reported results were valid, the paper would offer a practical route to forecasting from very sparse load data, and the broad model comparison would be a useful reference. The paper is clearly organized and states its imputation procedure and statistical tests explicitly. However, the central evaluation does not support the claims: the test set on the BUET data consists mainly of synthetic draws generated by the same per-hour Gaussian model used to create the training targets, so the reported MAPE values measure agreement with the imputation rule rather than forecasting skill. The internal stationarity and normality tests contradict the assumptions used to justify the imputation, and the Dayton experiment does not validate the imputation method. The headline conclusion therefore rests on circular evidence.

major comments (4)
  1. [2.2-2.3] The evaluation protocol in Sections 2.2 and 2.3 is circular. Section 2.2 fills every missing hour by sampling X = mu_h + sigma_h Z, where (mu_h, sigma_h) are estimated from the observed values; Section 2.3 then splits the completed dataset into training, validation, and test sets. Because the 'actual' values in the test set are synthetic draws from the same per-hour distributions that generated the training labels, a model that learns the hourly conditional mean will achieve low MAPE without any real forecasting ability. The paper never reports performance restricted to the originally observed test hours, so the 10.67% MAPE in Section 3.4 cannot be interpreted as load-forecasting accuracy.
  2. [Section 3.1] The statistical evidence reported in Section 3.1 contradicts the WSS/Gaussian assumptions that motivate the imputation. The KPSS test returns p<0.05, rejecting stationarity, which is incompatible with the WSS assumption invoked in Section 2.2; the chi-squared test rejects Gaussianity, and the appeal to the Central Limit Theorem is not justified for a strongly autocorrelated, non-identically distributed series (Fig. 3). The paper states these results but does not resolve the inconsistency before using the Gaussian-imputed data as ground truth.
  3. [Section 3.7] The Dayton experiment in Section 3.7 does not validate the interpolation method. The 1.55% MAPE is obtained on a completely observed dataset and therefore provides no evidence about Gaussian imputation on the sparse BUET data. The statement that this result 'validates our approach' (Section 3.7) overstates what the experiment can show.
  4. [Section 2.2] No comparison is made with alternative imputation methods under the same forecasting protocol. Section 2.2 asserts that linear, polynomial, or spline interpolation 'could not be used', but no experiments support this claim; without baselines such as linear interpolation, splines, KNN, or MICE, the paper's conclusion that Gaussian interpolation is 'suitable' is not supported.
minor comments (5)
  1. [Equation (3)] MAPE is undefined when y_i = 0, which can occur after clipping negative samples to zero in Section 2.2; the authors should specify how such cases are handled in the error computation.
  2. [Section 2.2] The paper uses WSS to justify per-hour Gaussian parameters, but WSS requires time-invariant mean and autocovariance; per-hour varying (mu_h, sigma_h) is better described as a periodic or cyclostationary assumption, and this distinction should be clarified.
  3. [Section 3.7] Section 3.7 reports MAE as '31.06%' without units; MAE for load data should be expressed in kW or as a percentage only if clearly defined.
  4. [Section 2] The 'supplementary section S1' referenced at the start of Section 2 is not included in the submitted manuscript; either provide the supplementary material or remove the reference.
  5. [Figure 2] Figure 2 is schematic and the caption does not describe the workflow shown; a short explanation in the caption or text would improve readability.

Circularity Check

1 steps flagged · score 8.0 of 10

Test-set 'actuals' are synthetic draws from the same per-hour Gaussian imputation used to build the training targets, so the headline 10.67% MAPE measures fit to the imputation rule, not real load.

  1. fitted input called prediction [Section 2.2 (Interpolation of Missing Data), Section 2.3 (Model Training), and Section 3.4 (Performance of RNN-based Models)]
    "we propose to impute the missing data-points by estimating a Gaussian probability density function (PDF) from the existing data-points, and then sampling from the PDF. ... We emphasize that the Gaussian PDF for each hour is different with different(µ,σ ), since we assume that the load data is WSS. ... The dataset was partitioned such that 66% of the samples were used for training, while the remaining portion were reserved for validation and testing purposes."

    The per-hour Gaussian parameters (µ,σ) are fitted to the observed load values, and the missing values are filled by sampling from those fitted distributions. Because this imputation is done before the train/validation/test split, the test-set 'actuals' are largely synthetic draws from the very same fitted distributions that generated the training targets. Evaluating forecasters with MAPE against those synthetic values (Section 3.4, 10.67% for LSTM) therefore measures how well each model reproduces the Gaussian imputation rule, not how well it predicts real load. A model that simply predicts each hour's fitted mean would score well by construction.

full rationale

The central claim — that Gaussian interpolation is suitable for load forecasting on the 62.45%-sparse BUET dataset — rests on forecast errors computed against a test set that was itself produced by the imputation procedure under evaluation. Section 2.2 estimates a per-hour Gaussian PDF from observed data and samples missing points from it; Section 2.3 partitions the imputed dataset into training, validation, and test splits. Since the split occurs after imputation, the test 'actuals' are outputs of the same fitted per-hour Gaussian model that created the training targets. The reported MAPE values (e.g., LSTM 10.67%, Section 3.4) are thus a measure of fit to the imputation rule, not of predictive accuracy on real load. The Dayton experiment (Section 3.7) is externally grounded and shows that LSTM can forecast clean hourly load data well, but it does not validate the Gaussian imputation method or the sparse-data claim. In addition, the paper's own statistical tests undermine the assumptions on which the imputation rests: Section 3.1 reports that the KPSS test rejects stationarity (contradicting the WSS assumption) and that the chi-squared test rejects Gaussianity, yet the paper invokes the Central Limit Theorem to treat the distribution as Gaussian. These are correctness and validity concerns independent of circularity, but they compound the evaluation problem because the imputation distribution is both contradicted by the data and used to generate the test targets. No separate observed-hours-only benchmark is reported, so the headline result cannot be separated from the fitted imputation process. Score 8 reflects that the central claim reduces, by construction, to consistency with the paper's own interpolation rule.

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

The central claim rests on per-hour Gaussian means and variances fitted from the observed data, the WSS assumption, and the assumption that missing values can be treated as independent Gaussian draws. The paper's own statistical tests contradict the WSS and Gaussianity assumptions, and no independent evidence supports the representativeness of the observed 16-hours-per-day values for the missing hours. No invented entities are introduced.

free parameters (3)
  • per-hour Gaussian mean mu_h = estimated from observed data for each hour
    Used to sample missing load values in Section 2.2; the forecast errors depend entirely on these fitted means.
  • per-hour Gaussian variance sigma_h^2 = estimated from observed data for each hour
    Controls the spread of imputed values; the reported MAPE partly measures this noise.
  • clipping bounds (0, 2000 kW) = 0 and 2000
    Imposed in Section 2.2 based on plant capacity; choice affects the imputed distribution.
assumptions (4)
  • domain assumption The load data is wide-sense stationary (WSS)
    Stated in Abstract and Section 2.2; used to justify estimating one Gaussian per hour and pooling across years. Contradicted by the paper's own KPSS test rejecting stationarity and by the non-stationary trend in Figure 4.
  • ad hoc to paper Per-hour load values follow a Gaussian distribution
    Used to define the imputation model in Section 2.2; the chi-squared test in Section 3.1 rejects this, and CLT is invoked without justification for dependent data.
  • domain assumption Missing values are independent of neighboring values and of each other
    The imputation samples X = mu + sigma Z independently for each missing point in Section 2.2, ignoring temporal autocorrelation, which load data strongly exhibits.
  • ad hoc to paper Observed 16-hours-per-day values are representative of missing hours
    Missing hours include night and unrecorded periods; no evidence is given that their load distribution equals the observed day-time distribution.

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Cite this review

Pith. "Pith review of Load Forecasting on A Highly Sparse Electrical Load Dataset Using Gaussian Interpolation." pith.science (2026). https://pith.science/paper/WZQS4O5J

@misc{pith2026250814069,
  author       = {Pith},
  title        = {Pith review of: Load Forecasting on A Highly Sparse Electrical Load Dataset Using Gaussian Interpolation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WZQS4O5J}},
  note         = {Machine review of arXiv:2508.14069}
}
read the original abstract

Sparsity, defined as the presence of missing or zero values in a dataset, often poses a major challenge while operating on real-life datasets. Sparsity in features or target data of the training dataset can be handled using various interpolation methods, such as linear or polynomial interpolation, spline, moving average, or can be simply imputed. Interpolation methods usually perform well with Strict Sense Stationary (SSS) data. In this study, we show that an approximately 62\% sparse dataset with hourly load data of a power plant can be utilized for load forecasting assuming the data is Wide Sense Stationary (WSS), if augmented with Gaussian interpolation. More specifically, we perform statistical analysis on the data, and train multiple machine learning and deep learning models on the dataset. By comparing the performance of these models, we empirically demonstrate that Gaussian interpolation is a suitable option for dealing with load forecasting problems. Additionally, we demonstrate that Long Short-term Memory (LSTM)-based neural network model offers the best performance among a diverse set of classical and neural network-based models.

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Works this paper leans on

69 extracted references · 42 canonical work pages

  1. [1]

    Palanivinayagam, R

    A. Palanivinayagam, R. Damaševičius, Effective handling of missing values in datasets for classification using machine learning methods, Information 14 (2) (2023). doi:10.3390/info14020092

    work page doi:10.3390/info14020092 2023

  2. [2]

    A. N. Gorban, I. Y. Tyukin, Blessing of dimensionality: mathematical founda- tions of the statistical physics of data, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2118) (2018) 20170237. doi:10.1098/rsta.2017.0237

    arXiv 2018

  3. [3]

    Fefferman, S

    C. Fefferman, S. Mitter, H. Narayanan, Testing the manifold hypothesis, Jour- nal of the American Mathematical Society 29 (4) (2016) 983–1049. doi: 10.1090/jams/852

    doi:10.1090/jams/852 2016

  4. [4]

    D. L. Donoho, Compressed sensing, IEEE Transactions on information theory 52 (4) (2006) 1289–1306.doi:10.1109/TIT.2006.871582

    arXiv 2006

  5. [5]

    E. J. Candès, J. Romberg, T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transac- tions on information theory 52 (2) (2006) 489–509.doi:10.1109/TIT.2005. 862083

    doi:10.1109/tit.2005 2006

  6. [6]

    D. W. Bunn, Short-term forecasting: A review of procedures in the electricity supply industry, The Journal of the Operational Research Society 33 (6) (1982) 533–545. doi:10.2307/2581037

    work page doi:10.2307/2581037 1982

  7. [7]

    C. Xu, Q. Li, T. Xiao, Y. Zhang, W. Zhou, H. Liu, Deep learning-based post- disaster energy management and faster network reconfiguration method for 15 improvement of restoration time, Electric Power Systems Research 238 (2025) 111081

    work page 2025

  8. [8]

    Haida, S

    T. Haida, S. Muto, Regression based peak load forecasting using a transforma- tion technique (1994).doi:10.1109/59.331433

    work page doi:10.1109/59.331433 1994

Show all 69 references
  1. [9]

    M. R. Dehbozorgi, M. Rastegar, et al., A deep learning deviation-based scheme to defend against false data injection attacks in power distribution systems, Electric Power Systems Research 238 (2025) 111076

    2025

  2. [10]

    X. He, W. Zhao, Z. Gao, L. Zhang, Q. Zhang, X. Li, Short-term load fore- casting by gru neural network and ddpg algorithm for adaptive optimization of hyperparameters, Electric Power Systems Research 238 (2025) 111119

    2025

  3. [11]

    A. K. Singh, Ibraheem, S. Khatoon, M. Muazzam, D. K. Chaturvedi, Load forecasting techniques and methodologies: A review, 2012 2nd International Conference on Power, Control and Embedded Systems (2012) 1–10doi:10. 1109/ICPCES.2012.6508132

    2012

  4. [12]

    Papalexopoulos, T

    A. Papalexopoulos, T. Hesterberg, A regression-based approach to short-term system load forecasting, in: Conference Papers Power Industry Computer Ap- plication Conference, 1989, pp. 414–423.doi:10.1109/PICA.1989.39025

    1989

  5. [13]

    W. R. Christiaanse, Short-term load forecasting using general exponential smoothing, IEEE Transactions on Power Apparatus and Systems PAS-90 (2) (1971) 900–911. doi:10.1109/TPAS.1971.293123

    1971

  6. [14]

    Masters, Neural, Novel and Hybrid Algorithms for Time Series Prediction, 1st Edition, John Wiley & Sons, Inc., USA, 1995.doi:10.5555/526065

    T. Masters, Neural, Novel and Hybrid Algorithms for Time Series Prediction, 1st Edition, John Wiley & Sons, Inc., USA, 1995.doi:10.5555/526065

    1995 doi

  7. [15]

    H. J. Sadaei, P. C. de Lima e Silva, F. G. Guimarães, M. H. Lee, Short-term load forecasting by using a combined method of convolutional neural networks and fuzzy time series, Energy 175 (2019) 365–377. doi:10.1016/j.energy. 2019.03.081

    2019 doi

  8. [16]

    Priyadarsini, N

    M. Priyadarsini, N. Sonekar, A cnn-based approach for anomaly detection in smart grid systems, Electric Power Systems Research 238 (2025) 111077. 16

    2025

  9. [17]

    A. O. Aseeri, Effective rnn-based forecasting methodology design for improving short-term power load forecasts: Application to large-scale power-grid time series, Journal of Computational Science 68 (2023) 101984.doi:10.1016/j. jocs.2023.101984

    2023

  10. [18]

    C. Li, Q. Guo, L. Shao, J. Li, H. Wu, Research on short-term load forecasting based on optimized gru neural network, Electronics 11 (22) (2022).doi:10. 3390/electronics11223834

    2022

  11. [19]

    P. Fan, D. Wang, W. Wang, X. Zhang, Y. Sun, A novel multi-energy load forecasting method based on building flexibility feature recognition technology and multi-task learning model integrating lstm, Energy 308 (2024) 132976. doi:10.1016/j.energy.2024.132976

    2024

  12. [20]

    Tulensalo, J

    J. Tulensalo, J. Seppänen, A. Ilin, An lstm model for power grid loss prediction, Electric Power Systems Research 189 (2020) 106823

    2020

  13. [21]

    Rosseel, B

    A. Rosseel, B. B. Zad, F. Vallée, Z. De Grève, Physics-informed machine learn- ing for forecasting power exchanges at the interface between transmission and distribution systems, Electric Power Systems Research 238 (2025) 111097

    2025

  14. [22]

    Huang, Missing data filling method based on linear interpolation and light- gbm, in: Journal of Physics: Conference Series, Vol

    G. Huang, Missing data filling method based on linear interpolation and light- gbm, in: Journal of Physics: Conference Series, Vol. 1754, IOP Publishing, 2021, p. 012187. doi:10.1088/1742-6596/1754/1/012187

    2021 doi

  15. [23]

    M. Noor, A. Yahaya, N. A. Ramli, A. M. Al Bakri, Filling missing data using interpolation methods: Study on the effect of fitting distribution, Key Engi- neering Materials 594 (2014) 889–895. doi:10.4028/www.scientific.net/ KEM.594-595.889

    2014 doi

  16. [24]

    W. R. Thompson, C. S. Weil, On the construction of tables for moving-average interpolation, Biometrics 8 (1) (1952) 51–54.doi:10.2307/3001525

    1952 doi

  17. [25]

    Gómez, A

    V. Gómez, A. Maravall, Estimation, prediction, and interpolation for nonsta- tionary series with the kalman filter, Journal of the American Statistical Asso- ciation 89 (426) (1994) 611–624.doi:10.2307/2290864. 17

    1994 doi

  18. [26]

    Z.Kai, W.Guanjun, J.Houzhong, T.Zhongyi, Nurbsinterpolationbasedonex- ponential smoothing forecasting, The International Journal of Advanced Manu- facturing Technology 39 (2008) 1190–1196.doi:10.1007/s00170-007-1297-0

    2008 doi

  19. [27]

    Wahba, Spline interpolation and smoothing on the sphere, SIAM Journal on Scientific and Statistical Computing 2 (1) (1981) 5–16.doi:10.1137/0902002

    G. Wahba, Spline interpolation and smoothing on the sphere, SIAM Journal on Scientific and Statistical Computing 2 (1) (1981) 5–16.doi:10.1137/0902002

    1981 doi

  20. [28]

    Rabbath, D

    C. Rabbath, D. Corriveau, A comparison of piecewise cubic hermite interpo- lating polynomials, cubic splines and piecewise linear functions for the approx- imation of projectile aerodynamics, Defence Technology 15 (5) (2019) 741–757. doi:10.1016/j.dt.2019.07.016

    2019 doi

  21. [29]

    Tjostheim, J

    D. Tjostheim, J. Thomas, Some properties and examples of random processes that are almost wide sense stationary, IEEE Transactions on Information The- ory 21 (3) (1975) 257–262.doi:10.1109/TIT.1975.1055385

    1975

  22. [30]

    Priestley, Power spectral analysis of non-stationary random processes, Jour- nal of Sound and Vibration 6 (1) (1967) 86–97.doi:10.1016/0022-460X(67) 90160-5

    M. Priestley, Power spectral analysis of non-stationary random processes, Jour- nal of Sound and Vibration 6 (1) (1967) 86–97.doi:10.1016/0022-460X(67) 90160-5

    1967 doi

  23. [31]

    Edition, A

    F. Edition, A. Papoulis, S. U. Pillai, Probability, random variables, and stochastic processes, McGraw-Hill Europe: New York, NY, USA, 2002.doi: 10.1109/TASSP.1985.1164715

    2002

  24. [32]

    T. C. Mills, T. C. Mills, Dealing with nonstationarity: Detrending, smoothing and differencing, The Foundations of Modern Time Series Analysis (2011) 261– 288doi:10.1057/9780230305021_10

    2011 doi

  25. [33]

    Dombi, A

    J. Dombi, A. Hussain, A new approach to fuzzy control using the distend- ing function, Journal of Process Control 86 (2020) 16–29. doi:10.1016/j. jprocont.2019.12.005

    2020 doi

  26. [34]

    Poulinakis, D

    K. Poulinakis, D. Drikakis, I. W. Kokkinakis, S. M. Spottswood, Machine- learning methods on noisy and sparse data, Mathematics 11 (1) (2023) 236. doi:10.3390/math11010236. 18

    2023 doi

  27. [38]

    Vaswani, Attention is all you need, Advances in Neural Information Process- ing Systems (2017)

    A. Vaswani, Attention is all you need, Advances in Neural Information Process- ing Systems (2017)

    2017

  28. [44]

    Aeronautics, S

    N. Aeronautics, S. A. N. L. R. C. L. P. of Worldwide Energy Re- source (POWER), Data access viewer (dav), accessed: Feb 10, 2023 (2023). 19

    2023

  29. [45]

    Molla, Pjm hourly energy consumption data, https://www.kaggle.com/ datasets/robikscube/hourly-energy-consumption/data (2018)

    R. Molla, Pjm hourly energy consumption data, https://www.kaggle.com/ datasets/robikscube/hourly-energy-consumption/data (2018)

    2018

  30. [46]

    Z. S. Priyambudi, Y. S. Nugroho, Which algorithm is better? an implemen- tation of normalization to predict student performance, in: AIP Conference Proceedings, Vol. 2926, AIP Publishing, 2024

    2024

  31. [47]

    J. R. Bence, Analysis of short time series: correcting for autocorrelation, Ecol- ogy 76 (2) (1995) 628–639.doi:10.2307/1941218

    1995 doi

  32. [48]

    C. Xu, M. Nayyeri, F. Alkhoury, H. S. Yazdi, J. Lehmann, Temporal knowledge graph embedding model based on additive time series decomposition, arXiv preprint arXiv:1911.07893 (2019). doi:10.48550/arXiv.1911.07893

    2019 doi arXiv

  33. [49]

    D. A. Dickey, W. A. Fuller, Distribution of the estimators for autoregressive time series with a unit root, Journal of the American statistical association 74 (366a) (1979) 427–431.doi:10.2307/2286348

    1979 doi

  34. [50]

    Kwiatkowski, P

    D. Kwiatkowski, P. C. Phillips, P. Schmidt, Y. Shin, Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?, Journal of econometrics 54 (1-3) (1992) 159–178

    1992

  35. [52]

    S. Ng, P. Perron, Unit root tests in arma models with data-dependent meth- ods for the selection of the truncation lag, Journal of the American Statistical Association 90 (429) (1995) 268–281.doi:10.1080/01621459.1995.10476510

    1995

  36. [53]

    S. R. Dubnicka, Kernel density estimation with missing data and auxiliary variables, Australian & New Zealand Journal of Statistics 51 (3) (2009) 247–

    2009

  37. [54]

    P. E. Greenwood, M. S. Nikulin, A guide to chi-squared testing, Vol. 280, John Wiley & Sons, 1996.doi:10.1080/00224065.1997.11979805. 20

    1996

  38. [55]

    R. M. Dudley, Uniform central limit theorems, Vol. 142, Cambridge university press, 2014. doi:10.1017/CBO9780511665622

    2014 doi

  39. [56]

    De Myttenaere, B

    A. De Myttenaere, B. Golden, B. Le Grand, F. Rossi, Mean absolute percentage error for regression models, Neurocomputing 192 (2016) 38–48

    2016

  40. [57]

    Giavarina, Understanding bland altman analysis, Biochemia medica 25 (2) (2015) 141–151

    D. Giavarina, Understanding bland altman analysis, Biochemia medica 25 (2) (2015) 141–151. doi:10.11613/BM.2015.015. 21

    2015 doi

  41. [59]

    Graves, J

    A. Graves, J. Schmidhuber, Framewise phoneme classification with bidirec- tional lstm and other neural network architectures, Neural Networks 18 (5) (2005) 602–610, iJCNN 2005. doi:https://doi.org/10.1016/j.neunet. 2005.06.042. URL https://www.sciencedirect.com/science/article...

    2005 doi

  42. [60]

    Huang, W

    Z. Huang, W. Xu, K. Yu, Bidirectional lstm-crf models for sequence tagging, arXiv preprint arXiv:1508.01991 (2015).doi:10.48550/arXiv.1508.01991

    2015 doi arXiv

  43. [61]

    Graves, S

    A. Graves, S. Fernández, J. Schmidhuber, Bidirectional lstm networks for im- proved phoneme classification and recognition, in: International conference on artificial neural networks, Springer, 2005, pp. 799–804

    2005

  44. [62]

    X. Shi, Z. Chen, H. Wang, D.-Y. Yeung, W. kin Wong, W. chun Woo, Convolu- tional lstm network: A machine learning approach for precipitation nowcasting (2015). arXiv:1506.04214. URL https://arxiv.org/abs/1506.04214

    2015 arXiv

  45. [63]

    W. Lu, J. Li, Y. Li, A. Sun, J. Wang, A cnn-lstm-based model to forecast stock prices, Complexity 2020 (1) (2020) 6622927.doi:10.1155/2020/6622927

    2020 doi

  46. [64]

    A. F. Agarap, Deep learning using rectified linear units (relu), arXiv preprint arXiv:1803.08375 (2018)

    2018 arXiv

  47. [65]

    W. Lu, J. Li, J. Wang, L. Qin, A cnn-bilstm-am method for stock price prediction, Neural Computing and Applications 33 (10) (2021) 4741–4753. doi:10.1007/s00521-020-05532-z

    2021 doi

  48. [66]

    Huang, M

    Z. Huang, M. Liang, J. Qin, S. Zhong, L. Lin, Understanding self- attention mechanism via dynamical system perspective, in: Proceedings of the IEEE/CVFInternationalConferenceonComputerVision, 2023, pp.1412–1422

    2023

  49. [67]

    Vaswani, Attention is all you need, Advances in Neural Information Process- ing Systems (2017)

    A. Vaswani, Attention is all you need, Advances in Neural Information Process- ing Systems (2017). 35

    2017

  50. [68]

    Cordonnier, A

    J.-B. Cordonnier, A. Loukas, M. Jaggi, Multi-head attention: Collaborate in- stead of concatenate, arXiv preprint arXiv:2006.16362 (2020)

    2020 arXiv

  51. [69]

    B. K. Jha, S. Pande, Time series forecasting model for supermarket sales using fb-prophet, in: 2021 5th International Conference on Computing Methodolo- gies and Communication (ICCMC), IEEE, 2021, pp. 547–554.doi:10.1109/ ICCMC51019.2021.9418033

    2021

  52. [70]

    A. Zeng, M. Chen, L. Zhang, Q. Xu, Are transformers effective for time series forecasting?, in: Proceedings of the AAAI conference on artificial intelligence, Vol. 37, 2023, pp. 11121–11128.doi:10.1609/aaai.v37i9.26317

    2023 doi

  53. [71]

    P. Chen, A. Niu, D. Liu, W. Jiang, B. Ma, Time series forecasting of tempera- turesusingsarima: Anexamplefromnanjing, IOPConferenceSeries: Materials Science and Engineering 394 (2018) 052024.doi:10.1088/1757-899X/394/5/ 052024

    2018 doi

  54. [72]

    G. E. Box, G. M. Jenkins, G. C. Reinsel, G. M. Ljung, Time series analysis: forecasting and control, John Wiley & Sons, 2015.doi:10.1111/jtsa.12194

    2015 doi

  55. [73]

    Anderson, The backshift operator in time series analysis, International Jour- nal of Mathematical Educational in Science and Technology 7 (2) (1976) 235– 241

    O. Anderson, The backshift operator in time series analysis, International Jour- nal of Mathematical Educational in Science and Technology 7 (2) (1976) 235– 241

    1976

  56. [74]

    A.K.Nandi, Datamodelingwithpolynomialrepresentationsandautoregressive time-series representations, and their connections, Ieee Access 8 (2020) 110412– 110424

    2020

  57. [75]

    Shao, G.-F

    Y.-H. Shao, G.-F. Gu, Z.-Q. Jiang, W.-X. Zhou, Effects of polynomial trends on detrending moving average analysis, Fractals 23 (03) (2015) 1550034

    2015

  58. [76]

    M. W. Ahmad, M. Mourshed, Y. Rezgui, Tree-based ensemble methods for predicting pv power generation and their comparison with support vector re- gression, Energy 164 (2018) 465–474. 36

    2018

  59. [77]

    T. Chen, C. Guestrin, Xgboost: A scalable tree boosting system, in: Proceed- ings of the 22nd acm sigkdd international conference on knowledge discovery and data mining, 2016, pp. 785–794.doi:10.1145/2939672.2939785

    2016

  60. [78]

    doi:10.17849/insm-47-01-31-39.1

    S.J.Rigatti, Randomforest, JournalofInsuranceMedicine47(1)(2017)31–39. doi:10.17849/insm-47-01-31-39.1. 37

    2017 doi

  61. [270]

    doi:10.1111/j.1467-842X.2009.00541.x

    2009 arXiv

Pith tools

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