Pith. sign in

REVIEW 4 major objections 5 minor 82 references

AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read One trained invertible network turns any point forecast into calibrated quantiles.

desk verdict AutoPQ is a solid, honest engineering extension: the cINN conversion is prior work, but the nested HPO, successive halving, and energy accounting are new; the main weakness is that calibration is asserted by citation rather than checked. read the letter →

arxiv 2412.00419 v1 pith:FG7ZF5PQ submitted 2024-11-30 cs.LG eess.SPstat.ML

Stefan Meisenbacher , Kaleb Phipps , Oskar Taubert , Marie Weiel , Markus Götz , Ralf Mikut , Veit Hagenmeyer This is my paper · ORCID
classification cs.LGeess.SPstat.ML
keywords probabilisticforecastingquantileestimationconditionalinvertibleneuralnetworkautomatedmachinelearninghyperparameteroptimizationsmartgridelectricityconsumptionuncertaintyquantification
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

AutoPQ claims to close a practical gap: most forecasting models used in smart-grid operations produce only point forecasts, while the decisions built on them need quantiles. The paper's solution attaches any point forecasting method to a conditional invertible neural network (cINN) that has been trained once on historical data to map between the data space and a Gaussian latent space; a point forecast is projected into that space, sampled around with a tunable width, and mapped back to produce quantile forecasts without assuming any distribution. AutoPQ automates the design choices — the sampling width, the choice of point forecaster among nine methods, and their hyperparameters — in two configurations with different compute budgets, and it reports the electricity each configuration consumes. On six datasets the advanced configuration improves the Continuous Ranked Probability Score by 9.1–30.8 percent on average over six baseline probabilistic forecasting methods and by 5.0 percent over AutoPQ-default, at a measured cost of 8.73 kWh per run.

What carries the argument

The central object is the conditional invertible neural network (cINN), a bijection $g: \mathcal{Y} \to \mathcal{Z}$ built from conditional-affine coupling blocks and trained to map the unknown distribution of the target time series into a multi-dimensional Gaussian latent space while conditioning on lag, cyclic, and exogenous features. Given a point forecast, the pipeline passes it forward through the cINN, samples the latent neighbourhood with variance $\lambda_q = \sigma$, and passes the samples backward to obtain quantiles; the sampling variance is the single knob that trades sharpness against coverage. Around this object AutoPQ builds an automated design loop: its default configuration optimizes only $\sigma$ against the CRPS using Bayesian optimization with tree-structured Parzen estimators, and its advanced configuration adds a joint hyperparameter search in which an asynchronous evolutionary algorithm proposes point-forecaster configurations in an outer loop while the Bayesian inner loop, initialized with a log-normal prior over $\sigma$ derived from previously evaluated configurations, finds the best sampling width for each trained model, with successive halving pruning whole forecasting methods. The nested structure is load-bearing because it evaluates several $\sigma$ values per trained point model, exploiting the paper's measured asymmetry that quantile generation is orders of magnitude cheaper than model training.

What would settle it

Compute the empirical coverage of the 90 percent prediction interval produced by AutoPQ on the held-out test sets of all six datasets and compare it with the nominal 90 percent (equivalently, inspect the probability integral transform histogram). If coverage deviates substantially on a dataset where the CRPS was nevertheless minimized, while a simple empirical- or conformal-residual benchmark achieves nominal coverage, the equivalence-of-uncertainty claim is falsified for that data. A second check: replace the selected point forecaster with a deliberately biased one and see whether the output quantiles move; stable quantiles would indicate the cINN captures the process's own uncertainty, while strongly shifting quantiles would show the uncertainty is an artifact of the point forecast.

Watch

Extended reading notes

Core claim

The paper's central claim is that one trained cINN is a universal quantile generator: because the network is a conditional bijection between the data space and a known Gaussian latent space, the authors assert that uncertainty in one space is equivalent to uncertainty in the other, so sampling in the latent neighbourhood of a point forecast's representation and passing the samples backward yields the full predictive distribution. AutoPQ then treats the sampling variance $\sigma$ as a task-dependent hyperparameter, optimizes it against the CRPS on validation data, selects among nine point forecasting methods from the statistical, machine-learning, and deep-learning families, and jointly tunes their hyperparameters. The claimed result of this automation is an average 5.0 percent CRPS improvement over AutoPQ-default, average improvements of 9.1–30.8 percent over six baseline probabilistic forecasting methods, significance in 38 of 42 comparisons, and a measured electricity cost that lets users trade forecast quality against energy consumption.

Load-bearing premise

The load-bearing premise is that the cINN trained on historical data is a calibrated conditional bijection, so that sampling around a point forecast's latent representation in Gaussian space and mapping back produces quantiles that are genuinely calibrated for the test period; the paper relies on the asserted 'equivalence of uncertainty in both spaces' and tunes the sampling width on validation CRPS rather than checking calibration directly.

Editorial extensions

If this is right

  • Any existing point forecaster — from exponential smoothing to a transformer — can be upgraded to a full probabilistic forecast by one trained cINN, with no distributional assumption and no uncertainty model retrained per forecaster.
  • Because the sampling variance $\sigma$ is a single tunable knob that trades sharpness against coverage, optimizing it on validation CRPS lets the same pipeline be re-targeted to different decision costs by changing one hyperparameter.
  • The advanced configuration's 5.0 percent average CRPS gain over the default is reported to add 2.9 kWh and about 23 US dollars per run in resource-aware settings, while a full advanced run consumes 8.73 kWh versus 0.57 kWh for the default.
  • The nested two-loop search locates good sampling widths early in the budget, which matters because successive halving prunes methods on early performance; the prior-knowledge initialization cuts the trials needed for the inner loop substantially at equal validation CRPS.
  • Dropping the three statistical methods, halving the time budget to 4 h, and using AutoPQ-default as the initial pruning round reduces the advanced configuration's energy use by about 60 percent, to 3.47 kWh.

Reading between the lines

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

  • If the calibration claim holds across data sets, the same trained cINN should transfer to new point forecasters — and possibly to new data sets with similar distributions — without retraining, which would amortize its training energy across many deployments; this reuse claim goes beyond the paper's evaluation.
  • A direct calibration check (empirical coverage or PIT histogram on the test period) would test the equivalence-of-uncertainty premise more decisively than CRPS tuning alone, since CRPS rewards sharpness and calibration jointly and can mask miscalibration; this is a cheap diagnostic the paper does not run.
  • Because the paper's ablation shows that default-configuration performance strongly predicts which forecasters win after full hyperparameter optimization, a simpler rule — pick the best default forecaster and tune only $\sigma$ — may capture most of the advanced configuration's advantage at the default configuration's energy cost.
  • The paper's own limitation discussion notes that feature selection stays manual and that CRPS is a proxy for what applications actually need; replacing the proxy with the direct decision cost (forecast value) is its stated future work, and the same nested-search argument would likely accelerate that search too.
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 / 5 minor

Summary. The paper introduces AutoPQ, an automated probabilistic forecasting pipeline that wraps an arbitrary point forecast with a conditional invertible neural network (cINN). The point forecast is mapped into a Gaussian latent space, samples are drawn around that latent representation with variance lambda_q, and the inverse map turns these samples into quantile forecasts. Two configurations are proposed: AutoPQ-default optimizes only the sampling variance for each default point forecaster, while AutoPQ-advanced jointly optimizes the point forecaster's hyperparameters and the sampling variance via a nested evolutionary/Bayesian optimization loop with successive halving. The evaluation on six smart-grid-related datasets compares CRPS against six baseline methods and reports average CRPS improvements of 9.1%–27.3% over the baselines and 5.0% over AutoPQ-default, together with an ablation study and measurements of electricity consumption and monetary cost.

Significance. If the empirical claims hold, AutoPQ is a practically useful contribution: it brings AutoML-style selection and hyperparameter optimization to probabilistic forecasting from point forecasts, it is accompanied by a public implementation, and its explicit reporting of electricity consumption is a welcome step for sustainable ML. The ablation study is a strength, particularly the comparison of the nested optimization structure (Algorithm 1 vs. Algorithm 3), the prior-knowledge initialization for Bayesian optimization, and the successive-halving pruning analysis. The central limitation is that the cINN-based predictive distribution is never directly checked for calibration, so the paper currently supports a claim about CRPS optimization but not yet a fully supported claim about unbiased and accurate uncertainty quantification.

major comments (4)
  1. [Section 3.1, footnote 4; Section 5.4] The central probabilistic claim rests on an unverified distributional equivalence. The method maps a point forecast to z_hat = g(y_hat), samples z ~ N(z_hat, sigma^2 I), and maps back through g^{-1}; footnote 4 justifies this by 'the equivalence of uncertainty in both spaces' with a citation to [19], but no derivation or test-set calibration check is provided. The cINN is trained to map the realization space to a Gaussian latent space, while at inference it is evaluated at point forecasts, which are not draws from the predictive distribution of the target; this is a distribution shift that the cited equivalence would need to cover. Tuning sigma on validation CRPS (Eq. 5) does not imply calibration, since CRPS can favor a sharp but miscalibrated forecast over a calibrated but less sharp one in finite samples. The paper reports no probability integral transform histograms, empirical coverage rates, or reliability diagrams in Section 4, and Section 5.4 explicitly leaves 'desirable probabilistic properties' as an open question. Because the title, abstract, and smart-grid motivation are about producing trustworthy quantile forecasts, the authors should either verify calibration of the final predictive distributions on the test sets or explicitly reframe the contribution as CRPS optimization without the stronger claim of unbiased uncertainty quantification.
  2. [Section 4.1.1, Table 3] The headline comparison to baselines is not a controlled one. AutoPQ-advanced receives an 8-hour CASH budget (Section 3.4.1, Algorithm 1) and jointly optimizes the point forecaster's hyperparameters and the sampling variance, whereas DeepAR, QRNNs, NNQF, and the Gaussian/Empirical/Conformal PI methods are evaluated with default or standard settings; only the best base point forecast is selected for the PI benchmarks, without tuning the underlying forecaster. The reported 9.1%–27.3% average CRPS improvements therefore conflate the proposed uncertainty-quantification mechanism with the benefit of hyperparameter optimization. The authors should compare against baselines that receive a comparable tuning budget, or make AutoPQ-default (fixed default point forecasts, only sigma optimized) the primary fair comparison and explicitly quantify the additional gain attributable to HPO.
  3. [Section 4.1.2, Table 3] The significance claims are based on 42 one-tailed t-tests with five runs each, with no correction for multiple testing. At alpha = 0.05 one would expect roughly two false positives among 42 tests, so the statement that improvements are 'significant in 38 out of 42 tests' is not a valid family-wise or false-discovery-rate statement. The authors should report adjusted p-values (for example, Benjamini-Hochberg) or clearly state which comparisons are confirmatory versus exploratory, and they should supplement the five-run t-tests with effect sizes and confidence intervals. This is particularly relevant for the non-significant entries in Table 3, such as QRNNs on PV at 0.0% and Empirical/Conformal PIs on Mobility, which the current presentation tends to obscure.
  4. [Section 4.1.1, footnotes 11 and 13; Table 2 caption] For four of the six datasets (Load-GCP, Mobility, Price, PV), the benchmark and AutoPQ-default numbers are taken from the authors' prior papers [19, 59], while the AutoPQ-advanced numbers are new in this manuscript. This creates a reproducibility gap: the reader cannot verify that the same cINN checkpoint, normalization, train/validation/test splits, quantile post-processing, and CRPS implementation were used for the old and new numbers. The inconsistency between footnote 11 (which attributes the results to [59]) and the Table 2 caption (which says they 'originate from [19]') makes this harder to resolve. The authors should either rerun the full benchmark suite with the released code or provide an explicit compatibility statement and the exact artifacts (splits, cINN weights, evaluation code) for all six datasets.
minor comments (5)
  1. [Section 3.1] The sentence 'a point forecast can be interpreted as a sample of the random variable Y' is conceptually imprecise: a point forecast is a conditional summary of the predictive distribution, not a random draw from it. This matters because the method's validity depends on how the point forecast is embedded in the cINN's latent space.
  2. [Section 4.1.1, Table 2 caption] The caption says the benchmark and AutoPQ-default results for Load-GCP, Mobility, Price, and PV 'originate from [19]', while Section 4.1.1 footnotes 11 and 13 attribute these results to [59]. Please align the references.
  3. [Section 3.4.1, Figure 3] The log-normal prior assumption for the optimal sampling hyperparameter is justified in the text as 'valid, as demonstrated in Figure 3a' with a single dataset/model (MLP on Load-BW). This should be presented as a heuristic or supported with evidence across multiple datasets, since the prior is used to initialize the inner-loop optimizer in AutoPQ-advanced.
  4. [Section 4.3] The electricity consumption accounting should state its system boundary explicitly: the reported kWh cover the AutoPQ design runs, but not cINN pretraining, data preprocessing, or baseline training. This is important for interpreting the 'electricity consumption required for performance improvements' claim.
  5. [Section 2.2] There is a typo in the second paragraph: 'a forecasting method's configuration hat delivers' should read 'that delivers'.

Circularity Check

1 steps flagged · score 4.0 of 10

The core cINN uncertainty mapping is asserted by self-citation to [19], and four of six datasets' baseline/AutoPQ-default results are borrowed from the authors' own prior work; the empirical comparison itself, however, is not constructed from its inputs.

  1. self citation load bearing [Section 3.1, footnote 4 (after 'Neighborhood analysis of the point forecast's latent space representation')]
    "This is valid due to the equivalence of uncertainty in both spaces [19]."

    The paper's quantile forecast is produced by mapping the point forecast into the latent space of a cINN, sampling around that representation with variance sigma, and pushing the samples back through the network. The claim that this yields the correct predictive uncertainty is the load-bearing premise of the entire method, and it is justified solely by footnote 4 citing [19], whose author list overlaps with the present paper. No derivation is given, and no test-set calibration check (e.g., PIT uniformity or empirical coverage) is reported; Section 5.4 instead lists 'desirable probabilistic properties' as an open question. Thus the central mechanism is imported from the authors' own prior work rather than established or independently verified in this paper.

full rationale

The paper's central claim is empirical: AutoPQ-advanced achieves lower CRPS than six baselines and AutoPQ-default on six datasets. That comparison is not a derivation, and I found no equation-level circularity in which a predicted quantity equals an input by construction. The sampling variance sigma is explicitly optimized on validation CRPS (Eq. 5), which is standard hyperparameter tuning, not a fitted parameter renamed as a prediction. The 'prior knowledge' in the inner optimizer is an adaptive initialization derived from the optimizer's own population; it is a heuristic warm start, not a circular input. The main circularity concern is load-bearing self-citation. Footnote 4 asserts 'the equivalence of uncertainty in both spaces' by citing [19], a prior paper by overlapping authors. This equivalence is the theoretical foundation for treating Gaussian samples around the point forecast's latent representation as valid quantile uncertainty. The present paper does not prove it, and it acknowledges in Section 5.4 that desirable probabilistic properties remain unclear. If [19] contains a rigorous proof, the citation would be legitimate support, but the present paper does not reproduce or verify that proof, so the central premise rests on an unexamined self-citation. Additionally, four of the six datasets' AutoPQ-default and baseline results are taken from [59], another prior paper by the same group. This weakens independence of the reported 5.0% average improvement over AutoPQ-default, but it is not circular in the logical sense: the comparison is between newly computed AutoPQ-advanced numbers and fixed prior numbers, not between a quantity and its own definition. Weighing these factors, the empirical evaluation has substantial independent content and is not forced by construction, but the method's core validity and part of the comparison baseline rely on the authors' own prior work. Score 4 reflects partial circularity through load-bearing self-citation, without reducing the central claim to a tautology.

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

The method's central knob is the latent-space sampling standard deviation, which is optimized per dataset; the early stopping rule and patience are hand-chosen. The paper assumes the cINN bijection is calibrated (inherited from [19]), that validation CRPS transfers to test performance, and that a log-normal prior is appropriate for the sampling hyperparameter. No new physical entities are introduced.

free parameters (3)
  • sampling_std (lambda_q) = optimized in [0.01, 3.0] per dataset
    Controls uncertainty magnitude; tuned to minimize validation CRPS; the central knob of the probabilistic forecast.
  • early stopping threshold = 0.0005
    Hand-chosen convergence threshold for the standard deviation of the five best HPO trials.
  • early stopping patience = 5 trials
    Hand-chosen number of trials without improvement before stopping the inner or outer HPO loop.
assumptions (3)
  • domain assumption The cINN provides a calibrated conditional bijection between the realization space and a Gaussian latent space, so latent-space uncertainty is equivalent to predictive uncertainty.
    Invoked in Section 3.1 and footnote 4; the paper inherits this from [19] rather than proving it.
  • domain assumption Validation-set CRPS is a valid proxy for test-set forecast quality and for the downstream utility of the forecast.
    The HPO tunes lambda_q and lambda_p on validation CRPS (Section 3.3, Equations 5-6) and assumes this transfers to the hold-out test set.
  • ad hoc to paper The optimal sampling hyperparameter follows a log-normal distribution, enabling a prior for Bayesian optimization.
    Assumed in Section 3.4.1 'Prior knowledge'; justified only by one empirical density plot (Figure 3a) for MLP on Load-BW.

how reviews work

0 comments
Cite this review

Pith. "Pith review of AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability." pith.science (2026). https://pith.science/paper/FG7ZF5PQ

@misc{pith2026241200419,
  author       = {Pith},
  title        = {Pith review of: AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FG7ZF5PQ}},
  note         = {Machine review of arXiv:2412.00419}
}
read the original abstract

Optimizing smart grid operations relies on critical decision-making informed by uncertainty quantification, making probabilistic forecasting a vital tool. Designing such forecasting models involves three key challenges: accurate and unbiased uncertainty quantification, workload reduction for data scientists during the design process, and limitation of the environmental impact of model training. In order to address these challenges, we introduce AutoPQ, a novel method designed to automate and optimize probabilistic forecasting for smart grid applications. AutoPQ enhances forecast uncertainty quantification by generating quantile forecasts from an existing point forecast by using a conditional Invertible Neural Network (cINN). AutoPQ also automates the selection of the underlying point forecasting method and the optimization of hyperparameters, ensuring that the best model and configuration is chosen for each application. For flexible adaptation to various performance needs and available computing power, AutoPQ comes with a default and an advanced configuration, making it suitable for a wide range of smart grid applications. Additionally, AutoPQ provides transparency regarding the electricity consumption required for performance improvements. We show that AutoPQ outperforms state-of-the-art probabilistic forecasting methods while effectively limiting computational effort and hence environmental impact. Additionally and in the context of sustainability, we quantify the electricity consumption required for performance improvements.

Figures

Figures reproduced from arXiv: 2412.00419 by the authors.

Figure 1
Figure 1. Overview of AutoPQ: Lag features, seasonal features, and exogenous features are selected and used as inputs by a point forecasting model to generate a point forecast in an unknown distribution. This point forecast and the features are combined in a cINN, resulting in a representation of the forecast in a known and tractable distribution. The neighborhood of this representation is analyzed to determine how to include… view at source ↗
Figure 2
Figure 2. Comparison of the average computational effort in terms of runtime across the six datasets used in the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Estimated BO prior distribution and its utilization [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Exemplary 40 %, 70 %, and 98 % PIs for the Mobility dataset. The probabilistic forecasts of AutoPQ￾advanced (a-c) are generated based on the point forecasting methods ETS (SM), XGB (ML), and TFT (DL), respec￾tively, showing different performance. Note that AutoPQ-advan…
Figure 6
Figure 6. Figure 6: Number of iterations required for the inner loop [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 5
Figure 5. Figure 5: Comparison of the convergence of Algorithm 1 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 8
Figure 8. Figure 8: The HPO of the sampling hyperparameter con [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Comparison of the computational effort for a [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

82 extracted references · 55 canonical work pages

  1. [19]

    Generating probabilis- tic forecasts from arbitrary point forecasts using a conditional invertible neural network,

    K. Phipps, B. Heidrich, M. Turowski, M. Wittig, R. Mikut, and V . Hagenmeyer, “Generating probabilis- tic forecasts from arbitrary point forecasts using a conditional invertible neural network,”Applied In- telligence, 2024, ISSN : 1573-7497. DOI: 10.1007/ s10489-024-05346-9

    work page 2024

  2. [59]

    Loss- customised probabilistic energy time series fore- casts using automated hyperparameter optimisation,

    K. Phipps, S. Meisenbacher, B. Heidrich, M. Tur- owski, R. Mikut, and V . Hagenmeyer, “Loss- customised probabilistic energy time series fore- casts using automated hyperparameter optimisation,” in Proceedings of the 14th ACM International Con- ference on Future Energy Systems , ser. e-Energy ’23, Orlando, USA: Association for Computing Ma- chinery, 2023,...

    work page arXiv 2023

  3. [1]

    Applications of prob- abilistic forecasting in smart grids: A review,

    H. Khajeh and H. Laaksonen, “Applications of prob- abilistic forecasting in smart grids: A review,”Ap- plied Sciences, vol. 12, no. 4, 2022, ISSN : 2076-

    2022

  4. [3]

    Data-driven distribution- ally robust optimal power flow for distribution sys- tems,

    R. Mieth and Y . Dvorkin, “Data-driven distribution- ally robust optimal power flow for distribution sys- tems,” IEEE Control Systems Letters, vol. 2, no. 3, pp. 363–368, 2018. 19 AutoPQ MEISENBACHER et al

    2018

  5. [4]

    On the use of probabilistic forecasts in scheduling of renew- able energy sources coupled to storages,

    R. R. Appino, J. Á. González Ordiano, R. Mikut, T. Faulwasser, and V . Hagenmeyer, “On the use of probabilistic forecasts in scheduling of renew- able energy sources coupled to storages,” Applied Energy, vol. 210, pp. 1207–1218, 2018, ISSN : 0306-

    work page 2018

  6. [5]

    Industrial peak shaving with battery storage using a probabilistic forecasting approach: Economic evaluation of risk attitude,

    S. Henni, J. Becker, P. Staudt, F. vom Scheidt, and C. Weinhardt, “Industrial peak shaving with battery storage using a probabilistic forecasting approach: Economic evaluation of risk attitude,”Applied En- ergy, vol. 327, p. 120 088, 2022, ISSN : 0306-2619. DOI: 10.1016/j.apenergy.2022.120088

    work page arXiv 2022

  7. [6]

    Customized uncertainty quantifi- cation of parking duration predictions for EV smart charging,

    K. Phipps, K. Schwenk, B. Briegel, R. Mikut, and V . Hagenmeyer, “Customized uncertainty quantifi- cation of parking duration predictions for EV smart charging,” IEEE Internet of Things Journal, vol. 10, no. 23, pp. 20 649–20 661, 2023. DOI: 10.1109/ JIOT.2023.3299201

    work page arXiv 2023

  8. [7]

    Probabilistic forecasts of time and energy flexibility in battery electric vehicle charging,

    J. Huber, D. Dann, and C. Weinhardt, “Probabilistic forecasts of time and energy flexibility in battery electric vehicle charging,” Applied Energy, vol. 262, p. 114 525, 2020, ISSN : 0306-2619. DOI: 10.1016/ j.apenergy.2020.114525

    work page arXiv 2020

Show all 82 references
  1. [8]

    Multivariate probabilistic forecasting and its performance’s impacts on long-term dispatch of hydro-wind hybrid systems,

    Y . Zhang, C. Cheng, R. Cao, G. Li, J. Shen, and X. Wu, “Multivariate probabilistic forecasting and its performance’s impacts on long-term dispatch of hydro-wind hybrid systems,” Applied Energy, vol. 283, p. 116 243, 2021, ISSN : 0306-2619. DOI: 10.1016/j.apenergy.2020.116243

    2021

  2. [9]

    A task-based day-ahead load forecasting model for stochastic economic dispatch,

    J. Han, L. Yan, and Z. Li, “A task-based day-ahead load forecasting model for stochastic economic dispatch,” IEEE Transactions on Power Systems , vol. 36, no. 6, pp. 5294–5304, 2021.DOI: 10.1109/ TPWRS.2021.3072904

    2021

  3. [10]

    N-BEATS: Neural basis expansion anal- ysis for interpretable time series forecasting,

    B. N. Oreshkin, D. Carpov, N. Chapados, and Y . Bengio, “N-BEATS: Neural basis expansion anal- ysis for interpretable time series forecasting,” in International Conference on Learning Representa- tions, 2020

    2020

  4. [11]

    Temporal Fusion Transformers for interpretable multi-horizon time series forecasting,

    B. Lim, S. Ö. Arık, N. Loeff, and T. Pfister, “Temporal Fusion Transformers for interpretable multi-horizon time series forecasting,”International Journal of Forecasting, vol. 37, no. 4, pp. 1748– 1764, 2021, ISSN : 0169-2070. DOI: 10.1016/j. ijforecast.2021.03.012

    2021 doi

  5. [12]

    N-HiTS: Neural hierarchical interpo- lation for time series forecasting,

    C. Challú, K. G. Olivares, B. N. Oreshkin, F. Garza Ramirez, M. Mergenthaler Canseco, and A. Dubrawski, “N-HiTS: Neural hierarchical interpo- lation for time series forecasting,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 37, 2023, pp. 6989–6997. D...

    2023 doi

  6. [13]

    Forecasting: Theory and prac- tice,

    F. Petropoulos et al., “Forecasting: Theory and prac- tice,” International Journal of Forecasting, vol. 38, no. 3, pp. 705–871, 2022, ISSN : 0169-2070. DOI: 10.1016/j.ijforecast.2021.11.001

    2022 doi

  7. [14]

    R. J. Hyndman and G. Athanasopoulos, Forecast- ing: principles and practice, Third. Melbourne, Aus- tralia: OTexts, 2021

    2021

  8. [15]

    On the generation of probabilistic fore- casts from deterministic models,

    E. Camporeale, X. Chu, O. V . Agapitov, and J. Bortnik, “On the generation of probabilistic fore- casts from deterministic models,” Space Weather, vol. 17, no. 3, pp. 455–475, 2019. DOI: 10.1029/ 2018SW002026

    2019

  9. [16]

    A simple method for the construction of empirical confi- dence limits for economic forecasts,

    W. H. Williams and M. L. Goodman, “A simple method for the construction of empirical confi- dence limits for economic forecasts,” Journal of the American Statistical Association, vol. 66, no. 336, pp. 752–754, 1971. DOI: 10 . 1080 / 01621459 . 1971.10482340

    1971

  10. [17]

    Conformal time series forecasting,

    K. Stankeviciute, A. M. Alaa, and M. van der Schaar, “Conformal time series forecasting,” in Ad- vances in Neural Information Processing Systems, M. Ranzato, A. Beygelzimer, Y . Dauphin, P. Liang, and J. W. Vaughan, Eds., vol. 34, Curran Associates, Inc., 2021, pp. 6216–6228

    2021

  11. [18]

    Modeling load forecast uncertainty using generative adver- sarial networks,

    Y . Wang, G. Hug, Z. Liu, and N. Zhang, “Modeling load forecast uncertainty using generative adver- sarial networks,” Electric Power Systems Research, vol. 189, p. 106 732, 2020, ISSN : 0378-7796. DOI: 10.1016/j.epsr.2020.106732

    2020

  12. [20]

    Hutter, L

    F. Hutter, L. Kotthoff, and J. Vanschoren,Automated machine learning: Methods, systems, challenges (The Springer Series on Challenges in Machine Learning). Cham, Switzerland: Springer Interna- tional Publishing, 2019. DOI: 10 . 1007 / 978 - 3 - 030-05318-5

    2019

  13. [21]

    Automated data-driven modeling of building energy systems via machine learning algo- rithms,

    M. Rätz, A. P. Javadi, M. Baranski, K. Finkbeiner, and D. Müller, “Automated data-driven modeling of building energy systems via machine learning algo- rithms,” Energy and Buildings, vol. 202, p. 109 384,

  14. [22]

    AutoAI-TS: AutoAI for time series forecasting,

    S. Y . Shah et al., “AutoAI-TS: AutoAI for time series forecasting,” in Proceedings of the 2021 In- ternational Conference on Management of Data , ser. SIGMOD ’21, Virtual Event, China: Associa- tion for Computing Machinery, 2021, pp. 2584– 2596, ISBN : 9781450383431. DOI: 10 ...

    2021

  15. [23]

    Efficient automated deep learning for time series forecasting,

    D. Deng, F. Karl, F. Hutter, B. Bischl, and M. Lindauer, “Efficient automated deep learning for time series forecasting,” in Machine Learning and Knowledge Discovery in Databases, M.-R. Amini, S. Canu, A. Fischer, T. Guns, P. Kralj Novak, and G. Tsoumakas, Eds., Cham, Switzerl...

    2023

  16. [24]

    AutoGluon–TimeSeries: AutoML for probabilistic time series forecasting,

    O. Shchur et al., “AutoGluon–TimeSeries: AutoML for probabilistic time series forecasting,” in Interna- tional Conference on Automated Machine Learning, PMLR, 2023, pp. 9–1

    2023

  17. [25]

    Reporting electricity consumption is essen- tial for sustainable AI,

    C. Debus, M. Piraud, A. Streit, F. Theis, and M. Götz, “Reporting electricity consumption is essen- tial for sustainable AI,” Nature Machine Intelli- gence, vol. 5, no. 11, pp. 1176–1178, 2023, ISSN : 2522-5839. DOI: 10.1038/s42256-023-00750- 1

    2023 doi

  18. [26]

    DeepAR: Probabilistic forecast- ing with autoregressive recurrent networks,

    D. Salinas, V . Flunkert, J. Gasthaus, and T. Januschowski, “DeepAR: Probabilistic forecast- ing with autoregressive recurrent networks,” In- ternational Journal of Forecasting, vol. 36, no. 3, pp. 1181–1191, 2020, ISSN : 0169-2070. DOI: 10. 1016/j.ijforecast.2019.07.001

    2020

  19. [27]

    End-to- end learning of coherent probabilistic forecasts for hierarchical time series,

    S. S. Rangapuram, L. D. Werner, K. Benidis, P. Mer- cado, J. Gasthaus, and T. Januschowski, “End-to- end learning of coherent probabilistic forecasts for hierarchical time series,” in Proceedings of the 38th International Conference on Machine Learning, M. Meila and T. Zhang, ...

    2021

  20. [28]

    Controlling non-stationarity and periodicities in time series generation using condi- tional invertible neural networks,

    B. Heidrich et al., “Controlling non-stationarity and periodicities in time series generation using condi- tional invertible neural networks,” Applied Intelli- gence, vol. 53, no. 8, pp. 8826–8843, 2023, ISSN : 1573-7497. DOI: 10.1007/s10489-022-03742- 7

    2023 doi

  21. [29]

    Quantile regression neural networks: Implementation in R and application to precipitation downscaling,

    A. J. Cannon, “Quantile regression neural networks: Implementation in R and application to precipitation downscaling,” Computers & Geosciences, vol. 37, no. 9, pp. 1277–1284, 2011, ISSN : 0098-3004. DOI: 10.1016/j.cageo.2010.07.005

    2011 doi

  22. [30]

    Probabilistic energy forecasting us- ing the nearest neighbors quantile filter and quantile regression,

    J. Á. González Ordiano, L. Gröll, R. Mikut, and V . Hagenmeyer, “Probabilistic energy forecasting us- ing the nearest neighbors quantile filter and quantile regression,” International Journal of Forecasting, vol. 36, no. 2, pp. 310–323, 2020, ISSN : 0169-2070. DOI: 10.1016/j.i...

    2020 doi

  23. [31]

    Deep generative quantile- copula models for probabilistic forecasting,

    R. Wen and T. Kari, “Deep generative quantile- copula models for probabilistic forecasting,” in Pro- ceedings of the 36th International Conference on Machine Learning, Paper: Time Series Workshop at ICML 2019, 2019

    2019

  24. [32]

    Multivariate proba- bilistic time series forecasting via conditioned nor- malizing flows,

    K. Rasul, A. -S. Sheikh, I. Schuster, U. M. Bergmann, and R. V ollgraf, “Multivariate proba- bilistic time series forecasting via conditioned nor- malizing flows,” in International Conference on Learning Representations, 2021

    2021

  25. [33]

    Jamgochian, D

    A. Jamgochian, D. Wu, K. Menda, S. Jung, and M. J. Kochenderfer, Conditional approximate normaliz- ing flows for joint multi-step probabilistic forecast- ing with application to electricity demand , 2022. arXiv: 2201.02753

    2022 arXiv

  26. [34]

    Short-term density forecasting of low-voltage load using Bernstein-polynomial nor- malizing flows,

    M. Arpogaus, M. V oss, B. Sick, M. Nigge-Uricher, and O. Dürr, “Short-term density forecasting of low-voltage load using Bernstein-polynomial nor- malizing flows,” IEEE Transactions on Smart Grid, vol. 14, no. 6, pp. 4902–4911, 2023.DOI: 10.1109/ TSG.2023.3254890

    2023

  27. [35]

    Probabilistic forecasting using deep gen- erative models,

    A. Fanfarillo, B. Roozitalab, W. Hu, and G. Cer- vone, “Probabilistic forecasting using deep gen- erative models,” GeoInformatica, vol. 25, no. 1, pp. 127–147, 2021, ISSN : 1573-7624. DOI: 10 . 1007/s10707-020-00425-8

    2021

  28. [36]

    Scenario forecasting of residential load profiles,

    L. Zhang and B. Zhang, “Scenario forecasting of residential load profiles,” IEEE Journal on Selected Areas in Communications, vol. 38, no. 1, pp. 84–95,

  29. [37]

    Modeling daily load profiles of distribu- tion network for scenario generation using flow- based generative network,

    L. Ge, W. Liao, S. Wang, B. Bak-Jensen, and J. R. Pillai, “Modeling daily load profiles of distribu- tion network for scenario generation using flow- based generative network,” IEEE Access , vol. 8, pp. 77 587–77 597, 2020. DOI: 10.1109/ACCESS. 2020.2989350

    2020

  30. [38]

    A deep generative model for probabilistic energy forecasting in power systems: Normalizing flows,

    J. Dumas, A. Wehenkel, D. Lanaspeze, B. Cornélusse, and A. Sutera, “A deep generative model for probabilistic energy forecasting in power systems: Normalizing flows,” Applied Energy , vol. 305, p. 117 871, 2022, ISSN : 0306-2619. DOI: 10.1016/j.apenergy.2021.117871

    2022

  31. [39]

    Multivariate probabilistic forecasting of intraday electricity prices using normalizing flows,

    E. Cramer, D. Witthaut, A. Mitsos, and M. Dahmen, “Multivariate probabilistic forecasting of intraday electricity prices using normalizing flows,” Applied Energy, vol. 346, p. 121 370, 2023,ISSN : 0306-2619. DOI: 10.1016/j.apenergy.2023.121370

    2023

  32. [40]

    Distri- butional conformal prediction,

    V . Chernozhukov, K. Wüthrich, and Y . Zhu, “Distri- butional conformal prediction,” Proceedings of the National Academy of Sciences , vol. 118, no. 48, e2107794118, 2021. DOI: 10 . 1073 / pnas . 2107794118

    2021

  33. [41]

    Adaptive conformal predictions for time series,

    M. Zaffran, O. Féron, Y . Goude, J. Josse, and A. Dieuleveut, “Adaptive conformal predictions for time series,” in International Conference on Ma- chine Learning, PMLR, 2022, pp. 25 834–25 866

    2022

  34. [42]

    A state space framework for au- tomatic forecasting using exponential smoothing methods,

    R. J. Hyndman, A. B. Koehler, R. D. Snyder, and S. Grose, “A state space framework for au- tomatic forecasting using exponential smoothing methods,” International Journal of Forecasting , vol. 18, no. 3, pp. 439–454, 2002. DOI: 10.1016/ S0169-2070(01)00110-8

    2002

  35. [43]

    Automatic time series forecasting: The forecast package for R,

    R. J. Hyndman and Y . Khandakar, “Automatic time series forecasting: The forecast package for R,” Journal of Statistical Software, vol. 27, no. 3, pp. 1– 22, 2008. DOI: 10.18637/jss.v027.i03

    2008 doi

  36. [44]

    Forecasting time series with complex seasonal pat- terns using exponential smoothing,

    A. M. De Livera, R. J. Hyndman, and R. D. Snyder, “Forecasting time series with complex seasonal pat- terns using exponential smoothing,” Journal of the American Statistical Association, vol. 106, no. 496, pp. 1513–1527, 2011. DOI: 10.1198/jasa.2011. tm09771. 21 AutoPQ MEISENB...

    2011 doi

  37. [45]

    Au- tomatic time series analysis for electric load fore- casting via support vector regression,

    S. Maldonado, A. González, and S. Crone, “Au- tomatic time series analysis for electric load fore- casting via support vector regression,” Applied Soft Computing, vol. 83, p. 105 616, 2019. DOI: 10 . 1016/j.asoc.2019.105616

    2019

  38. [46]

    SVR-FFS: A novel forward feature selection approach for high- frequency time series forecasting using support vec- tor regression,

    J. M. Valente and S. Maldonado, “SVR-FFS: A novel forward feature selection approach for high- frequency time series forecasting using support vec- tor regression,” Expert Systems with Applications, vol. 160, p. 113 729, 2020. DOI: 10.1016/j.eswa. 2020.113729

    2020

  39. [47]

    ELM- based improved layered ensemble architecture for time series forecasting,

    S. Fan, X. Qin, Z. Jia, X. Qi, and M. Lin, “ELM- based improved layered ensemble architecture for time series forecasting,” IEEE Access , vol. 7, pp. 97 827–97 837, 2019. DOI: 10.1109/ACCESS. 2019.2927047

    2019

  40. [48]

    Em- pirical study on the impact of different sets of pa- rameters of gradient boosting algorithms for time- series forecasting with LightGBM,

    F. S. Barros, V . Cerqueira, and C. Soares, “Em- pirical study on the impact of different sets of pa- rameters of gradient boosting algorithms for time- series forecasting with LightGBM,” in PRICAI 2021: Trends in Artificial Intelligence, D. N. Pham, T. Theeramunkong, G. Gover...

    2021

  41. [49]

    AutoCTS: Automated correlated time series forecasting,

    X. Wu, D. Zhang, C. Guo, C. He, B. Yang, and C. S. Jensen, “AutoCTS: Automated correlated time series forecasting,” Proc. VLDB Endow., vol. 15, no. 4, pp. 971–983, 2021, ISSN : 2150-8097. DOI: 10.14778/3503585.3503604

    2021

  42. [50]

    Effect of automatic hyperparame- ter tuning for residential load forecasting via deep learning,

    W. Konget al., “Effect of automatic hyperparame- ter tuning for residential load forecasting via deep learning,” in 2017 Australasian Universities Power Engineering Conference (AUPEC), 2017, pp. 1–6. DOI: 10.1109/AUPEC.2017.8282478

    2017

  43. [51]

    A hybrid deep learning model with evolutionary al- gorithm for short-term load forecasting,

    A. Al Mamun, M. Hoq, E. Hossain, and R. Bayindir, “A hybrid deep learning model with evolutionary al- gorithm for short-term load forecasting,” in 2019 8th International Conference on Renewable En- ergy Research and Applications (ICRERA), 2019, pp. 886–891. DOI: 10.1109/ICRERA...

    2019

  44. [52]

    R. C. Smith, Uncertainty quantification: Theory, im- plementation, and applications, First. Philadelphia, USA: Society for Industrial and Applied Mathemat- ics, 2013. DOI: 10.1137/1.9781611973228

    2013 doi

  45. [53]

    Review of automated time series forecasting pipelines,

    S. Meisenbacher et al., “Review of automated time series forecasting pipelines,” WIREs Data Mining and Knowledge Discovery , vol. 12, no. 6, e1475,

  46. [54]

    Random search for hy- perparameter optimization,

    J. Bergstra and Y . Bengio, “Random search for hy- perparameter optimization,” Journal of Machine Learning Research, vol. 13, pp. 281–305, 2012

    2012

  47. [55]

    Ardizzone, C

    L. Ardizzone, C. Lüth, J. Kruse, C. Rother, and U. Köthe, Guided image generation with conditional invertible neural networks , 2019. arXiv: 1907 . 02392

    2019

  48. [56]

    Forecasting energy time series with profile neural networks,

    B. Heidrich, M. Turowski, N. Ludwig, R. Mikut, and V . Hagenmeyer, “Forecasting energy time series with profile neural networks,” in Proceedings of the Eleventh ACM International Conference on Future Energy Systems, ser. e-Energy ’20, Virtual Event, Australia: Association for ...

    2020

  49. [57]

    Short-term electricity load forecasting using the Temporal Fu- sion Transformer: Effect of grid hierarchies and data sources,

    E. Giacomazzi, F. Haag, and K. Hopf, “Short-term electricity load forecasting using the Temporal Fu- sion Transformer: Effect of grid hierarchies and data sources,” in Proceedings of the 14th ACM International Conference on Future Energy Sys- tems, ser. e-Energy ’23, Orlando, ...

    2023 doi

  50. [58]

    Day-ahead electricity load prediction based on calendar features and temporal convolutional networks,

    L. Richter, F. Bauer, S. Klaiber, and P. Bretschnei- der, “Day-ahead electricity load prediction based on calendar features and temporal convolutional networks,” in Theory and Applications of Time Se- ries Analysis and Forecasting, O. Valenzuela, F. Ro- jas, L. J. Herrera, H. ...

    2023

  51. [60]

    Making a sci- ence of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures,

    J. Bergstra, D. Yamins, and D. Cox, “Making a sci- ence of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures,” in Proceedings of the 30th International Confer- ence on Machine Learning, ser. ICML ’13, Proceed- ings of Machine Learning...

    2013

  52. [61]

    Massively parallel genetic op- timization through asynchronous propagation of populations,

    O. Taubert et al., “Massively parallel genetic op- timization through asynchronous propagation of populations,” in High Performance Computing, A. Bhatele, J. Hammond, M. Baboulin, and C. Kruse, Eds., Cham, Switzerland: Springer Nature, 2023, pp. 106–124, ISBN : 978-3-031-32041-5

    2023

  53. [62]

    Hyperparameter optimization: Foundations, algorithms, best practices, and open challenges,

    B. Bischl et al. , “Hyperparameter optimization: Foundations, algorithms, best practices, and open challenges,” WIREs Data Mining and Knowledge Discovery, vol. 13, no. 2, e1484, 2023. DOI: 10 . 1002/widm.1484

    2023

  54. [63]

    Open Power System Data: Friction- less data for electricity system modelling,

    F. Wieseet al., “Open Power System Data: Friction- less data for electricity system modelling,” Applied Energy, vol. 236, pp. 401–409, 2019, ISSN : 0306-

    2019

  55. [64]

    Trindade, Electricity load diagrams 2011-2014, UCI Machine Learning Repository, 2015

    A. Trindade, Electricity load diagrams 2011-2014, UCI Machine Learning Repository, 2015. DOI: 10. 24432/C58C86

    2011

  56. [65]

    Fanaee-T, Bike sharing dataset, UCI Machine Learning Repository, 2013

    H. Fanaee-T, Bike sharing dataset, UCI Machine Learning Repository, 2013. DOI: 10 . 24432 / C5W894

    2013

  57. [66]

    Probabilistic energy fore- casting: Global energy forecasting competition 2014 and beyond,

    T. Hong, P. Pinson, S. Fan, H. Zareipour, A. Troc- coli, and R. J. Hyndman, “Probabilistic energy fore- casting: Global energy forecasting competition 2014 and beyond,” International Journal of Forecasting, vol. 32, no. 3, pp. 896–913, 2016, ISSN : 0169-2070. DOI: 10.1016/j.ij...

    2014 doi

  58. [67]

    Prob- abilistic forecasts, calibration and sharpness,

    T. Gneiting, F. Balabdaoui, and A. E. Raftery, “Prob- abilistic forecasts, calibration and sharpness,” Jour- nal of the Royal Statistical Society: Series B (Statisti- cal Methodology), vol. 69, no. 2, pp. 243–268, 2007. DOI: 10.1111/j.1467-9868.2007.00587.x

    2007

  59. [68]

    PyTorch Forecasting

    J. Beitner. “PyTorch Forecasting.” (2020), [On- line]. Available: https://towardsdatascience. com / introducing - pytorch - forecasting - 64de99b9ef46 (visited on 01/02/2021)

    2020

  60. [69]

    1016 / j

    DOI: 10 . 1016 / j . apenergy . 2018 . 11

    2018

  61. [70]

    Scikit-learn: Machine learning in Python,

    F. Pedregosa et al., “Scikit-learn: Machine learning in Python,” Journal of Machine Learning Research, vol. 12, no. 85, pp. 2825–2830, 2011

    2011

  62. [71]

    Amazon EC2 G4 in- stances

    Amazon Web Services, Inc. “Amazon EC2 G4 in- stances.” (2024), [Online]. Available: https : / / aws.amazon.com/ec2/instance- types/g4/ (visited on 05/01/2024)

    2024

  63. [72]

    Minimum redundancy fea- ture selection from microarray gene expression data,

    C. Ding and H. Peng, “Minimum redundancy fea- ture selection from microarray gene expression data,” in Computational Systems Bioinformatics. CSB2003. Proceedings of the 2003 IEEE Bioinfor- matics Conference. CSB2003, 2003, pp. 523–528. DOI: 10.1109/CSB.2003.1227396

    2003 arXiv

  64. [73]

    The impact of fore- cast characteristics on the forecast value for the dispatchable feeder,

    D. Werling, M. Beichter, B. Heidrich, K. Phipps, R. Mikut, and V . Hagenmeyer, “The impact of fore- cast characteristics on the forecast value for the dispatchable feeder,” in Companion Proceedings of the 14th ACM International Conference on Fu- ture Energy Systems, ser. e-Ene...

    2023

  65. [74]

    sktime: A unified inter- face for machine learning with time series,

    M. Löning, A. Bagnall, S. Ganesh, V . Kazakov, J. Lines, and F. J. Király, “sktime: A unified inter- face for machine learning with time series,” in 2019 Workshop on Systems for ML at NeurIPS, Vancou- ver, Canada, 2019

    2019

  66. [75]

    Multi-step-ahead time series prediction using multiple-output support vec- tor regression,

    Y . Bao, T. Xiong, and Z. Hu, “Multi-step-ahead time series prediction using multiple-output support vec- tor regression,” Neurocomputing, vol. 129, pp. 482– 493, 2014, ISSN : 0925-2312. DOI: 10 . 1016 / j . neucom.2013.09.010

    2014

  67. [76]

    Chollet et al., Keras, https://keras.io, 2015

    F. Chollet et al., Keras, https://keras.io, 2015

    2015

  68. [83]

    XGBoost: A scalable tree boosting system,

    T. Chen and C. Guestrin, “XGBoost: A scalable tree boosting system,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , ser. KDD ’16, San Francisco, USA: Association for Computing Ma- chinery, 2016, pp. 785–794, ISBN : 97814...

    2016

  69. [97]

    Available: https://open-power- system-data.org/

    [Online]. Available: https://open-power- system-data.org/. 22 AutoPQ MEISENBACHER et al

  70. [2019]

    DOI: 10.1016/j.enbuild.2019.109384

    2019

  71. [2020]

    DOI: 10.1109/JSAC.2019.2951973

    2019

  72. [2022]

    DOI: 10.1002/widm.1475

    doi

  73. [2619]

    1016 / j

    DOI: 10 . 1016 / j . apenergy . 2017 . 08 . 133

    2017

  74. [3417]

    DOI: 10.3390/app12041823

    doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.