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REVIEW 4 major objections 5 minor 39 references

Customer Lifetime Value Prediction with Uncertainty Estimation Using Monte Carlo Dropout

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

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Pith's one-line read Running dropout at test time adds uncertainty estimates to lifetime-value forecasts and roughly halves top-5% MAPE on mobile-game data.

desk verdict Applies Monte Carlo dropout to LTV prediction, with a novel-looking confidence metric that is statistically invalid and does not support the paper's central contribution. read the letter →

arxiv 2411.15944 v1 pith:IDZ3ZEDV submitted 2024-11-24 cs.LG

Xinzhe Cao , Yadong Xu , Xiaofeng Yang This is my paper · ORCID
classification cs.LG
keywords customerlifetimevalueLTVpredictionMonteCarlodropoutuncertaintyestimationconfidenceintervalsDCNv2mobilegamemonetizationtopspender
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

Customer lifetime value (LTV) prediction in industry usually returns a single dollar amount per user, with no sense of how much the model trusts it. This paper tries to establish that Monte Carlo dropout—keeping dropout active during prediction and averaging many stochastic forward passes—attaches an uncertainty estimate to each LTV forecast without adding a new module or retraining procedure. Benchmarking on roughly three million users from a mobile game with over one billion downloads, the authors report that this inference-time change improves normalized Gini and top-5% hit rate, and cuts top-5% MAPE from 0.4835 to 0.1858 on an MLP and from 0.4226 to 0.2003 on DCNv2, a deep-and-cross network. If the claim holds, businesses could flag low-confidence predictions and make safer spending and targeting decisions using the same neural networks they already deploy.

What carries the argument

The load-bearing mechanism is Monte Carlo Dropout treated as approximate Bayesian inference. Instead of switching dropout off at test time, the model runs $T$ stochastic forward passes and combines them by $\hat{y} = \frac{1}{T}\sum_{j=1}^{T} f(x; w\cdot d_j)$, where $d_j$ is the dropout mask for trial $j$; the sample variance $\hat{\sigma}_i$ across trials measures prediction uncertainty. The paper's confidence metric is built from the interval $\hat{y}_i \pm z \hat{\sigma}_i/\sqrt{T}$ with a confidence threshold $z\in[0,1]$, and accuracy is the fraction of true labels inside that interval. This machinery supplies uncertainty at inference time without modifying training or adding a Gaussian-process block, which is what keeps the method cheap enough for production LTV prediction.

What would settle it

Take the same data and models, compute the empirical coverage of the proposed intervals at $z=1.96$, and check whether about 95% of true LTV values fall inside; if coverage falls far short of 95% and does not track the threshold, the confidence measure is uncalibrated and the core novelty fails.

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Extended reading notes

Core claim

The paper's central claim is that Monte Carlo dropout is the first uncertainty quantification for LTV prediction that is purely neural-network-based and needs no auxiliary modules. The framework treats each trained network's weights as an approximate Bayesian model: for each test user, it performs T forward passes with randomly sampled dropout masks, takes the mean as the forecast, and takes the variance as the model's uncertainty. On the paper's dataset this procedure improves the normalized Gini coefficient, top-5% hit rate, and top-5% MAPE for both the MLP and DCNv2 architectures, with the largest gains on the weaker MLP baseline. The authors also present accuracy-versus-confidence curves as a new evaluation dimension for choosing between LTV models.

Load-bearing premise

The load-bearing premise is that the interval $\hat{y}_i \pm z \hat{\sigma}_i/\sqrt{T}$, with $z$ chosen between 0 and 1, is a meaningful confidence measure; if that interval does not actually track the chance that the true value falls inside it, the paper's uncertainty claim collapses.

Editorial extensions

If this is right

  • Top-5% MAPE drops from 0.4835 to 0.1858 for MLP and from 0.4226 to 0.2003 for DCNv2, so the inference-time change alone can roughly halve error on the highest-value users.
  • Uncertainty estimates are available per user with no extra trained module, so existing neural LTV models can be upgraded by changing only the inference procedure.
  • The accuracy-versus-confidence curve gives an extra axis for model selection; in the paper's experiments MCD-DCNv2 is more confident at every threshold than MCD-MLP, while trading only a small drop in Gini and MAPE.
  • Both MCD models improve as the number of stochastic passes increases and converge, suggesting a practical knob for balancing compute and accuracy.

Reading between the lines

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

  • Because the paper restricts $z$ to $[0,1]$, its interval is narrower than a conventional confidence interval; extending the accuracy-versus-confidence curve to $z=1.96$ and checking whether coverage approaches 95% would test whether the confidence score is calibrated.
  • If the uncertainty scores are trustworthy, businesses could filter out low-confidence predictions before acting, for example by excluding the least certain top-spender candidates from a campaign; the resulting revenue lift is directly measurable.
  • The same inference-time averaging could be combined with ensemble-based uncertainty estimates and used as a feature in user segmentation, directions the paper's future-work section already anticipates.
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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 applying Monte Carlo Dropout (MCD) to customer lifetime value (LTV) prediction, using T stochastic forward passes at inference to estimate a predictive mean and variance. Two neural architectures (MLP and DCNv2) are augmented with MCD and evaluated on a large mobile-game dataset. The authors report improvements in normalized Gini, Top-5% MAPE, and hit-rate over raw models and a Ziln baseline, and introduce an 'accuracy vs confidence' curve based on intervals yhat ± z*sigma/sqrt(T) with z in [0,1].

Significance. If the reported gains are reproducible, applying MCD to LTV would offer a low-cost way to obtain both point predictions and uncertainty estimates in production, which is practically valuable for identifying high-value users. The paper also attempts to evaluate uncertainty calibration in this domain, a topic that is underrepresented in LTV research. However, the proposed confidence metric is statistically invalid as defined, and the empirical evaluation lacks the rigor needed to support the claimed improvements. The core MCD idea is sound, but the manuscript in its current form does not provide a credible uncertainty quantification contribution.

major comments (4)
  1. [§3.2 (CI formula)] The interval CI = yhat_i ± z*sigma_i/sqrt(T) uses the standard error of the mean, not the predictive standard deviation. For coverage of individual true labels, the interval should scale with the predictive standard deviation or a calibrated quantile, not shrink as 1/sqrt(T). With z restricted to [0,1] and T typically large, the interval width tends to zero, so the empirical coverage of true labels will approach zero rather than track any meaningful confidence level. The accuracy-versus-z curve in Figure 1 is therefore not a valid confidence measure, and contribution 3 is unsupported as stated.
  2. [§3.2 / Table 1] The paper states that 'best performed MCD settings were selected' but does not describe the selection protocol, such as whether a validation set was used, what hyperparameters were tuned, or what dropout rates and T values were chosen. With no repeated runs, no error bars, and no statistical significance tests, the dramatic MAPE improvements (e.g., MLP Top-5% MAPE from 0.4835 to 0.1858) may be optimistically biased or due to overfitting the test set. A rigorous evaluation with multiple seeds and a validation-based selection procedure is needed to support contribution 2.
  3. [§3.1 and Appendix A] The dataset is described only as approximately 3 million users from a mobile game; the appendix is referenced for 'standard LTV prediction metrics' but contains only figures and no metric definitions. Feature descriptions, preprocessing steps, train/validation/test split, hyperparameters, dropout rates, T values, and Ziln training details are all missing. These omissions prevent reproducibility and make it difficult to assess whether the comparison against Ziln is fair.
  4. [§1 (Contribution 1)] The claim that this is 'the first LTV prediction model purely based on neural networks that provide uncertainty quantification' is not substantiated by a literature review. Prior work on Bayesian deep learning, deep ensembles, and uncertainty quantification in regression should be discussed, particularly any applications to LTV or similar economic prediction tasks. Without a systematic comparison or at least a targeted search, the 'first' claim is too strong and should be qualified or removed.
minor comments (5)
  1. [§2, Eq. (1)] The notation 'w · dj' is ambiguous; please specify that dj is a binary dropout mask applied element-wise to the weights or activations.
  2. [§3.2] The term 'confidence interval' is misleading in this context; if the intent is to quantify predictive uncertainty for individual outcomes, the term 'prediction interval' or 'credible interval' would be more appropriate.
  3. [§3.2 / Figure 1] Figure 1 does not report the dropout rate, the number of Monte Carlo trials T, or the base model architecture used to generate the curves, so the reader cannot interpret the accuracy-versus-confidence relationship.
  4. [§3.2] The sentence 'there remains a performance gap of 10%' is unclear; please specify whether this is an absolute percentage-point difference in accuracy or a relative difference, and at which z value it is evaluated.
  5. [Appendix A] The appendix is referenced as containing 'additional details on standard LTV prediction metrics,' but it only shows supplementary figures; the promised metric definitions (Gini, MAPE, hit-rate) are missing.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the MCD framework is an externally established method, and the reported LTV metrics are standard benchmark quantities that no fitted parameter is constructed to match.

full rationale

The paper's central derivation is the Monte Carlo Dropout prediction formula (Eq. 1), taken directly from the published drop-out-as-Bayesian-approximation framework of Gal and Ghahramani, not from the authors' own prior work. The empirical claims are evaluated with standard LTV metrics: normalized Gini coefficient, Top 5% MAPE, and Top 5% hit-rate. None of these metrics is used to define or fit the model; they are external benchmark quantities computed after training. The proposed confidence metric, CI = yhat ± z * sigma / sqrt(T), is an evaluation tool rather than a fitted prediction, and even though the interval formula and the z in [0,1] restriction are statistically questionable, that is a correctness or calibration concern, not circularity. There are no self-citations that carry the argument, no uniqueness theorem imported from the authors' own work, and no ansatz smuggled in via citation. The paper is self-contained against external baselines and benchmarks, so the appropriate circularity score is 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper's central claim rests on the well-known MCD approximation, an unproved assumption about the reliability of the confidence interval formula, and the representativeness of a single proprietary game dataset. No new entities are introduced.

free parameters (2)
  • dropout rate
    Standard hyperparameter for MCD; not reported in the paper, but affects both the uncertainty estimates and the predictive accuracy.
  • number of MC trials T
    Chosen by the authors as 'best performed MCD settings', not derived; affects variance and runtime.
assumptions (3)
  • domain assumption Dropout training in DNNs approximates Bayesian inference in deep Gaussian processes (Gal & Ghahramani, 2016).
    Invoked in Section 2 to justify using MCD for uncertainty quantification.
  • domain assumption The label distribution is zero-inflated, so top 5% MAPE is used instead of global MAPE because global MAPE is infinite.
    Assumed to justify the evaluation metric; no alternative metric validation.
  • domain assumption The dataset of about 3 million users from a single mobile game is representative enough for generalizable conclusions.
    The paper uses this dataset without evidence of external validity.

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Cite this review

Pith. "Pith review of Customer Lifetime Value Prediction with Uncertainty Estimation Using Monte Carlo Dropout." pith.science (2026). https://pith.science/paper/IDZ3ZEDV

@misc{pith2026241115944,
  author       = {Pith},
  title        = {Pith review of: Customer Lifetime Value Prediction with Uncertainty Estimation Using Monte Carlo Dropout},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IDZ3ZEDV}},
  note         = {Machine review of arXiv:2411.15944}
}
read the original abstract

Accurately predicting customer Lifetime Value (LTV) is crucial for companies to optimize their revenue strategies. Traditional deep learning models for LTV prediction are effective but typically provide only point estimates and fail to capture model uncertainty in modeling user behaviors. To address this limitation, we propose a novel approach that enhances the architecture of purely neural network models by incorporating the Monte Carlo Dropout (MCD) framework. We benchmarked the proposed method using data from one of the most downloaded mobile games in the world, and demonstrated a substantial improvement in predictive Top 5\% Mean Absolute Percentage Error compared to existing state-of-the-art methods. Additionally, our approach provides confidence metric as an extra dimension for performance evaluation across various neural network models, facilitating more informed business decisions.

Figures

Figures reproduced from arXiv: 2411.15944 by the authors.

Figure 1
Figure 1. Model accuracy across different confidence intervals [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Major metrics using different MCD trials. Both the normalized Gini coefficient and MAPE [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

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Reference graph

Works this paper leans on

39 extracted references · 20 canonical work pages

  1. [1]

    Rfm and clv: Using iso-value curves for customer base analysis

    Peter S Fader, Bruce GS Hardie, and Ka Lok Lee. Rfm and clv: Using iso-value curves for customer base analysis. Journal of marketing research, 42(4):415–430, 2005

    work page 2005

  2. [2]

    counting your customers

    Peter S Fader, Bruce GS Hardie, and Ka Lok Lee. “counting your customers” the easy way: An alternative to the pareto/nbd model. Marketing science, 24(2):275–284, 2005

    work page 2005

  3. [3]

    Estimating customer lifetime value based on rfm analysis of customer purchase behavior: Case study

    Mahboubeh Khajvand, Kiyana Zolfaghar, Sarah Ashoori, and Somayeh Alizadeh. Estimating customer lifetime value based on rfm analysis of customer purchase behavior: Case study. Procedia computer science, 3:57–63, 2011

    work page 2011

  4. [4]

    A deep probabilistic model for customer lifetime value prediction

    Xiaojing Wang, Tianqi Liu, and Jingang Miao. A deep probabilistic model for customer lifetime value prediction. arXiv preprint arXiv:1912.07753, 2019

    arXiv 1912

  5. [5]

    percltv: A general system for personalized customer lifetime value prediction in online games

    Shiwei Zhao, Runze Wu, Jianrong Tao, Manhu Qu, Minghao Zhao, Changjie Fan, and Hongke Zhao. percltv: A general system for personalized customer lifetime value prediction in online games. ACM Transactions on Information Systems, 41(1):1–29, 2023

    work page 2023

  6. [6]

    Customer lifetime value in video games using deep learning and parametric models

    Pei Pei Chen, Anna Guitart, Ana Fernández del Río, and Africa Periánez. Customer lifetime value in video games using deep learning and parametric models. In 2018 IEEE international conference on big data (big data), pages 2134–2140. IEEE, 2018

    work page 2018

  7. [7]

    Out of the box thinking: Improving customer lifetime value modelling via expert routing and game whale detection

    Shijie Zhang, Xin Yan, Xuejiao Yang, Binfeng Jia, and Shuangyang Wang. Out of the box thinking: Improving customer lifetime value modelling via expert routing and game whale detection. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pages 3206–3215, 2023

    work page 2023

  8. [8]

    Bayesian quicknat: Model uncertainty in deep whole-brain segmentation for structure-wise quality control

    Abhijit Guha Roy, Sailesh Conjeti, Nassir Navab, Christian Wachinger, Alzheimer’s Dis- ease Neuroimaging Initiative, et al. Bayesian quicknat: Model uncertainty in deep whole-brain segmentation for structure-wise quality control. NeuroImage, 195:11–22, 2019

    work page 2019

Show all 39 references
  1. [9]

    Training confidence-calibrated classifiers for detecting out-of-distribution samples

    Kimin Lee, Honglak Lee, Kibok Lee, and Jinwoo Shin. Training confidence-calibrated classifiers for detecting out-of-distribution samples. arXiv preprint arXiv:1711.09325, 2017

    2017 arXiv

  2. [10]

    On the validity of bayesian neural networks for uncertainty estimation

    John Mitros and Brian Mac Namee. On the validity of bayesian neural networks for uncertainty estimation. arXiv preprint arXiv:1912.01530, 2019

    1912 arXiv

  3. [11]

    Can you trust your model’s uncertainty? evaluating predictive uncertainty under dataset shift

    Yaniv Ovadia, Emily Fertig, Jie Ren, Zachary Nado, David Sculley, Sebastian Nowozin, Joshua Dillon, Balaji Lakshminarayanan, and Jasper Snoek. Can you trust your model’s uncertainty? evaluating predictive uncertainty under dataset shift. Advances in neural information processi...

    2019

  4. [12]

    Test-time data augmentation for estimation of heteroscedastic aleatoric uncertainty in deep neural networks

    Murat Seckin Ayhan and Philipp Berens. Test-time data augmentation for estimation of heteroscedastic aleatoric uncertainty in deep neural networks. In Medical Imaging with Deep Learning, 2018

    2018

  5. [13]

    On calibration of modern neural networks

    Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q Weinberger. On calibration of modern neural networks. In International conference on machine learning, pages 1321–1330. PMLR, 2017

    2017

  6. [14]

    Bayesian deep learning and a probabilistic perspective of generalization

    Andrew G Wilson and Pavel Izmailov. Bayesian deep learning and a probabilistic perspective of generalization. Advances in neural information processing systems, 33:4697–4708, 2020

    2020

  7. [15]

    Uncertainty in deep learning

    Yarin Gal et al. Uncertainty in deep learning. 2016

    2016

  8. [16]

    Geometry and uncertainty in deep learning for computer vision

    Alex Guy Kendall. Geometry and uncertainty in deep learning for computer vision. PhD thesis, University of Cambridge, 2019

    2019

  9. [17]

    Weight uncertainty in neural network

    Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty in neural network. In International conference on machine learning, pages 1613–1622. PMLR, 2015

    2015

  10. [18]

    Dropconnect is effective in modeling uncertainty of bayesian deep networks

    Aryan Mobiny, Pengyu Yuan, Supratik K Moulik, Naveen Garg, Carol C Wu, and Hien Van Nguyen. Dropconnect is effective in modeling uncertainty of bayesian deep networks. Scientific reports, 11(1):5458, 2021. 6

    2021

  11. [19]

    Spatial uncertainty sampling for end-to-end control

    Alexander Amini, Ava Soleimany, Sertac Karaman, and Daniela Rus. Spatial uncertainty sampling for end-to-end control. arXiv preprint arXiv:1805.04829, 2018

    2018 arXiv

  12. [20]

    Bayesian hypernetworks

    David Krueger, Chin-Wei Huang, Riashat Islam, Ryan Turner, Alexandre Lacoste, and Aaron Courville. Bayesian hypernetworks. arXiv preprint arXiv:1710.04759, 2017

    2017 arXiv

  13. [21]

    Non-parametric calibration for classification

    Jonathan Wenger, Hedvig Kjellström, and Rudolph Triebel. Non-parametric calibration for classification. In International Conference on Artificial Intelligence and Statistics , pages 178–190. PMLR, 2020

    2020

  14. [22]

    Simple and scalable predictive uncertainty estimation using deep ensembles

    Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems, 30, 2017

    2017

  15. [23]

    Deep sub-ensembles for fast uncertainty estimation in image classifi- cation

    Matias Valdenegro-Toro. Deep sub-ensembles for fast uncertainty estimation in image classifi- cation. arXiv preprint arXiv:1910.08168, 2019

    1910 arXiv

  16. [24]

    Batchensemble: an alternative approach to efficient ensemble and lifelong learning

    Yeming Wen, Dustin Tran, and Jimmy Ba. Batchensemble: an alternative approach to efficient ensemble and lifelong learning. arXiv preprint arXiv:2002.06715, 2020

    2002 arXiv

  17. [25]

    Dropout as a bayesian approximation: Representing model uncertainty in deep learning

    Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. Ininternational conference on machine learning, pages 1050–1059. PMLR, 2016

    2016

  18. [26]

    Harnessing model uncertainty for detecting adversarial examples

    MINA Rawat, Martin Wistuba, and Maria-Irina Nicolae. Harnessing model uncertainty for detecting adversarial examples. In NIPS Workshop on Bayesian Deep Learning, 2017

    2017

  19. [27]

    Understanding measures of uncertainty for adversarial example detection

    Lewis Smith and Yarin Gal. Understanding measures of uncertainty for adversarial example detection. arXiv preprint arXiv:1803.08533, 2018

    2018 arXiv

  20. [28]

    Adversarial examples-a complete characterisation of the phenomenon

    Alexandru Constantin Serban, Erik Poll, and Joost Visser. Adversarial examples-a complete characterisation of the phenomenon. arXiv preprint arXiv:1810.01185, 2018

    2018 arXiv

  21. [29]

    Predictive uncertainty estimation via prior networks.Advances in neural information processing systems, 31, 2018

    Andrey Malinin and Mark Gales. Predictive uncertainty estimation via prior networks.Advances in neural information processing systems, 31, 2018

    2018

  22. [30]

    Information robust dirichlet networks for predictive uncertainty estimation, April 8 2021

    Theodoros Tsiligkaridis. Information robust dirichlet networks for predictive uncertainty estimation, April 8 2021. US Patent App. 17/064,046

    2021

  23. [31]

    Evidential deep learning to quantify classification uncertainty

    Murat Sensoy, Lance Kaplan, and Melih Kandemir. Evidential deep learning to quantify classification uncertainty. Advances in neural information processing systems, 31, 2018

    2018

  24. [32]

    Ensemble distribution distillation

    Andrey Malinin, Bruno Mlodozeniec, and Mark Gales. Ensemble distribution distillation. arXiv preprint arXiv:1905.00076, 2019

    1905 arXiv

  25. [33]

    Direct uncertainty prediction for medical second opinions

    Maithra Raghu, Katy Blumer, Rory Sayres, Ziad Obermeyer, Bobby Kleinberg, Sendhil Mul- lainathan, and Jon Kleinberg. Direct uncertainty prediction for medical second opinions. In International Conference on Machine Learning, pages 5281–5290. PMLR, 2019

    2019

  26. [34]

    Dcn v2: Improved deep & cross network and practical lessons for web-scale learning to rank systems

    Ruoxi Wang, Rakesh Shivanna, Derek Cheng, Sagar Jain, Dong Lin, Lichan Hong, and Ed Chi. Dcn v2: Improved deep & cross network and practical lessons for web-scale learning to rank systems. In Proceedings of the web conference 2021, pages 1785–1797, 2021

    2021

  27. [35]

    Free-to-play: About addicted whales, at risk dolphins and healthy minnows

    Michael Dreier, Klaus Wölfling, Eva Duven, Sebastián Giralt, Manfred E Beutel, and Kai W Müller. Free-to-play: About addicted whales, at risk dolphins and healthy minnows. moneta- rization design and internet gaming disorder. Addictive behaviors, 64:328–333, 2017

    2017

  28. [36]

    Whales, dolphins, or minnows? towards the player clustering in free online games based on purchasing behavior via data mining technique

    Wanshan Yang, Gemeng Yang, Ting Huang, Lijun Chen, and Youjian Eugene Liu. Whales, dolphins, or minnows? towards the player clustering in free online games based on purchasing behavior via data mining technique. In 2018 IEEE International Conference on Big Data (Big Data), pag...

    2018

  29. [37]

    From minnows to whales: An empirical study of purchase behavior in freemium social games

    Savannah Wei Shi, Mu Xia, and Yun Huang. From minnows to whales: An empirical study of purchase behavior in freemium social games. International Journal of Electronic Commerce, 20(2):177–207, 2015. 7

    2015

  30. [38]

    Ensemble deep learning: A review

    Mudasir A Ganaie, Minghui Hu, Ashwani Kumar Malik, Muhammad Tanveer, and Ponnuthu- rai N Suganthan. Ensemble deep learning: A review. Engineering Applications of Artificial Intelligence, 115:105151, 2022

    2022

  31. [39]

    Deep ensembles: A loss landscape perspective

    Stanislav Fort, Huiyi Hu, and Balaji Lakshminarayanan. Deep ensembles: A loss landscape perspective. arXiv preprint arXiv:1912.02757, 2019. 8 A Appendix: Supplementary Figures In the previous results section, the optimal prediction outcomes generated by various model architec-...

    1912 arXiv

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