Learning to Simulate from Heavy-Tailed Distribution via Diffusion Model

Published Online:https://doi.org/10.1287/opre.2024.1450

References

  • Agrawal S, Juneja S, Glynn P (2020) Optimal delta-correct best-arm selection for heavy-tailed distributions. Proc. 31st Internat. Conf. Algorithmic Learn. Theory (PMLR, New York), 61–110.Google Scholar
  • Araman VF, Glynn PW (2023) Gaussian limits for scheduled traffic with super-heavy tailed perturbations. Preprint, submitted March 10, https://arxiv.org/abs/2303.05939.Google Scholar
  • Biloš M, Rasul K, Schneider A, Nevmyvaka Y, Günnemann S (2023) Modeling temporal data as continuous functions with stochastic process diffusion. Proc. 40th Internat. Conf. Machine Learn. (PMLR, New York), 2452–2470.Google Scholar
  • Blanchet J, Glynn P (2008) Efficient rare-event simulation for the maximum of heavy-tailed random walks. Ann. Appl. Probab. 18(4):1351–1378.Crossref, Google Scholar
  • Blanchet J, Lam H (2012) State-dependent importance sampling for rare-event simulation: An overview and recent advances. Surveys Oper. Res. Management Sci. 17(1):38–59.Crossref, Google Scholar
  • Boxma OJ, Cohen J (1999) Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions. Queueing Systems 33(1–3):177–204.Google Scholar
  • Cao H, Tan C, Gao Z, Xu Y, Chen G, Heng PA, Li SZ (2024) A survey on generative diffusion models. IEEE Trans. Knowledge Data Engrg. 36(7):2814–2830.Crossref, Google Scholar
  • Chen N, Zhang Y, Zen H, Weiss RJ, Norouzi M, Chan W (2021) WaveGrad: Estimating gradients for waveform generation. 9th Internat. Conf. Learn. Representations (ICLR 2021), held virtually, May 3–7 (OpenReview.net).Google Scholar
  • Coletta A, Gopalakrishan S, Borrajo D, Vyetrenko S (2023) On the constrained time-series generation problem. Preprint, submitted September 14, https://arxiv.org/abs/2307.01717.Google Scholar
  • Cont R, Cucuringu M, Xu R, Zhang C (2025) Tail-GAN: Learning to simulate tail risk scenarios. Management Sci. 72(4):2917–2936.Google Scholar
  • Deasy J, Simidjievski N, Liò P (2021) Heavy-tailed denoising score matching. Preprint, submitted December 17, https://arxiv.org/abs/2112.09788.Google Scholar
  • Dhariwal P, Nichol A (2021) Diffusion models beat GANs on image synthesis. Adv. Neural Inform. Processing Systems, vol. 34 (Curran Associates, Red Hook, NY), 8780–8794.Google Scholar
  • Down D, Meyn SP, Tweedie RL (1995) Exponential and uniform ergodicity of Markov processes. Ann. Probab. 23(4):1671–1691.Crossref, Google Scholar
  • Esteban C, Hyland SL, Rätsch G (2017) Real-valued (medical) time series generation with recurrent conditional GANs. Preprint, submitted December 4, https://arxiv.org/abs/1706.02633.Google Scholar
  • Fan L, Glynn PW (2025) The fragility of optimized bandit algorithms. Oper. Res. 73(6):3173–3198.Google Scholar
  • Fanaee-T H, Gama J (2014) Event labeling combining ensemble detectors and background knowledge. Progress Artificial Intelligence 2(2–3):113–127.Crossref, Google Scholar
  • Glynn PW, Whitt W (1994) Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. J. Appl. Probab. 31(A):131–156.Crossref, Google Scholar
  • Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2020) Generative adversarial networks. Commun. ACM 63(11):139–144.Crossref, Google Scholar
  • Graikos A, Malkin N, Jojic N, Samaras D (2022) Diffusion models as plug-and-play priors. Adv. Neural Inform. Processing Systems, vol. 35 (Curran Associates, Red Hook, NY), 14715–14728.Crossref, Google Scholar
  • He S, Jiang G, Lam H, Fu MC (2023) Adaptive importance sampling for efficient stochastic root finding and quantile estimation. Oper. Res. 72(6):2612–2630.Link, Google Scholar
  • Henderson SG, Nelson BL (2006) Handbooks in Operations Research and Management Science: Simulation (Elsevier, Amsterdam).Google Scholar
  • Hill BM (1975) A simple general approach to inference about the tail of a distribution. Ann. Statist. 3(5):1163–1174.Crossref, Google Scholar
  • Ho J, Salimans T (2022) Classifier-free diffusion guidance. Preprint, submitted July 26, https://arxiv.org/abs/2207.12598.Google Scholar
  • Ho J, Jain A, Abbeel P (2020) Denoising diffusion probabilistic models. Adv. Neural Inform. Processing Systems, vol. 33 (Curran Associates, Red Hook, NY), 6840–6851.Google Scholar
  • Kim S, Kim H (2016) A new metric of absolute percentage error for intermittent demand forecasts. Internat. J. Forecasting 32(3):669–679.Crossref, Google Scholar
  • Kong Z, Ping W, Huang J, Zhao K, Catanzaro B (2020) DiffWave: A versatile diffusion model for audio synthesis. 9th Internat. Conf. Learn. Representations (ICLR 2021), held virtually, May 3–7 (OpenReview.net).Google Scholar
  • Kotelnikov A, Baranchuk D, Rubachev I, Babenko A (2023) TabDDPM: Modelling tabular data with diffusion models. Internat. Conf. Machine Learn. (PMLR, New York), 17564–17579.Google Scholar
  • Lam H, Mottet C (2017) Tail analysis without parametric models: A worst-case perspective. Oper. Res. 65(6):1696–1711.Link, Google Scholar
  • Li Y, Schwing A, Wang KC, Zemel R (2017) Dualing GANs. Adv. Neural Inform. Processing Systems, vol. 30 (Curran Associates, Red Hook, NY), 5607–5617.Crossref, Google Scholar
  • Loretan M, Phillips PC (1994) Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets. J. Empirical Finance 1(2):211–248.Crossref, Google Scholar
  • Mescheder L, Nowozin S, Geiger A (2017) The numerics of GANs. Adv. Neural Inform. Processing Systems, vol. 30 (Curran Associates, Red Hook, NY).Google Scholar
  • Mogren O (2016) Continuous recurrent neural networks with adversarial training. Preprint, submitted November 29, https://arxiv.org/abs/1611.09904.Google Scholar
  • Niu C, Song Y, Song J, Zhao S, Grover A, Ermon S (2020) Permutation invariant graph generation via score-based generative modeling. Proc. 23rd Internat. Conf. Artificial Intelligence Statist., Proceedings of Machine Learning Research, vol. 108 (PMLR, New York), 4474–4484.Google Scholar
  • Roberts GO, Tweedie RL (1996) Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 2(4):341–363.Crossref, Google Scholar
  • Saharia C, Ho J, Chan W, Salimans T, Fleet DJ, Norouzi M (2023) Image super-resolution via iterative refinement. IEEE Trans. Pattern Anal. Machine Intelligence 45(4):4713–4726.Google Scholar
  • Schmidt T (2006) Coping with copulas. Rank J, ed. Copulas: From Theory to Applications in Finance (Risk Books, London), 1–31.Google Scholar
  • Sigman K (1999) A primer on heavy-tailed distributions. Queueing Systems 33(1–3):261.Crossref, Google Scholar
  • Simchi-Levi D, Zheng Z, Zhu F (2022) A simple and optimal policy design for online learning with safety against heavy-tailed risk. Adv. Neural Inform. Processing Systems, vol. 35 (Curran Associates, Red Hook, NY), 33795–33805.Google Scholar
  • Simchi-Levi D, Zheng Z, Zhu F (2025) A simple and optimal policy design with safety against heavy-tailed risk for stochastic bandits. Management Sci. 71(7):6298–6318.Link, Google Scholar
  • Song Y, Ermon S (2019) Generative modeling by estimating gradients of the data distribution. Adv. Neural Inform. Processing Systems, vol. 32 (Curran Associates, Red Hook, NY), 11895–11907.Google Scholar
  • Song Y, Ermon S (2020) Improved techniques for training score-based generative models. Adv. Neural Inform. Processing Systems, vol. 33 (Curran Associates, Red Hook, NY), 12438–12448.Google Scholar
  • Tang W (2024) Fine-tuning of diffusion models via stochastic control: Entropy regularization and beyond. Preprint, submitted March 10, https://arxiv.org/abs/2403.06279v1.Google Scholar
  • Tang W, Zhao H (2024) Score-based diffusion models via stochastic differential equations—A technical tutorial. Preprint, submitted February 12, https://arxiv.org/abs/2402.07487v1.Google Scholar
  • Tang W, Zhou XY (2023) Tail probability estimates of continuous-time simulated annealing processes. Numer. Algebra Control Optim. 13(3–4):473–485.Crossref, Google Scholar
  • Tashiro Y, Song J, Song Y, Ermon S (2021) CSDI: Conditional score-based diffusion models for probabilistic time series imputation. Adv. Neural Inform. Processing Systems, vol. 34 (Curran Associates, Red Hook, NY), 24804–24816.Google Scholar
  • Vincent P (2011) A connection between score matching and denoising autoencoders. Neural Comput. 23(7):1661–1674.Crossref, Google Scholar
  • Welling M, Teh YW (2011) Bayesian learning via stochastic gradient Langevin dynamics. Proc. 28th Internat. Conf. Machine Learn. ICML-11 (Omnipress, Madison, WI), 681–688.Google Scholar
  • Yang L, Zhang Z, Song Y, Hong S, Xu R, Zhao Y, Zhang W, Cui B, Yang MH (2024) Diffusion models: A comprehensive survey of methods and applications. ACM Comput. Surveys 56(4):105.Crossref, Google Scholar
  • Yoon J, Jarrett D, Van der Schaar M (2019) Time-series generative adversarial networks. Adv. Neural Inform. Processing Systems, vol. 32 (Curran Associates, Red Hook, NY), 5508–5518.Google Scholar
  • Yoon EB, Park K, Kim S, Lim S (2023) Score-based generative models with Lévy processes. Adv. Neural Inform. Processing Systems, vol. 36 (Curran Associates, Red Hook, NY), 40694–40707.Google Scholar
  • Yu Y, Yu L (2026) Diffusion models with heavy-tailed targets: Score estimation and sampling guarantees. Preprint, submitted January 10, https://arxiv.org/abs/2601.06715.Google Scholar
  • Zeevi A, Glynn PW (2004) Recurrence properties of autoregressive processes with super-heavy-tailed innovations. J. Appl. Probab. 41(3):639–653.Crossref, Google Scholar
  • Zhang T, Zheng H, Yao J, Wang X, Zhou M, Zhang Y, Wang Y (2024) Long-tailed diffusion models with oriented calibration. 12th Internat. Conf. Learn. Representations (ICLR 2024), Vienna, Austria, May 7–11 (OpenReview.net).Google Scholar
  • Zhao H, Chen H, Zhang J, Yao DD, Tang W (2024) Scores as actions: A framework of fine-tuning diffusion models by continuous-time reinforcement learning. Preprint, submitted September 12, https://arxiv.org/abs/2409.08400.Google Scholar
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