无似然时基于校准核与比率估计的后验推断方法

doi:10.7523/j.ucas.2024.023

摘要/Abstract

摘要： 在贝叶斯推断中常遇到的一个困难是似然函数难以评估或没有显示的表达式,这种情况被称为无似然贝叶斯问题,此时后验分布只能通过基于特定参数生成的样本来间接推断。无似然贝叶斯问题的主要挑战之一是如何在有限的样本生成次数内有效逼近后验分布,现有的计算方法包括近似贝叶斯计算、合成似然及贝叶斯优化等。Miller等（2022）提出了一种新的序贯比率估计方法,创新地将似然与证据比的估计转化为多分类问题,从而高效地推断后验分布。基于此方法,本研究进一步发展了一种基于校准核的比率估计新方法：校准比率后验推断方法,通过校准核为分类任务的样本赋予额外权重,增强了原方法的训练效率和性能。本文首先说明了新方法的收敛性,随后通过数值实验验证了其在有限样本生成条件下在多个指标上对参数后验分布估计的准确度有显著提高。

关键词: 无似然贝叶斯推断, 序贯比率估计, 对比学习

Abstract: Bayesian inference often faces challenges where the likelihood function is difficult to evaluate or lacks explicit expression, known as likelihood-free Bayesian problems, where posterior distributions can only be inferred indirectly through samples generated under specific parameters. Existing methods like approximate Bayesian computation, synthetic likelihood, and Bayesian optimization focus on address these issues. This paper extends Miller et al.'s (2022) sequential neural ratio estimation method for likelihood-free Bayesian problems by transforming likelihood-to-evidence ratio estimation into a multi-class problem for efficient posterior estimation. We introduce a new calibration kernel-based ratio estimation method (CKRE), to enhance the original method's training efficiency and performance. The convergence of our proposed methods is proven, and numerical experiments demonstrate its significant improvement in accurately estimating posterior distributions under limited sample generation conditions.

Key words: Likelihood-free Bayesian inference, Sequential neural ratio estimation, Contrastive learning

中图分类号:

O212.1

熊逸飞, 张三国. 无似然时基于校准核与比率估计的后验推断方法[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2024.023.

XIONG Yifei, ZHANG Sanguo. Calibration kernel-based ratio estimation for likelihood-free posterior inference^∗[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2024.023.

参考文献

[1] Paninski L, Cunningham J P.Neural data science: accelerating the experiment-analysis-theory cycle in large-scale neuroscience[J]. Current Opinion in Neurobiology, 2018, 50: 232-241. DOI: 10.1016/j.conb.2018.04.007.
[2] Brehmer J, Louppe G, Pavez J, et al.Mining gold from implicit models to improve likelihood-free inference[J]. PNAS, 2020, 117(10): 5242-5249. DOI: 10.1073/pnas.1915980117.
[3] Gonçalves P J, Lueckmann J M, Deistler M, et al.Training deep neural density estimators to identify mechanistic models of neural dynamics[J]. eLife, 2020, 9: e56261. DOI: 10.7554/eLife.56261.
[4] Hashemi M, Vattikonda A N, Jha J, et al.Amortized Bayesian inference on generative dynamical network models of epilepsy using deep neural density estimators[J]. Neural Networks, 2023, 163: 178-194. DOI: 10.1016/j.neunet.2023.03.040.
[5] Clarke R, Ressom H W, Wang A T, et al.The properties of high-dimensional data spaces: Implications for exploring gene and protein expression data[J]. Nature Reviews. Cancer, 2008, 8(1): 37-49. DOI: 10.1038/nrc2294.
[6] Romaszko L, Williams C K I, Moreno P, et al. Vision-as-inverse-graphics: Obtaining a rich 3D explanation of a scene from a single image[C]//2017 IEEE International Conference on Computer Vision Workshops (ICCVW). Venice, Italy. IEEE, 2017: 940-948. DOI: 10.1109/ICCVW.2017.115.
[7] Beaumont M A, Zhang W Y, Balding D J.Approximate Bayesian computation in population genetics[J]. Genetics, 2002, 162(4): 2025-2035. DOI: 10.1093/genetics/162.4.2025.
[8] Marin J M, Pudlo P, Robert C P, et al.Approximate Bayesian computational methods[J]. Statistics and Computing, 2012, 22(6): 1167-1180. DOI: 10.1007/s11222-011-9288-2.
[9] Wood S N.Statistical inference for noisy nonlinear ecological dynamic systems[J]. Nature, 2010, 466(7310): 1102-1104. DOI: 10.1038/nature09319.
[10] Price L F, Drovandi C C, Lee A, et al.Bayesian synthetic likelihood[J]. Journal of Computational and Graphical Statistics, 2018, 27(1): 1-11. DOI: 10.1080/10618600.2017.1302882.
[11] Gutmann M U, Corander J.Bayesian optimization for likelihood-free inference of simulator-based statistical models[J]. Journal of Machine Learning Research, 2016, 17(1): 4256-4302.DOI:10.48550/arXiv.1501.03291.
[12] Andrieu C, Roberts G O.The pseudo-marginal approach for efficient Monte Carlo computations[J]. The Annals of Statistics, 2009, 37(2): 697-725. DOI: 10.1214/07-aos574.
[13] Andrieu C, Doucet A, Holenstein R.Particle Markov chain Monte Carlo methods[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2010, 72(3): 269-342. DOI: 10.1111/j.1467-9868.2009.00736.x.
[14] Barthelmé S, Chopin N.Expectation propagation for likelihood-free inference[J]. Journal of the American Statistical Association, 2014, 109(505): 315-333. DOI: 10.1080/01621459.2013.864178.
[15] Kobyzev I, Prince S J D, Brubaker M A. Normalizing flows: an introduction and review of current methods[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021, 43(11): 3964-3979. DOI: 10.1109/TPAMI.2020.2992934.
[16] Papamakarios G, Sterratt D C, Murray I. Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows[EB/OL]. 2018: arXiv: 1805.07226. (2019-01-21)[2024-04-02]. http://arxiv.org/abs/1805.07226.
[17] Papamakarios G, Murray I. Fast ε-free inference of simulation models with Bayesian conditional density estimation[C/OL]//Proceedings of the 30th International Conference on Neural Information Processing Systems. December 5 - 10, 2016, Barcelona, Spain. ACM,2016: 1036-1044.(2016-12-10)[2024-04-02]. https://proceedings.neurips.cc/paper_files/paper/2016/hash/6aca97005c68f1206823815f66102863-Abstract.html.
[18] Lueckmann J M, Goncalves P J, Bassetto G, et al. Flexible statistical inference for mechanistic models of neural dynamics[C/OL]//Proceedings of the 31st International Conference on Neural Information Processing Systems. December 4-9, 2017, Long Beach, California,USA.ACM,2017: 1289-1299.(2017-12-10)[2024-04-02].https://proceedings.neurips.cc/paper/2017/hash/addfa9b7e234254d26e9c7f2af1005cb-Abstract.html.
[19] Greenberg D, Nonnenmacher M, Macke J. Automatic posterior transformation for likelihood-free inference[C/OL]// International Conference on Machine Learning. PMLR, 2019: 2404-2414. (2019-11-03)[2024-04-02]. https://proceedings.mlr.press/v97/greenberg19a.html.
[20] Hermans J, Begy V, Louppe G. Likelihood-free MCMC with amortized approximate ratio estimators[C/OL]//Proceedings of the 37th International Conference on Machine Learning. ACM, 2020: 4239-4248. (2020-12-27)[2024-04-02]. http://proceedings.mlr.press/v119/hermans20a.
[21] Durkan C, Murray I, Papamakarios G. On contrastive learning for likelihood-free inference[C/OL]//Proceedings of the 37th International Conference on Machine Learning. ACM, 2020: 2771-2781. (2020-12-27)[2024-04-02]. https://proceedings.mlr.press/v119/durkan20a.html.
[22] Miller B K,Weniger C, Forre P. Contrastive neural ratio estimation[J/OL]. Advances in Neural Information Processing Systems,2022,35:3262-3278.(2022-09-21)[2024-04-02]. https://proceedings.neurips.cc/paper_files/paper/2022/hash/159f7fe5b51ecd663b85337e8e28ce65-Abstract-Conference.html.
[23] Delaunoy A, Hermans J, Rozet F, et al. Towards reliable simulation-based inference with balanced neural ratio estimation[J/OL]. Advances in Neural Information Processing Systems, 2022, 35: 20025-20037. (2022-09-21)[2024-04-02]. https://proceedings.neurips.cc/paper_files/paper/2022/hash/7e6288bfb68182db7d6e328b0aefa89a-Abstract-Conference.html.
[24] Cranmer K, Brehmer J, Louppe G.The frontier of simulation-based inference[J]. Proceedings of the National Academy of Sciences of the United States of America, 2020, 117(48): 30055-30062. DOI: 10.1073/pnas.1912789117.
[25] Lueckmann J M, Boelts J, Greenberg D S, et al. Benchmarking simulation-based inference[EB/OL]. 2021: arXiv: 2101.04653. (2021-01-31)[2024-04-02]. http://arxiv.org/abs/2101.04653.
[26] Blum M G B, François O. Non-linear regression models for Approximate Bayesian Computation[J]. Statistics and Computing, 2010, 20(1): 63-73. DOI: 10.1007/s11222-009-9116-0.
[27] Gutmann M, Hyvarinen A. Noise-contrastive estimation of unnormalized statistical models, with applications to natural image statistics[J]. Journal of Machine Learning Research, 2012, 13: 307-361. (2012-11-09)[2024-04-02]. https://www.jmlr.org/papers/volume13/gutmann12a/gutmann12a.pdf.
[28] He Z J, Xu Z H, Wang X Q.Unbiased MLMC-based variational Bayes for likelihood-free inference[J]. SIAM Journal on Scientific Computing, 2022, 44(4): A1884-A1910. DOI: 10.1137/21M1449051.
[29] Gretton A, Borgwardt K M, Rasch M J, et al. A kernel two-sample test[J]. Journal of Machine Learning Research, 2012, 13: 723-773. (2012-10-08)[2024-04-02]. https://www.jmlr.org/papers/volume13/gretton12a/gretton12a.pdf.