Reproducible Model Selection Using Bagged Posteriors.
Reproducible Model Selection Using Bagged Posteriors.
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DOI：
10.1214/21-ba1301
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发表时间：
2023-03
影响因子：
4.4
通讯作者：
Miller JW
中科院分区：
文献类型：
--
作者：
Huggins JH;Miller JW
贝叶斯模型的选择是基于数据是从其中一个假设模型生成的假设。然而，在许多应用程序中，所有这些模型都是不正确的（即存在错误指定）。当模型被错误指定时，两个或多个模型可以为数据提供几乎同样好的拟合，在这种情况下，贝叶斯模型选择可能非常不稳定，可能导致自相矛盾的结果。为了纠正这种不稳定性，我们建议在后验分布上使用装袋（“BayesBag”）-也就是说，在许多自举数据集上平均后验模型概率。我们提供的理论结果表征的渐近行为的后和袋装后（误指定）模型选择设置。我们经验性地评估了合成和真实世界数据的BayesBag方法（i）线性回归的特征选择和（ii）系统发育树重建。我们的理论和实验表明，当所有模型都被错误指定时，与通常的贝叶斯后验相比，BayesBag（a）提供了更好的再现性，（B）将后验质量更可靠地放置在最优模型上;另一方面，在正确的规范下，Bayes Bag比通常的后验概率略保守，在这个意义上，贝叶斯袋后验概率倾向于稍微远离0和1的极端。总体而言，我们的研究结果表明，BayesBag提供了一种易于使用和广泛适用的方法，通过使其更稳定和可重复来改进贝叶斯模型选择。
Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are misspecified, two or more models can provide a nearly equally good fit to the data, in which case Bayesian model selection can be highly unstable, potentially leading to self-contradictory findings. To remedy this instability, we propose to use bagging on the posterior distribution (“BayesBag”) – that is, to average the posterior model probabilities over many bootstrapped datasets. We provide theoretical results characterizing the asymptotic behavior of the posterior and the bagged posterior in the (misspecified) model selection setting. We empirically assess the BayesBag approach on synthetic and real-world data in (i) feature selection for linear regression and (ii) phylogenetic tree reconstruction. Our theory and experiments show that, when all models are misspecified, BayesBag (a) provides greater reproducibility and (b) places posterior mass on optimal models more reliably, compared to the usual Bayesian posterior; on the other hand, under correct specification, BayesBag is slightly more conservative than the usual posterior, in the sense that BayesBag posterior probabilities tend to be slightly farther from the extremes of zero and one. Overall, our results demonstrate that BayesBag provides an easy-to-use and widely applicable approach that improves upon Bayesian model selection by making it more stable and reproducible.
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