The Cold Posterior Effect (CPE) is a phenomenon in Bayesian Deep Learning (BDL), where tempering the posterior to a cold temperature often improves the predictive performance of the posterior predictive distribution (PPD). Although the term `CPE' suggests colder temperatures are inherently better, the BDL community increasingly recognizes that this is not always the case. Despite this, there remains no systematic method for finding the optimal temperature beyond grid search. In this work, we propose a data-driven approach to select the temperature that maximizes test log-predictive density, treating the temperature as a model parameter and estimating it directly from the data. We empirically demonstrate that our method performs comparably to grid search, at a fraction of the cost, across both regression and classification tasks. Finally, we highlight the differing perspectives on CPE between the BDL and Generalized Bayes communities: while the former primarily focuses on predictive performance of the PPD, the latter emphasizes calibrated uncertainty and robustness to model misspecification; these distinct objectives lead to different temperature preferences.

翻译：冷后验效应（CPE）是贝叶斯深度学习（BDL）中的一种现象，即对后验分布进行低温回火处理通常能提升后验预测分布（PPD）的预测性能。尽管“CPE”这一术语暗示较低温度本质上更优，但BDL领域日益认识到实际情况并非总是如此。尽管如此，目前仍缺乏超越网格搜索的系统性方法来寻找最优温度。本研究提出一种数据驱动的方法来选择最大化测试对数预测密度的温度，将温度视为模型参数并直接从数据中估计。我们通过实证研究表明，在回归和分类任务中，该方法以网格搜索一小部分的计算成本实现了与之相当的性能。最后，我们指出BDL与广义贝叶斯学界对CPE的不同视角：前者主要关注PPD的预测性能，后者则强调校准不确定性和对模型误设的鲁棒性；这些不同的目标导致了相异的温度偏好。