关于回火后验的细节
The fine print on tempered posteriors
AI总结：
本文详细调查回火后验，发现在真实模型与Laplace近似下随机性通常不提升测试准确率且校准增益以准确率下降为代价，并通过Frequentist指标和PAC-Bayesian分析解释了温度参数$λ$的必要性及其非先验或似然修复的本质。
摘要：
我们对回火后验进行了详细调查，并发现了许多关键且此前未被讨论的问题。与先前的结果相反，我们首先表明，对于真实的模型和数据集，以及在后验的 Laplace 近似这一严格受控的情况下，随机性通常不会提高测试准确率。最冷的温度往往是最佳的。人们可能认为，具有一定随机性的 Bayesian 模型至少能在校准方面获得改进。然而，我们凭经验表明，当获得增益时，这通常是以测试准确率下降为代价的。然后，我们讨论了如何使用 Bayesian 模型瞄准 Frequentist 指标，从而为在优化目标中需要温度参数 $λ$ 提供了一个简单的解释。与先前的工作相反，我们最后通过 PAC-Bayesian 分析表明，温度 $λ$ 不能被简单地视为修复了错误指定的先验或似然。
英文摘要：
We conduct a detailed investigation of tempered posteriors and uncover a number of crucial and previously undiscussed points. Contrary to previous results, we first show that for realistic models and datasets and the tightly controlled case of the Laplace approximation to the posterior, stochasticity does not in general improve test accuracy. The coldest temperature is often optimal. One might think that Bayesian models with some stochasticity can at least obtain improvements in terms of calibration. However, we show empirically that when gains are obtained this comes at the cost of degradation in test accuracy. We then discuss how targeting Frequentist metrics using Bayesian models provides a simple explanation of the need for a temperature parameter $λ$ in the optimization objective. Contrary to prior works, we finally show through a PAC-Bayesian analysis that the temperature $λ$ cannot be seen as simply fixing a misspecified prior or likelihood.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
