提出双贝叶斯决策框架，揭示决策内在不确定性并提升可解释性。
Double-Bayesian Learning
- 将决策建模为双重贝叶斯过程，引入内在不确定性机制
- 发现黄金比例可描述满足贝叶斯定理的解，具数学美学意义
- 建议采用文献中神经网络训练的动量与学习率参数
当代机器学习方法力求逼近贝叶斯误差，即任何模型能达到的最低误差。本文提出，任何决策均由两个贝叶斯决策构成，因此决策本质上是双贝叶斯过程。该框架揭示了决策中的内在不确定性，并融合可解释性。研究指出，贝叶斯学习等价于寻找衡量不确定性的对数函数的基底，其解为不动点。进一步表明，黄金比例可描述满足贝叶斯定理的可能解。双贝叶斯框架建议在使用随机梯度下降训练神经网络时，采用文献中常见的学习率与动量权重。
原文摘要 · Abstract (English)
Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that decision-making is, therefore, a double-Bayesian process. The paper shows how this duality implies intrinsic uncertainty in decisions and how it incorporates explainability. The proposed approach understands that Bayesian learning is tantamount to finding a base for a logarithmic function measuring uncertainty, with solutions being fixed points. Furthermore, following this approach, the golden ratio describes possible solutions satisfying Bayes' theorem. The double-Bayesian framework suggests using a learning rate and momentum weight with values similar to those used in the literature to train neural networks with stochastic gradient descent.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。