Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
哪些模型有用？迈向统一的贝叶斯模型分类体系AI 解读 ↓
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哪些模型有用？迈向统一的贝叶斯模型分类体系
- 研究问题
- 如何清晰定义贝叶斯模型，并在不同推断目标下，综合评价其有用性及模型构建过程中各评价维度的取舍？
- 方法与思路
- 作者提出PAD分类，以联合分布、后验近似器和训练数据的组合定义四类模型，并建立十个效用维度及决策树示例。
- 材料陈述的贡献
- 摘要所述贡献是统一贝叶斯模型的概念分类，并提供涵盖预测、解释、收敛、稳健性等维度的评价框架。
- 阅读关注点
- 应核对四类模型的边界、十个维度的可操作定义，以及示例决策树如何随推断目标确定优先次序和权衡。
- 阅读边界
- 这是arXiv预印本，同行评审或期刊接收未获核验；摘要未说明评价框架的实证验证，不能据此判断其普遍适用性。
原文摘要
Probabilistic (Bayesian) modeling has experienced a surge of applications in almost all quantitative sciences and industrial areas. This development is driven by a combination of several factors, including better probabilistic estimation algorithms, flexible software, increased computing power, and a growing awareness of the benefits of probabilistic learning. However, a principled Bayesian model building workflow is far from complete and many challenges remain. To aid future research and applications of a principled Bayesian workflow, we ask and provide answers for what we perceive as two fundamental questions of Bayesian modeling, namely (a) "What actually is a Bayesian model?" and (b) "What makes a good Bayesian model?". As an answer to the first question, we propose the PAD model taxonomy that defines four basic kinds of Bayesian models, each representing some combination of the assumed joint distribution of all (known or unknown) variables (P), a posterior approximator (A), and training data (D). As an answer to the second question, we propose ten utility dimensions according to which we can evaluate Bayesian models holistically, namely, (1) causal consistency, (2) parameter recoverability, (3) predictive performance, (4) fairness, (5) structural faithfulness, (6) parsimony, (7) interpretability, (8) convergence, (9) estimation speed, and (10) robustness. Further, we propose two example utility decision trees that describe hierarchies and trade-offs between utilities depending on the inferential goals that drive model building and testing.