Mira通过联合采样评估条件分布准确性，无需计算证据即可进行贝叶斯模型比较。
MIRA: A Score for Conditional Distribution Accuracy and Model Comparison
- 基于真实数据联合采样，用样本统计量衡量条件分布匹配度
- 可计算理论参考值与不确定性估计，支持模型间定量对比
- 适合需要直接验证后验分布的贝叶斯推断与模型选择场景
我们提出Mira，一种基于样本的评分方法，仅使用真实数据生成过程的联合样本，即可评估候选条件分布的准确性。基于分布相等当且仅当对所有区域赋予相同概率质量的原理，我们推导出Mira统计量的解析表达式，其期望即为Mira评分。该形式进一步允许在候选分布与真分布一致时计算理论参考值和不确定性估计。该框架可通过量化候选模型条件分布与真实数据生成过程的对齐程度，实现模型比较，从而在不需计算困难的边际似然情况下，实现贝叶斯模型比较。我们在多个简单问题和贝叶斯推断任务中展示了其有效性。
原文摘要 · Abstract (English)
We introduce Mira, a sample-based score for assessing the accuracy of a candidate conditional distribution using only joint samples from the true data-generating process. Relying on the principle that distributions coincide if they assign equal probability mass to all regions, we derive an analytic expression for the Mira statistic, whose average defines the Mira score. This formulation further allows us to compute theoretical reference values and uncertainty estimates when the candidate distribution matches the true one. This framework enables model comparison by quantifying the alignment between the conditional distribution of a candidate model and the true data generating process. Consequently, Mira enables Bayesian model comparison through direct posterior validation, bypassing the challenging evidence computation. We demonstrate its effectiveness across several toy problems and Bayesian inference tasks.
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。