揭示了置信预测区域与模糊高密度区域的等价性
Conformal Prediction Regions are Imprecise Highest Density Regions
- 通过云概念建立置信预测与模糊概率的新联系
- 证明同音置信集对应的模糊高密度区域即经典预测区域
- 发现同音似然函数具有半群同态性质，具代数新意义
近期，Cella 和 Martin 证明，在称为同音性的假设下，可从传递性置信预测的置信变换器导出一个可信集（即闭合凸的概率集）。我们证明，该可信集对应的模糊高密度区域（IHDR）等价于经典的置信预测区域。在证明过程中，我们通过模糊概率中的‘云’概念建立了置信预测与模糊概率理论之间的新关联。此外，我们的分析还发现，同音似然函数是半群同态，这是模糊概率工具的一项全新代数属性。
原文摘要 · Abstract (English)
Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool.
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