Assessment Measure for Discriminability of Multi-Classification Markers
碩士 === 國立臺灣大學 === 數學研究所 === 99 === To evaluate overall discrimination capacity of a marker for multi-class classification tasks, the performance function is a natural assessment tool and fully provides the essential ingredients in receiver operating characteristic (ROC) analysis. The connection betw...
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| Format: | Others |
| Language: | en_US |
| Published: |
2011
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| Online Access: | http://ndltd.ncl.edu.tw/handle/80578359007768157229 |
| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 99 === To evaluate overall discrimination capacity of a marker for multi-class classification tasks, the performance function is a natural assessment tool and fully provides the essential ingredients in receiver operating characteristic (ROC) analysis. The connection between admissible and utility classifiers facilitates illustrating the optimality of likelihood ratio scores as well as constructing a parameterized optimal ROC manifold. The manifolds supply a geometric characterization of the magnitude of separation among multiple classes. It is shown that the hypervolume under the optimal ROC manifold (HUM) is a well-defined and meaningful accuracy measure only in suitable ROC subspaces. Moreover, we provide a rigorous proof for the equality of HUM and its alternative form, the correctness probability, which is directly related to an explicit U-estimator. Our theoretical framework further allows more sophisticated modeling on performance of markers and helps practitioners examine the optimality of applied classification procedures.
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