anytime algorithms for learning anytime classifiers saher ... - Technion

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Technion - Computer Science Department - Ph.D. Thesis PHD-2008-12 - 2008 Table 4.10: Comparison of C4.5, EG2, DTMC, ACT, and ICET when misclassification costs are nonuniform. FP denotes the penalty for a false positive and FN the penalty for a false negative. γ denotes the basic mc unit. γ = 500 γ = 5000 FP γ γ γ γ 2γ 4γ 8γ FN 8γ 4γ 2γ γ γ γ γ C4.5 29.2 34.2 41.3 49.9 43.6 39.0 36.3 EG2 30.1 33.0 37.2 42.5 39.3 37.5 36.8 DTCM 12.4 20.3 29.8 37.7 32.5 22.9 15.8 ICET 23.3 27.0 31.5 36.3 34.2 31.8 29.2 ACT 11.9 18.5 27.2 34.5 29.1 20.4 13.8 C4.5 27.0 31.3 39.2 53.3 44.0 39.0 36.3 EG2 30.9 35.2 43.1 57.3 47.7 42.4 39.7 DTCM 13.8 23.6 38.0 57.6 42.5 29.3 20.1 ICET 21.4 25.6 32.7 45.7 37.4 32.8 29.8 ACT 12.9 19.1 28.8 41.5 31.1 22.5 14.6 of error might be higher than the penalty for another type. Our next experiment examines ACT in the nonuniform scenario. Let FP denote the penalty for a false positive and FN the penalty for false negative. When there are more than 2 classes, we split the classes into 2 equal groups according to their order (or randomly if no order exists). We then assign a penalty FP for misclassifying an instance that belongs to the first group and FN for one that belongs to the second group. To obtain a wide view, we vary the ratio between FP and FN and also examine different absolute values. Table 4.10 and Figure 4.12 give the average results. It is easy to see that ACT consistently outperforms the other methods. Interestingly, the graphs are slightly asymmetric. The reason could be that for some datasets, for example medical ones, it is more difficult to reduce negative errors than positive ones, or vice versa. A similar phenomenon is reported by Turney (1995). The highest cost for all algorithms is observed when FP = FN because, when the ratio between FP and FN is extremely large or extremely small, the learner can easily build a small tree whose leaves are labeled with the class that minimizes costs. When misclassification costs are more balanced, however, the learning process becomes much more complicated. 94
Technion - Computer Science Department - Ph.D. Thesis PHD-2008-12 - 2008 ACT Cost 100 100 80 60 40 20 100 80 60 40 20 0 0 20 40 60 80 100 ICET Cost 0 0 20 40 60 80 100 80 60 40 20 ICET Cost 0 0 20 40 60 80 100 ICET Cost Figure 4.8: Illustration of the differences in performance between ACT and ICET for mc = 100, 1000, 10000 (from left to right). Each point represents a dataset. The x-axis represents the cost of ICET while the y-axis represents that of ACT. The dashed line indicates equality. Points are below it if ACT performs better and above it if ICET is better. 95
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