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Sensitivity Analysis of Enumerated Trees of Increasing Boolean 枚举树增加布尔的敏感性分析
Sensitivity Analysis of Enumerated Trees of Increasing Boolean Expressions Enumeration and Selection of Optimum Decision Tree The cost of each tree is evaluated and the optimum tree selected. Enumeration and Selection of Optimum Decision Tree The decision trees are constructed using 4 sensors For three sensors, there are 114 monotonic and complete boolean expressions. These can be implemented using 11808 distinct trees. The trees are evaluated and ranked using the cost function1. The tree with the lowest cost is selected as the optimum decision tree. Cost Function used for evaluating the decision trees. CTot = CFalsePositive *PFalsePositive + CFalseNegative *PFalseNegative + Cfixed Probability of Error for Individual Sensors For ith sensor, the type 1 (P(Yi=1|X=0)) and type 2 (P(Yi=0|X=1)) errors are modeled using Gaussian distributions. State of nature X=0 represents absence of a bomb. State of nature X=1 represents presence of a bomb. Yi represents the outcome of sensor i. It is characterized by: Ki, discrimination coefficient Ti, decision threshold Σi, variance of the distributions Receiver Operating Characteristic (ROC) Curve The ROC curve is the plot of the Probability of correct detection (PD) vs. the Probability of false positive (PF). The ROC curve is used to select an operating point, which provides the trade off between the PD and PF Each sensor has a ROC curve and the combination of the sensors into a decision tree has a composite ROC curve. The parameter which is varied to get different operating points on the ROC curve is the sensor Threshold and a combination of Thresholds for the decision tree. Equal Error Rate (EER) is the operating point on the ROC curve where, PF = 1 - PD Stroud-Saeger Experiments Stroud-Saeger ranked all trees formed from four given sensors A, B, C and D according to increasing tree costs. The cost function used was as shown in earlier slides. Values used in their experiment: CA = .25; KA = 4.37; ΣA = 1; CB = .25; KB =
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