Two trained classifiers – A and B – are available to classify tissue samples as
ID: 672870 • Letter: T
Question
Two trained classifiers – A and B – are available to classify tissue samples asbenign or malignant. Each classifier is prone to two types of errors. The table below summarizes the probability of these errors:
Classifiers
False Positive Error Probability
False Negative Error Probability
A
0.06
0.01
B
0.04
0.02
False Positive error probability is defined as the conditional probability of classifying a healthy tissue sample as malignant.
False Negative error probability is defined as the conditional probability of classifying an infected tissue sample as benign.
Historical data suggests that 10 percent of the tissue samples are infected.
A) If the cost of classifying an infected tissue sample as benign is 100 times the cost of classifying a healthy tissue as malignant, which classifier should a risk neutral rational decision maker use? Why?
B ) We assumed that 10% of the tissue samples are infected. At least how low should the percentage of infected tissues be for a risk neutral rational decision maker to prefer classifier B? Assume that all other parameters remain as specified in (a) and (b).
C) .We assumed that the ratio of the cost of classifying an infected tissue sample asbenign to the cost of classifying a healthy tissue as malignant is 100. At least how low must this ratio be for a risk neutral rational decision maker to prefer classifier B? Assume that all other parameters remain as specified in (a) and (b).
Classifiers
False Positive Error Probability
False Negative Error Probability
A
0.06
0.01
B
0.04
0.02
Explanation / Answer
A)
Since it takes 100 times cost of classifying.. we consider this extra cost leading
to profit...
So classifier A has false positive Error probability has 0.06 So, risk neutral rational decision maker
use classifier A.
B)
For classifier B ...given False positive Error probability is 0.04
So 0.04 % of 10% ==== 0.4%
C)
For classifier B given details are:
False Postive Error probability 0.04
False Negative Error probability 0.02
Ratio is given as 0.04 / 0.02 == 0.02
So for cost of 100 x 0.02 = 2%
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