Supplementary Material
Professor: Daniel Egger
October 14, 2015

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1.1

Binary Classification
Diagram of Confusion Matrix with Basic Definitions

In the confusion matrix, you have two classifications, “Positive” or “Negative,” with the underlying, true conditions being either “+” or “-”.
Examples of Binary Conditions:
Radar - Enemy Bomber/No Enemy Bomber
Diagnostics - Cancer/No Cancer
Credit Scoring - Borrower defaults/does not default

Outcome

Y

Table 1: Confusion Matrix.
Classification/Test,X
“Test Positive” “Test Negative” c d
“+” a e f
“-” b g h

Where,
(a,b) is the Marginal Probability Distribution of Condition p(Y ). Note that the rarer of the two is traditionally assigned to “+” and the probability p(a) is called the “incidence” of a.
(c,d) is the Marginal Probability Distribution of the Classification p(X)
(e,f,g,h) is the Joint Probability Distribution of the Condition and the Classification, p(X, Y ).
Another way of representing the confusion matrix is:

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Outcome

1.2

Table 2: Confusion Matrix, another representation.
Classification/Test,X
“Test Positive”
“Test Negative” c d
”+” a ”True Positive” (TP) ”False Negative” (FN)
Y
”-” b ”False Positive” (FP) ”True Negative” (TN)

Important Measures of the Confusion Matrix

True Positive (TP) Rate: The conditional probability that someone with the condition has a positive test. e = p(T estP ositive|+) a False Negative (FN) Rate: The conditional probability that someone with the condition has a Negative test. f = p(T estN egative|+) a Note that T P rate + F N rate = 1.
False Positive (FP) Rate: The conditional probability that someone who does not have the condition has a positive test. g = p(T estP ositive| ) b True Negative (TN) Rate: The conditional probability that someone who does not have the condition has a negative test h = p(T