Question

Using the following values on some evaluation measures:
# Instances = 1000
Accuracy = 70%
Precision = 62.5%
Recall = 71.43%

A) Reconstruct the corresponding confusion matrix.
B) Report the TPR value of that confusion matrix.
C) Report the FPR value of that confusion matrix.

Answer 1

We know that the total values are 1000.

Actual\Predicted	True	False
True	a	b
False	c	d

We know that:

i. accuracy is 70%

Thus,

(a+d) / (a+b+c+d) = 70/100

ii. precision is 62.5%

Thus,

a / (a+c) = 62.5/100

iii. Recall is 71.43%

Thus,

a / (a+b) = 71.43/100

We know that a+b+c+d is 1000.

Thus,

(a+d)= 700

Thus, (b+c)= 300

a / (a+c) = 62.5/100

Thus,

100a= 62.5a+62.5c

37.5a= 62.5c

Thus,

c= 37.5a/ 62.5

a / (a+b) = 71.43/100

Thus,

100a= 71.43a+71.43b

28.57a= 71.43b

b= 28.57a / 71.43

Thus,

(b+c)= 300

[ 28.57a / 71.43 ] + [ 37.5a/ 62.5 ] = 300

[(28.57*62.5)a + (37.5*71.43)a] / 71.43*62.5 = 300

1785.625a + 2678.625a = 4464.375*300

4464.25a =1339313

Thus,

a= 1339313/4464.25

= 300.0085 ~ 300

Thus,

300+d=700

d= 400

300/ (300+c)= 62.5/100

30000= 62.5c+18750

11250= 62.5c

Thus, c= 180

b+c=300

Thus, b= 120

Actual\Predicted	True	False
True	300	120
False	180	400

TPR= TP/ (TP+FN)

= 300/ (300+120)

= 0.7142857

FPR= FP/(FP+TN)

= 180/(180+400)

= 0.3103448