Association algorithm - Importance of a rule

Question

Can anyone tell me, how the Business Íntelligence Studio calculates the importance of a rule. I can't find the formula. I know some formulas, but the result in SQL Server is completly different.

Thanks!

Answer 1

For rules, the importance is calculated using the following formula:

 

Importance (A=>B) = log ( p(a|b) / p(b|not a) )

 

An importance of 0 means there is no association between A and B. A positive

importance score means that the probability of B goes up when A is true. A

negative importance score means that the probability of B goes down when A

is true.

 

Below is an example of the correlation counts of donut and muffin derived

from a purchase database. Each cell value represents the number of

transactions. For example, 15 out of 100 transactions include a customer

purchasing both donuts and muffins.

 

                  Donut        Not Donut      Total

Muffin        15              5                    20

Not muffin  75              5                    80

Total          90              10                  100

 

The support, probability, and importance of related itemsets and rules for

donut and muffin:

 

Support({Donut}) = 90

Support({Muffin}) = 20

Support ({Donut, Muffin}) = 15

Probability({Donut}) = 90/100 = 0.9

Probability({Muffin}) = 20/100 = 0.2

Probability({Donut, Muffin}) = 15/100 = 0.15

 

Probability(Donut|Muffin) = 15/20 = 0.75

Probability(Muffin|Donut) = 15/90 = 0.167

 

Importance({Donut, Muffin}) = 0.15/(0.2*0.9) = 0.833

Importance (Donut=>Muffin) = ln(Probability(Donut|Muffin)

/Probability(Donult|Not Muffin))= ln(0.8) = -0.223

Importance(Muffin=>Donut) = ln(Probability(Muffin|Donut)

/Probability(Muffin| Not Donut)) = ln(0.33) = -1.100

 

From the importance of the itemset {Donut, Muffin}, we can see Donut and

Muffin are negatively correlated; it is rather unlikely for someone who buys

a Muffin to also buy a Donut.

 

The Importance score is also known as Weight of Evidence (WOE).

 

 

**** Fixed importance formule - denominator was reversed

Answer 2

Hi,thanks a lot for your answer!

I recalculated the importance with your formulas and compared this with the results of the microsoft association algorithm.

Your formula for the importance is almost right, but it calculates the importance for

Muffin =>Donut and not Donut => Muffin

and it must be "log" and not "ln" !!

So at the end, this must be the right formula:

Importance(Muffin =>Donut) = log(Probability(Donut|Muffin) / Probability(Donut|Not Muffin) )

and for

Importance(Donut=> Muffin) = log(Probability(Muffin|Donut) / Probability(Muffin|Not Donut) )

UllaH

Answer 3

Acutually at the beginning of Jamie's answer, the formular has been already there correctly:

Importance (A=>B) = log ( p(a|b) / p(a|not b) )

Regards,

Answer 4

Importance (A=>B) = log ( p(a|b) / p(a|not b) )

It makes more sense to me if a and b are switched in the log function

 

Can some one point me to a Microsoft Research Paper "With all due respect to all" not just odiscussion Onions that discusses the theoretical background for calculating Rule importance?

 

Musa

Answer 5

Dear all,

I try to run the "donuts and muffins" example by using SQL 2005 BI but I didnot have the results as the formula you instruct (Importance (A=>B) = log ( p(a|b) / p(a|not b) ) ). Please explain me more detail.

probability	importance
0.938	0.105302438	F3 = NotMuffin -> F2 = Donut
0.833	0.218055761	F2 = Donut -> F3 = NotMuffin
0.75	-0.105302438	F3 = Muffin -> F2 = Donut
0.5	-0.218055761	F2 = NotDonut -> F3 = NotMuffin
0.5	0.458637849	F2 = NotDonut -> F3 = Muffin

Thank you very much.
Your truthly,

Answer 6

I understand Mr. MacLennan's explanation and appreciate the time he took to explain how importance works.  However, like the user with username "sang", I also ran the data in BI 2005 and got the same results listed by the aforementioned user.  I did this using the following data:

 

donut	muffin
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
y	y
n	y
n	y
n	y
n	y
n	y

etc.

 

The rule muffin -> donut has an importance of -0.105302438, which is not the same as Mr. MacLennan's results.  I tried switching the roles of  a and b in a -> b and using different bases on the logarithms.  I don't get the result of -0.105302438 with any of these.

Answer 7

Musa1, sang, cheryl8150 -- I hope my answer here http://forums.microsoft.com/MSDN/ShowPost.aspx?PostID=2844838&SiteID=1 clarifies the number mismatch