Results 1 to 3 of 3

Math Help - Information Gain for 2x2 Contingency Table

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Edinburgh
    Posts
    2

    Information Gain for 2x2 Contingency Table

    Hi all,

    This is probably a somewhat elementary question, but I've been working on it for some time without any luck.

    I have a 2x2 contingency table:

    1 0
    Y 3 92
    N 8 743

    1,0 refers to a word (w=1 means word present; w=0 means word absent). N,Y refers to a disease (D=1 means disease present; D=0 means disease absent).

    I need to calculate the information gain using the statistic (sorry for poor formatting):

    I(w,D)=Sigmaj=0,1Sigmak=0,1P(w=k,D=j)log2 P(w=k,D=j)
    P(w=k)P(D=j)

    The probability calculations are straightforward, but I am unsure how the statistics should look when expanded out - should there be 4 different calculations? For instance, (w=1,D=1)+(w=1,D=0)+(w=0,D=1)+(w=0,D=0)

    Any assistance gratefully received!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    762

    Re: Information Gain for 2x2 Contingency Table

    Hey CSHowe.

    Your expansion should have four terms as you have pointed out since you have summations that have independent indices of 2 each so 2*2 gives 4 terms in total.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Edinburgh
    Posts
    2

    Re: Information Gain for 2x2 Contingency Table

    Hi Chiro,

    Thank you very much for the clarification.

    C
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability and expected gain
    Posted in the Statistics Forum
    Replies: 4
    Last Post: March 15th 2010, 12:12 AM
  2. Simpson's Rule with a table of information
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 2nd 2009, 02:11 AM
  3. contingency tables
    Posted in the Advanced Statistics Forum
    Replies: 12
    Last Post: June 27th 2009, 11:40 AM
  4. critical gain
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 8th 2009, 01:29 PM
  5. Kalman Gain
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: June 5th 2009, 08:31 AM

Search Tags


/mathhelpforum @mathhelpforum