2. (10 points) Recall our table for the Restaurant problem: Num Alt Bar Fri Hun Pat...

 

Transcribed Image Text:

2. (10 points) Recall our table for the Restaurant problem: Num Alt Bar Fri Hun Pat Price Rain Res Type Est Wait 888 French 0-10 $ S $ yes no Z1 Fr Is Iz To 27 Is yes no yes some yes full yes no no no yes no no yes yes yes yes no some full full some $$ none $ no yes some 88 full no yes no yes no yes no yes no no no yes yes no yes yes yes yes no no no no none Ig Iso F11 12 yes yes yes yes $ $$$ $ 0000 $ no yes no no no no Burger yes yes yes yes yes no no a) Hungry Gain (Hungry) = 1- [7/12 B (5/7) + 5/12 B (1/5)] yes Thai 30-60 no yes yes no 0-10 Thai 10-30 yes French >60 yes Italian 0-10 no Burger 0-10 Thai 0-10 b) Bar Gain (Bar) = 1- [6/12 B (3/6)+ 6/12 B (3/6)] no Burger >60 yes Italian 10-30 no Thai 0-10 no Burger 30-60 Using the Shannon entropy formula and our formula for Gain, calculate the amount of information obtained by choosing the attribute: yes yes no no no yes 2. (10 points) Recall our table for the Restaurant problem: Num Alt Bar Fri Hun Pat Price Rain Res Type Est Wait 888 French 0-10 $ S $ yes no Z1 Fr Is Iz To 27 Is yes no yes some yes full yes no no no yes no no yes yes yes yes no some full full some $$ none $ no yes some 88 full no yes no yes no yes no yes no no no yes yes no yes yes yes yes no no no no none Ig Iso F11 12 yes yes yes yes $ $$$ $ 0000 $ no yes no no no no Burger yes yes yes yes yes no no a) Hungry Gain (Hungry) = 1- [7/12 B (5/7) + 5/12 B (1/5)] yes Thai 30-60 no yes yes no 0-10 Thai 10-30 yes French >60 yes Italian 0-10 no Burger 0-10 Thai 0-10 b) Bar Gain (Bar) = 1- [6/12 B (3/6)+ 6/12 B (3/6)] no Burger >60 yes Italian 10-30 no Thai 0-10 no Burger 30-60 Using the Shannon entropy formula and our formula for Gain, calculate the amount of information obtained by choosing the attribute: yes yes no no no yes