El [University] Jr 'H. ra nlc_1,.#" grant} I'm nl-cj "w. E ii lei Figure 2: The decision tree that L.|niI|.rersit'_.r of Excellence is using to

Question 2: Consider the criteria for accepting graduate students at the hypothetical Univ. of Excellence. Each candidate is evaluated according to four attributes:

1. the grade point average (GPA)

2. the quality of the undergraduate degree

3. the publication record

4. the strength of the recommendation letters

To simplify our example, let us discretize and limit the possible values of each attribute: Possible GPA scores are 4.0, 3.6, and 3.3; universities are categorized as rank_1, rank_2, and rank_3; publication record is a binary attribute - either the applicant has published previously or not; and recommendation letters are similarly binary, they are either good or normal. Finally, the candidates are classified into two classes: accepted, or P (for âpositiveâ) and rejected, or N (for ânegativeâ). Figure 2 provides an example of one possible decision tree determining acceptance. An applicant doesnât know this decision tree, but does have the data regarding twelve of last yearâs applicants as in Table 1.

• Attachment 1
• Attachment 2

El [University] Jr 'H. ra nlc_1,.#” grant}I’m nl-cj “w. E ii lei Figure 2: The decision tree that L.|niI|.rersit'_.r of Excellence is using to detennine acceptance. a} Dues the prd'lrided tree currectiy' categclrize the prcnlided examples? b} The applicant uses the decisipn tree algprithm shdwn in clan {with the infnrmatinn gaincampu'lzltigns fclr' selecting split uariatrla} ta induce the decisidn tree empldyed by U. gf E.gfficials. What tree will the algprithm EDITIE up with? She-H the cum putaticlns intrghred. in additign [l] the decisidn tree ilseif.IHin'L' The infermatidn content clfthe examples before chdnsing any split variable is'_ E- E E- E- E E: ;__=_—: ———l —=1btclfnf I:[1212:1 1299212 12”“12 ' 'Dmam Thu have ta find the attribute that has the hig hat infcln'rlaticln gain: pl + £1;er Gamm1=fl — p+np+n1§p+nflm+mp¢+ntl where attribute A divides the exampla inth isuhsels. and p.- and n4 repraent the number pfpdsiti'u'e and negative examples in sutlset r'_] c} Is the tree that fan get in part b] equivalent tn the tree presided here {i.e.. do the title treesclassilig,I every applicatidn in the same way-l1" if the answer is yes. explain 'H'I'IEli'lEr this is a cninciclence er nclt. lfthe answer is nclr give an example at a data case that will be classifieddi‘l‘l'eren'dy' by the tum treu