IIR #08 Exercise

IIR

Evelyone pls check my answers and my English.

  • Exercise 8.1

Precision=8/(8+10)=.444
Recall==8/20=.4

  • Exercise 8.2

Better harmonic mean has better max-min{precision,recall} than arithmetic mean.

  • Exercise 8.3

1. beta^2=(1-alpha)/alpha
2. alpha=1/(beta^2+1)
2->1: beta^2=(1-1/(beta^2+1))(beta^2+1)=(beta^2+1-1)=beta^2
1->2: alpha=1/(beta^2+1)=1/((1-alpha)/alpha+1)=alpha
so 1<->2

  • Exercise 8.4

(#all relevant documents)/(#all documents)<=(interpolated precision at a recall level of 0)<=1

  • Exercise 8.5

Yes?

  • Exercise 8.6

break-eleven point is maximal of F_1 (not maximum).

  • Exercise 8.7

Precision=tp/(tp+fp)
Recall=tp/(tp+fn)
Dice(X,Y)=2tp/(2tp+fn+fp)
F_1=2PR/(P+R)=2(tp)^2/(tp+fp)/(tp+fn)/{tp(2tp+fn+fp)/(tp+fp)(tp+fn)}=2tp/(2tp+fn+fp)

  • Exercise 8.8
    • a.

MAPof1=(1+2/3+3/9+4/10)/4=0.6
MAPof2=(1/2+2/5+3/6+4/7)/4=(1.4+4/7)/4=0.4928
System 1 has higher MAP than System 2.

    • b

top of retrieved documents list is important to obtain good MAP

    • c

R-Precision of 1 and 2 are .5 and .25 respectively.
So R-Precision decide different system as good against MAP.

  • Exercise 8.9
    • a

6/20=.3

    • b

P=.3
R=6/8=.75
F1=2PR/(P+R)=.45/1.05=3/7=.429

    • c

25% of 8 relevant documents means 2.
precision at 25% recall is 1.

    • d

minimum number over 33% of 8 relevant documents is 3
precision at 3rd relevant document is 3/9=.3333
precision at 4th relevant document is 4/11=.3636
precision at 5th relevant document is 5/15=.3333
precision at 6th relevant document is 6/20=.3
precision at 7th relevant document is less than equal 7/21=.3333
precision at 8th relevant document is less than equal 8/22=.3636
So the interpolated precision at 33% recall is .3636

    • e

(1/1+2/2+3/9+4/11+5/15+6/20)/8=2.3+2/3+4/11=3.330303/8=.4163

    • f

(1/1+2/2+3/9+4/11+5/15+6/20+7/21+8/22)/8=3.3+8/11=4.02727/8=.5034

    • g

(1/1+2/2+3/9+4/11+5/15+6/20+7/9999+8/10000)/8=2.3001+2/3+4/11+7/9999=.4164

    • h
(e)-(f) =.0871
  • Exercise 8.10
    • a

Kappa=(P(A)-P(E))/(1-P(E))=(4/12-.5)/.5=-1/3=-0.333

    • b

P=1/5=.2
R=1/4=.25
F_1=.222

    • c

P=5/5=1
R=5/10=.5
F_1=2/3=.666