D D D LL—l sheet LL Li LL uvo LL Li
Give formulas for estimating a text retrieval system’s precision, recall, the F1 measure [2 points],
and the mean average precision (MAP) [1 point] given the following lists of results for queries C11,
and (12, where R is a relevant result, and N is a non-relevant result:
0 Results for ql : RNNRR (10 relevant results for Q1 exist in the collection.)
0 Results for q2 : NRRNNN (3 relevant results for q2 exist in the collection.)
Three judges 9'1, jg, and jg were appointed to assess the relevance of ten documents. Estimate
the Cohen’s kappa H; given the following lists of the judges’ relevance judgements: [2 points]
0 Relevance judgements of j1 : NNNRNRRNNR
0 Relevance judgements of jg : NRNRRRRNNN
0 Relevance judgements of jg : RNRNRRNRNR
Are the judges in agreement according to your estimate of Fe?
-3 __3; _$ _Z
72:5 ”m «2-;- 21-3-7 1‘ I 44 1.
MACVO ’AVKV‘ma/lohar P' K MfCVO *QVirnatk3/
3+1:
_ _, 4‘1 “' 1):: u 5__
l>-<l>q4+P1)/Z-§:olhe é+e— M "W5
=K+K Z:Ei_ v. 'zL’d‘Zzi: Yblé
R (14 43/ 60 _ mm R ms 43 (as
"WO*AVchda:;a F4 ‘ Mfcvo-AVQVAafna F4 “49’0" 'WQVAJCMG F4
._ .£.p 5- __
ZEP: :1‘05‘192. 2.25.941”: E399 F'Z 7" “20.946
F: 1+9 ms FM 241+ h 5 1 Rip AL
-Z'ifi P,__Q *
Elt— gl+9111‘z~‘01“
/ Hm,“ «Ll/2’39””:
L 3 ,1
MAP—i<_<_+‘+‘>+—<£+£>
40 (4 S S L
_. A —1j>(g)=./;_i—.-4_9: i>(N)=’lg”; ’P(E)= PM”NW: 1
- D A ~ NE) - g“;
PUPILS“? H L __.,_.4' NE) j_5_ 3
40
“9| Vlu Judau and ho+ lo") “JVeehwh
PR
F4
E
F
More mum/«aft? F4
:1aWP ,
-—— -~ ‘: $30.9
4 24+ P“ 5
3%;“32930:
1 Qiz+P1L Z ‘
__ -440: "
-<Fqn+Fql)/Z‘;‘5 0‘91.
I Write your solution only on this side of the sheet!
K 17 K 17 K 17 F, ,7 F, ,7 T, H 7, fl 7, fl 7, H 7, fl 7, H
D D D H I H H E H H H H H H H H H H H H H H H H H H H H
LL S he8 t L 1 u 50 LL 1 LL 1 LL 1 LL 1 LL 1 LL 1 Ll 1 p 0 in ts LL 1 LL 1 Ll 1
You are given the following training dataset containing observations of two classes (0 and Cl):
Is your dataset linearly separable? [2 points] Construct a linear classifier using the two closest
points from dz’fi‘erent classes, and draw the separating hyperplane. [2 points] What is the training
error (the ratio of incorrectly classified observations and all observations) of your linear classifier?
[1 point]
NO! +h¢V¢ :8 (no qypgy‘oévw M SCPW’MOS {41... {—um
classes.
The 44/1»:th 9.on 78 {'2' —"= 0,033:
Write your solution only on this side of the sheet!
K 17 K 17 K 17 F, ,7 F, ,7 T, H 7, fl 7, fl 7, H 7, fl 7, H
D D D H I H H a H H H H H H H H H H H H H H H H H H H H
LL S he8 t L 1 u 50 LL 1 LL 1 LL 1 LL 1 LL 1 LL 1 L? 1 p 0 in ts LL 1 LL 1 L? 1
Explain the following aspects of the K-means flat clustering algorithm [2 points]:
1. What do we need to decide before using the algorithm?
2. What is the input and the output of the algorithm?
3. What are the two steps that take place in every epoch?
4. How do we decide when to stop the algorithm?
' a o
4,W€, haul Lo Qhow I’LL («amber 04 caSSCS K “ML lhthon( ”1th
esa°m1es (58615): 2.111 mpw m ““45sz rain: (M K seals.
34 Mfiam‘g ’00:”). ”WNW“; unveil). (-1. (MM/0M} (mu/(999“,
Given the points 0, and the seeds CI, run the K-means algorithm for three epochs. Draw the
state of the algorithm at the beginning and after every epoch; no computation should be necessary.
What is the output of the algorithm? [2 points]
Mn‘emrob‘mc can”: .
the above dataset into three classes using the single-link
hierarchical agglomerative clustering algorithm. Is the output the same as the output of the K-means
flat hierarchical clustering algorithm above? [1 point] 0 °
7/Q5 ( N’ l S :
auroral: wflverydPerform
a hierarchical clust
I Write your solution only on this side of the sheet!
Fr .7 Fr .7 Fr .7 F, ,7 F, ,7 T, H T, H T, H T, H T, H T, H
D D D H I H H q H H H H H H H H H H H H H H H H H H H H
LL S he8 t L 1 LL u 50 LL 1 LL 1 LL 1 LL 1 LL 1 LL 1 L 1 p 0 in ts LL 1 LL 1 L 1
You maintain a text retrieval system. Let E1 denote the complete set of documents in the index of
your system and let E2 denote the complete set of documents in the index of a competing system.
Suppose the indices of both systems are independent uniform random samples without replacement
from the World Wide Web N. The size of E1 is lEll : 130 trillion (130 - 1012) documents. You take
a uniform random subsample of documents without replacement from E1 and you submit each
document to the competing system. This gives you an estimate a: : 0.2 of the conditional probability
P(d E E2 l d E E1), d E N. You repeat the same procedure with E2, obtaining an estimate y : 0.4
of the conditional probability P(d E E1 l d E E2), d E N. Assume the estimates :12, y are the true
probabilities. What is the size lEgl of the competing system’s index? [3 points]
The grey parrot, native to equatorial Africa, is categorized as an endangered species by the
International Union for Conservation of Nature (IUCN). Suppose you take a uniform random
sample M without replacement of size lM l : 8 000 from the grey parrot population N and mark the
sampled animals. After returning the marked animals back into the population, you take a second
independent uniform random sample T without replacement of the same size lTl : 8 000 from the
population. The number of marked animals R : M H T in the second sample is lRl : 10. What is
the most likely size lN l of the grey parrot population? [2 points]
pM’W'wrN T )VLxérNZ’F(X6M)=m P<XQK):{£IN I
K ' TOG-T): m
VXWN 73(xe2): Fae-M 7U)
IHHT‘
f“ ‘ 3 P(X6‘M)P(7"TT): ”“2. O
my,1mm_ mm: woo"
-——- >Nll=-= ~—-——-== MaW ((W- Ill
54 -- E2. JfléNg T<ME1H454)3 0‘2,
?(XéE/l (AéEL)0"
i :(deé‘ )= “,3,“ PM»?
“* l (ELI
. 01‘ 4'50'401
0.2.20«fl—W 42> lELl= ' 265.40”?43040“ (W4
W
Write your solution only on this side of the sheet!