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Perform the boolean query VIKINGS AND SPAM given the following inverted index:
0 mecs: m1%”, 31, 37, 41, ,53, 59,61 [PI : 46 LINN J = ‘1
. "‘ J 4-.. SPAM. 5&8, 29, 31, 43, 47, 59 ”’1 __ ‘1 ”up“ , 3
Present the result of the query [1 point] and the number of comparisons with [2 points], and
without [2 points] a skip list. Assume the skip list has frequency [M |P|] , where |P| is the cardinality
of a posting P and [.j is thefloorfunction. (Example: P = {1, 2, 3}, |P| = 3, \/|P| m 1.73, [x/IPH = 1)
[Burns 04 [a Mir/g 6" 43, 42, 25, 17,4, 04, H, 54
NMMLQV o4 com‘aavfsons‘é
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(2,5)! (44'6”), ($1 5)] (5,5), (W3), (44, 43),
(M, 45)[ (43143), (4}, 42), (as, 23), (14,24)! (34,34)
(33,93). (Mm), (HIM), (Law)! (53, 5'1), (57,74),
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(2,5), (as), (as), mm, mm, mm), mm
(as, 23), (M' M)' (s4, 54)
(“1.“), (fl, 6‘4), (Sam)
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Compute an unbiased estimate of a text retrieval system’s precision, recall, and the F1 measure on the
first five results [3‘ points], and the precision at 40% recall [2 points] given the following lists of results
for queries ql, and q2, Where R is a relevant result, and N is a non-relevant result:
0 Results for ql : RNNRRNR (10 relevant results for q1 exist in the collection.)
0 Results for (12 : NRNRRRRN (5 relevant results for qg exist in the collection.)
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Define the two assumptions the Naive Bayes classifier makes [2 points]. Explain the advantage of
computing a product of probability estimates as a sum in the logarithmic space [1 point]. Given
an observation x, and the classes cl, and c2, is the knowledge of P(x | cl)P(cl) > P(x | 02)P(62)
sufficient to decide whether P(c1 | x) > P(c2 | x)? Why or why not? [2 points]
Given the following list of observations, use the Naive Bayes classifier to decide whether to play
golf when it is sunny, hot, windy, and the humidity is normal. [5 points]
Sunny
Sunny
Overcast
Overcast
Sunny
Rainy
Sunny
Overcast
Overcast
Rainy
Rainy
Rainy
Sunny
Rainy
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7‘- ’1‘: 4495“;
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4 3 s so
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P<7efl5mn/, ”0+! Wowmé TVMZ) > pC'VO’ Snowy. Ho; Nomad
TIN/‘2): Wm 449m, [0&7 aCeéfr
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I.‘ Sheet I.‘ ‘_I I.‘ “60 I_‘ _I _I I.‘ L“ _I L I_ I_‘ ‘_1 p0 Ints I.‘ ‘_I I_‘ ‘_I I.“ ‘_I
Given a directed graph G that represents three Web pages V(G) = {(1, b, c}, and the links E(G) =
{(b, a), (c, a), (e, b), (b, 0)} between these three pages, draw G [1 point] and produce the adjacency
matrix (also known as the link matrix) A [1 point], and the Markov transition matrix P [2 points].
Describe the intuition behind the PageRank algorithm [1 point]. Compute the PageRank of the
pages a, b, and C using a single iteration of the PageRank algorithm [2 points].
Describe what we mean, when we call a page a hub, or an authority [1 point]. Compute the hub,
and authority scores of the pages a, b, and c [2 points].
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