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Unformatted text preview: that a book would be
rated as positive rather than negative, where a user rating
of 1 5 is interpreted as negative and 6 10 as positive. As
described below, the exact numerical ratings of the training examples are used to weight the training examples when
estimating the parameters of the model.
Speci cally, we employ a multinomial text model 21 ,
in which a document is modeled as an ordered sequence
of word events drawn from the same vocabulary, V . The
naive Bayes" assumption states that the probability of each
word event is dependent on the document class but independent of the word's context and position. For each class, cj ,
and word or token, wk 2 V , the probabilities, P cj and
P wk jcj must be estimated from the training data. Then
the posterior probability of each class given a document, D,
is computed using Bayes rule:
P cj jD = P cj
P D Y P a jc
Dj j ij i=1 1 where ai is the ith word in the document, and jDj is the
length of the document in words. Since for any given document, the prior P D is a constant, this factor can be ignored
if all that is desired is a ranking rather than a probability
estimate. A ranking is produced by sorting documents by
their odds ratio, P c1 jD=P c0 jD, where c1 represents the
positive class and c0 represents the negative class. An example is classi ed as positive if the odds are greater than 1,
and negative otherwise.
In our case, since books are represented as a vector of
documents," dm , one for each slot where sm denotes the
mth slot, the probability of each word given the category
and the slot, P wk jcj ; sm , must be estimated and the posterior category probabilities for a book, B , computed using:
P cj jB = P cj
P B Y Y P a
S jdm j m=1 i=1 mi jcj ; sm 2 where S is the number of slots and ami is the ith word in
the mth slot.
Parameters are estimated from the training examples as
follows. Each of the N training books, Be 1 e N is
given two real weights, 0 ej 1, based on scaling it's
user rating, r 1 r 10 : a positive weight, e1 = r ,
1=9, and a negative weight e0 = 1 , e1 . If a word appears
n times in an example Be , it is counted as occurring e1 n
times in a positive example and e0 n times in a negative
example. The model parameters are therefore estimated as
follows:
N
P cj =
3
ej =N X
Xn
P w jc ; s =
kj m N e=1 e=1 ej kem =Lcj ; sm 4 Slot
WORDS
WORDS
WORDS
WORDS
SUBJECTS
AUTHOR
WORDS
WORDS
RELATEDTITLES
RELATEDTITLES
AUTHOR
AUTHOR
AUTHOR
RELATEDAUTHORS
RELATEDAUTHORS
WORDS
WORDS
WORDS
RELATEDTITLES
RELATEDTITLES The Fabric of Reality:
The Science of Parallel Universes And Its Implications
by David Deutsch recommended because: Word
Strength
ZUBRIN
9.85
SMOLIN
9.39
TREFIL
8.77
DOT
8.67
COMPARATIVE
8.39
8.04
D GOLDSMITH
ALH
7.97
MANNED
7.97
SETTLE
7.91
CASE
7.91
R ZUBRIN
7.63
R WAGNER
7.63
H MORAVEC
7.63
B DIGREGORIO
7.63
A RADFORD
7.63
LEE
7.57
MORAVEC
7.57
WAGNER
7.57
CONNECTIONIST
7.51
BELOW
7.51 Slot
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
WORDS
SUBJECTS
TITLE
WORDS
WORDS Table 1: Sampl...
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 Fall '13

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