Question

Assume that we have training data for texts with two words, w1 and w2, with two classes C1 and C2. From the training data we have estimated: P(w1|C1) = a1, P(w2|C1) = b1, P(C1) = c1 P(w1|C2) = a2, P(w2|C2) = b2, and P(C2) = c2 Given a document D with words {w1,w2,w1}, what is the formula giving the log-odds-ratio of the probability that document is classed as C1 to the probability that document is classed as C2 using the natural logarithm? I.e. ln left parenthesis fraction numerator P left parenthesis C 1 vertical line D right parenthesis over denominator P left parenthesis C 2 vertical line D right parenthesis end fraction right parenthesis ?

a)(ln(a1)*ln(b1)-ln(c1)) /(ln(a2) *ln(b2) - ln(c2))

b)2ln(a1)+ln(b1)+ln(c1) -2ln(a2) -ln(b2) - ln(c2)

c)2ln(a1)+ln(b1)+2ln(c1) -2ln(a2) -ln(b2) - 2ln(c2)

d)ln(a1)*ln(b1)*ln(c1) /(ln(a2) *ln(b2) * ln(c2))

e)ln(a1)+ln(b1)+ln(c1) -ln(a2) -ln(b2) - ln(c2)

Answer 1

Assume that we have training data for texts with two words, w1 and w2, with two classes C1 and C2. From the training data we have estimated:

P(w1|C1) = a1, P(w2|C1) = b1, P(C1) = c1

P(w1|C2) = a2, P(w2|C2) = b2, P(C2) = c2

Given a document D with words {w1,w2,w1},

the formula giving the log-odds-ratio of the probability that document is classed as C1 to the probability that document is classed as C2 using the natural logarithm is

ln(a1)*ln(b1)*ln(c1) /(ln(a2) *ln(b2) * ln(c2))

option- (a)