Question

2. (20 pts.) Consider the Binary Independence Model for text document. Given a vocabulary V (w., wa) of all English words (and tokens), assume that a text document is rep- resented as a vector of binary features x-(x1, ,xd)t such that xỉ 1s I if the word wi appears in the document, and r, is 0 otherwise. We want to classify text documents into c categories. Let P(wj) be the prior probability for the class w for j-1,..., c. Assume that the components of ? are statistically independent given the category (Naive Bayes model), i.e. i= i Assume we could estimate the following probability from the training data Show that the minimum probability of error is achieved by the following decision rule: De- cide ah if gk(x) gi(t) for all jメk, where the discriminant function is given in the form of Give the expressions of ciy and b

Answer 1

solution Given data- Assume we coceld estimate the following probability from the training data poi a p (xix Alwi) iz !, ..., d sel,..C. show that the minimem probability of erroris the following decision vole: Decide achieved by Wk it gx (i) z gi (x) for all stk, where the function is given in the form of discrimincent g; B) Cij zitti (Ů Thad the point value Inding in between probability . + X104 and 104

1 P x 10-4 L 104 → PCXL 104)- p (XS-2X164) >> P [zki]-P [75-2] q value Find z Value's lesing salistical calculation - p (== 1) = 0.84134 P (z S-2) = 0.97725 → 0.84134 -0.97725 - PE 2X10 4 2 10-4) 2 -0.15641 Please give me thumb up.