Combining four experts about a label

University · ●●○○○ 20 pts

Four independent experts have probabilities

p_1=0.8

p_2=0.7

p_3=0.6

and

p_4=0.5

of being correct about a binary label

L\in\{+1,-1\}

, with a uniform prior on

L

. Expert 1 reports

L_1=-1

, expert 2 reports

L_2=+1

and expert 3 reports

L_3=+1

(expert 4's report is not given). Using the classifier

C(S)=\sum_i \frac{L_i}{2}\log\left(\frac{p_i}{1-p_i}\right)

, find

\Pr(L=+1\mid S)

. Round to two decimal places.