Transcribed Text
Generative Models
1 Costsensitive classification with generative models.
You are designing a pregnancy test based on a new set of features. You have a
generative model with the following profile:
Class 0 (not pregnant): probability distribution Po(x), mixing welght To
Class 1 (pregnant): probability distribution P1 (x), mixing welght 71
(Note: mixing weight, or the mix proportion, is the proportion of each
class in a mixture model, i.e., the probability Po(y = 1) for a class (.)
Based on this model, you want to decide whether a person with features X is
pregnant or not. However, in this case the cost of misclassification is not
symmetric: here's the cost you incur if you predict wrong.
Cost Matrix
True
Label
1
Prediction
100
I
10
Assuming your model is perfectly correct, how should you predict on x, to
minimize expected cost?(Given a prediction rule based on Pn (x), P1(x),
2 In a probabilistic model for classification using a mixture of Normal distributions
with equal covariance the joint probability of a label y together with input x is
p(x,y;0)=q(y)(N(x;0y,D)
Where, a(y) is the mixture component for y. The classification on a new point x
is then,

(
Note that this can also be written as
f(x) =sign[logp(x,+1;0)logp(x,1;0)] 
Show that ((x) is a linear classifier, i.e. that it can be written in the form
sign[@.x+ 00].
Define 0 and 0. as a function of q(+1), q(1), and
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