Generative Models 1- Cost-sensitive classification with generative...

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Generative Models 1- Cost-sensitive 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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