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Mock Midterm 2017_Pb3_Q2

Hello,
In the second question of Problem 3 (Proportional Hazard Model), in order to compute the joint probability of Y given the data, I don't see why we should introduce a whole vector y_tilde (defined using one hot encoding, as far as I understood) instead of just using the label y_n (an integer taking values in the set {1,2,..., K}) for each data point and compute the probability as the product (n: 1 -> N) of the given posterior distribution .
Thank you in advance !
Capture d’écran 2022-01-12 à 19.09.11.jpg

if you check the lecture notes, I believe it is a relatively common way to solve the problem.

Thanks for your answer, could you tell me which part of the lecture notes you are referring to ?
Because, for instance, when we showed that classic least-squares linear regression can be interpreted as a MLE (very beginning of the course) we didn't transform the labels into vectors for each data point or anything. Capture d’écran 2022-01-12 à 22.44.47.jpg

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