The probabilistic/statistical formulation of linear regression mean of
y is assumed to be linearly related to
x with a Gaussian zero mean error. Then we train to learn the parameters
w that maximize the likelihood function
p(y|x,w). But I don't understand why we learn probability of
y, when we need to predict a value of
x? We are not calculating the probabilities of every possible values o f
y and then predicting the one with maximum probability. So how the prediction works after training?
Please note: I am looking for an theoretical understanding, not some library function that do the regression.