Question: Algorithm 1 is logistic regression ( you may use built - in methods for this ) . Algorithm 2 is gradient descent where you train

Algorithm 1 is logistic regression (you may use built-in methods for this).
Algorithm 2 is gradient descent where you train a model of the form \sigma (w x)(with parameter w) with respect to square loss, i.e. the loss function is 21(\sigma (w x) y)2, averaged over the points in the training set (code this up yourself, including calculating the gradient).
Algorithm 3 is stochastic gradient descent again with respect to square loss, where during each iteration we use the gradient at one random point from the training set.

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