Def logistic_$\_$regression($($X,$,$ y,$,$ max_$\_$iter, alpha)$)$: 

 

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Trains the logistic regression classifier on data X and labels y using gradient descent for max_$\_$iter iterations with learning rate alpha.

Returns the weight vector, bias term, and losses at each iteration AFTER updating the weight vector and bias.

Input:

X: data matrix of shape nxd

y: n−$-$dimensional vector of data labels (+1$(+1$ or −1)$-1)$

max_$\_$iter: number of iterations of gradient descent to perform

alpha: learning rate for each gradient descent step

Output:

w,$,$ b,$,$ losses

w: d−$-$dimensional weight vector

b: scalar bias term

losses: max_$\_$iter−$-$dimensional vector containing negative log likelihood values AFTER a gradient descent in each iteration

'''" id="MathJax-Element-18-Frame" role="presentation" style="font-size: 121%; position: relative;" tabindex="0">'''$\text{'}\text{'}\text{'}$

n,$,$ d =$=$ X.$.$shape

w =$=$ np.$.$zeros($($d)$)$

b =0.0$=0\mathrm{.}0$

losses =$=$ np.$.$zeros($($max_$\_$iter)$)$

for step in range($($max_$\_$iter)$)$:

# YOUR CODE HERE.