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df$.$head $(3)$

$\backslash$table$[[,$User ID$,$Gender,Age,EstimatedSalary,Purchased$],[0,15624510,$Male,$19,19000,0],[1,15810944,$Male,$35,20000,0],[2,15668575,$Female,$26,43000,0]]$

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Generate code with $df$

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After looking at the data, drop irrelevant features $($such that have no learnability meaning$)$ and make sure your remaining features are numeric.

# Implement here

Plot on the densities of the features, choose the scaler we will be using.

Write here your answer and explain it

$1$s

from sklearn.model$\_$selection import train$\_$test$\_$split # Implement here

Split the data into $80\%$ train samples and $20\%$ test samples, with random state $42.$

Split the train into real train $(70\%)$ and validation $(30\%)$ with random state $42.$

Apply the scaler on the train, validation and test sets.

Remember: when scaling the test, it should use all the training data.

Tip: For minimizing the loss function, what labels did we look at$?$ Are they the same here?

$[]$ # Import scaling library

# Implement here

Implement the function Logistic$\_$Regression$\_$via$\_$GD$($P$,$y$,$Ir$)$:

Input: an np array $\text{'}P\text{'}$ of $\text{'}n\text{'}$ rows and $\text{'}d\text{'}$ columns, a label vector $\text{'}y\text{'}$ of $\text{'}n\text{'}$ entries and learning rate parameter $\text{'}$Ir$\text{'}.$

Output: The function computes the output vector $\text{'}w\text{'}($and $\text{'}b\text{'})$ which minimzes the logistic regression cost function on $\text{'}P\text{'}$ and $\text{'}y\text{'}.$

The implementation should be fully yours. Don't use library implementation!

It should be done by implementing Gradient descent $($with $\text{'}$Ir$\text{'}$ as the learning rate$)$ to solve logistic regression.

Tip: The gradients may be large, you can use $\frac{1}{n}$gradL $($which is the true empirical loss' gradient$)$