Logistic Regression from Scratch

Code Walk-Through

Importing Libraries

import numpy as np 
from numpy import log,dot,e,shape
import matplotlib.pyplot as plt

We are gonna be using sklearn’s make_classification dataset with 4 features

from sklearn.datasets import make_classification
X,y = make_classification(n_features = 4,n_classes=2)
from sklearn.model_selection import train_test_split  
X_tr,X_te,y_tr,y_te = train_test_split(X,y,test_size=0.1)

print(X_tr.shape, X_te.shape)

💡 Running the above code we get: **(90, 4) (10, 4)**

The output basically means The training data (X_tr) consists of 90 samples, each with 4 features, while the testing data (X_te) consists of 10 samples, also with 4 features each

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Standardization

Standardization is a technique used to scale the features of your data so that they have a mean of zero and a standard deviation of one. This process helps to bring all features onto a similar scale, making it easier for machine learning algorithms to process them.

Say $X$ is feature in your dataset, the standardized value $Z$ is calculated as:

$$ Z = \frac{X - \mu}{\sigma} $$

Here $\mu$ is the mean of the feature $X$ and $\sigma$ is the standard deviation.

def standardize(X_tr):
    for i in range(shape(X_tr)[1]):
        X_tr[:,i] = (X_tr[:,i] - np.mean(X_tr[:,i]))/np.std(X_tr[:,i])

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Initializing the Parameters