Lecture 43:- Logistic Regression intuition

Logistic Regression is a fundamental algorithm in the field of machine learning and is commonly used for binary classification tasks. Despite its name, it's actually a classification algorithm rather than a regression algorithm. It's particularly useful when you want to predict the probability of an event occurring based on one or more input features.

Let's break down the intuition behind Logistic Regression step by step:

1. Sigmoid Function: Logistic Regression uses the sigmoid function (also called the logistic function) to transform the output of a linear equation into a value between 0 and 1. The sigmoid function "squashes" any input into this range, making it suitable for representing probabilities.

   The sigmoid function is defined as:

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   S(z) = 1 / (1 + e^-z)

   where z is the linear combination of the input features and their corresponding weights.

2. Linear Combination: Logistic Regression calculates a linear combination of the input features by multiplying each feature with its corresponding weight and summing them up. This linear combination is represented by z in the sigmoid function.

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   z = w0 + w1*x1 + w2*x2 + ... + wn*xn

   • w0, w1, w2, ..., wn are the weights assigned to each feature.
   • x1, x2, ..., xn are the input features.

3. Probability Interpretation: The output of the sigmoid function S(z) represents the estimated probability that the given input belongs to the positive class (class 1). In a binary classification problem, there are two classes: 0 and 1 (or negative and positive). So, the probability of belonging to the negative class is 1 - S(z).

4. Decision Boundary: To make a classification prediction, a threshold is applied to the estimated probability. Typically, if the probability is greater than or equal to 0.5, the input is classified as class 1; otherwise, it's classified as class 0. The decision boundary is the value of z at which the probability crosses the threshold (0.5).

5. Training: During the training process, the algorithm adjusts the weights (w0, w1, w2, ..., wn) to minimize the difference between the predicted probabilities and the actual class labels in the training data. This is typically done using optimization techniques like gradient descent.

In summary, Logistic Regression is a way to model the probability of a binary outcome using a linear equation and a sigmoid function. It's a simple yet powerful algorithm that forms the foundation for more complex classification techniques and is widely used in various fields, including medicine, finance, marketing, and more.