Logistic Regression is a fundamental machine learning algorithm used for binary classification problems. Unlike linear regression which predicts continuous values, logistic regression predicts the probability that an input belongs to one of two classes. The key component is the sigmoid function, which maps any real number to a value between 0 and 1, making it perfect for probability estimation.
The heart of logistic regression is the sigmoid function, also known as the logistic function. This S-shaped curve takes any real number as input and outputs a value between 0 and 1. The input z is a linear combination of features and their weights, just like in linear regression. As z increases, the probability approaches 1, and as z decreases, it approaches 0. The steep transition around z equals zero makes it ideal for classification decisions.
The classification process in logistic regression follows a clear sequence. First, we calculate the linear combination of input features and weights. Then we apply the sigmoid function to get a probability between 0 and 1. Finally, we use a threshold, typically 0.5, to make the binary decision. If the probability is above the threshold, we predict class 1, otherwise class 0. This creates two distinct regions separated by the decision boundary.
Training a logistic regression model involves finding the optimal weights through an iterative process. We start with random weights and make predictions. Then we calculate the cost using the log-likelihood function, which measures how well our predictions match the actual labels. Using gradient descent, we update the weights to minimize this cost. The decision boundary gradually improves as the algorithm learns to separate the two classes more effectively.
Logistic regression is widely used across many domains. In healthcare, it helps predict disease outcomes. In finance, it's used for credit scoring and fraud detection. Email providers use it for spam filtering, and marketers use it to predict customer responses. The algorithm's key advantages include providing probabilistic outputs, making no assumptions about data distribution, being less prone to overfitting, and running efficiently. Performance is typically evaluated using metrics like accuracy, precision, and recall from the confusion matrix.