Logistic regression is a popular supervised machine learning algorithm used for binary classification problems. It is a probabilistic, linear model that can be used to predict the probability of an event occurring based on some given input variables.

Key Concepts

  • Binary Classification: Logistic regression is used for binary classification problems, where the target variable has only two possible outcomes.
  • Sigmoid Function: The sigmoid function, also known as the logistic function, is used to map the input to a value between 0 and 1. This function is defined as: $$ \sigma(z) = \frac{1}{1 + e^{-z}} $$
  • Cost Function: The cost function used in logistic regression is the logarithmic loss, also known as the cross-entropy loss.

How it Works

  1. Model Representation: The logistic regression model can be represented as: $$ y = \sigma(\theta^T x) $$ where $y$ is the predicted probability, $\theta$ is the parameter vector, and $x$ is the input feature vector.
  2. Parameter Estimation: The parameters $\theta$ are estimated using gradient descent, which minimizes the cost function.
  3. Prediction: Once the parameters are estimated, the model can be used to predict the probability of the event occurring for new data points.

Applications

  • Sentiment Analysis
  • Spam Detection
  • Credit Scoring
  • Medical Diagnosis

Further Reading

For more information on logistic regression, you can refer to the following resources:

Machine Learning