Logistic regression is a statistical method used for binary classification problems. It models the probability that a given input belongs to a particular class. It's a type of regression analysis where the dependent variable is categorical (binary in this case), unlike linear regression where the dependent variable is continuous.
In logistic regression, the logistic function (also known as the sigmoid function) is used to model the probability:
The cost function in logistic regression is used to measure the accuracy of the model's predictions. A common cost function for logistic regression is the binary cross-entropy loss function, also known as log loss:
The goal is to minimize this cost function by adjusting the parameters during the training process using optimization algorithms like gradient descent.
A confusion matrix is a table that is often used to describe the performance of a classification model on a set of test data for which the true values are known. It allows visualization of the performance of an algorithm.
Here's how a confusion matrix is typically structured for binary classification:
From the confusion matrix, various performance metrics like accuracy, precision, recall, and F1-score can be calculated, which provide insight into the model's performance.
These topics covered provide a fundamental understanding of logistic regression for classification, the associated cost function, and how performance is evaluated using a confusion matrix.