About Machine Learning ( Part 3: Logistic Regression )
Classification Problem
In machine learning, when we are predicting a discrete label, such as determining whether an email is spam or not, we are dealing with a classification problem. Logistic regression is commonly used for binary classification tasks, where the goal is to predict one of two classes, typically represented as 0 or 1.
The logistic function (also called the sigmoid function) is the core of logistic regression, as it maps input features to probabilities between 0 and 1. These probabilities represent the likelihood of the sample belonging to a particular class.
The logistic function is defined as:
$$
\sigma(z) = \frac{1}{1 + e^{-z}}
$$
Where $z = \omega_0 + \mathbf{\omega}^T \mathbf{x}$, the linear combination of the input features $\mathbf{x}$ and the model’s parameters $\mathbf{\omega}$.