Equation:
where:
Logistic regression models the probability of a binary outcome following a Bernoulli distribution. The Bernoulli distribution is a discrete probability distribution of a random variable that takes only two values - typically 0 and 1, with p being the probability of success (1) and 1-p being the probability of failure (0).
In logistic regression, we estimate p (the probability of the positive class) based on a given dataset of independent variables. The model outputs a probability between 0 and 1, which matches the Bernoulli distribution's parameter p. This probability can then be used to make binary predictions by applying a threshold (typically 0.5).
While commonly used for classification tasks, logistic regression is fundamentally a probabilistic model that estimates Bernoulli probabilities using a linear decision boundary. This means the input features need to be linearly separable for the model to perform well.
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