Logistic Regression

Logistic regression is a machine learning algorithm used for classification problems. The term logistic is derived from the cost function (logistic function) which is a type of sigmoid function known for its characteristic S-shaped curve. A logistic regression model predicts probability values which are mapped to two (binary classification) or more (multiclass classification) classes.


  • 1 = the curve's maximum value

  • S(z) = output between 0 and 1 (probability estimate)

  • z = the input

  • e = base of natural log (also known as Euler's number)

In multiclass classification with logistic regression, a softmax function is used instead of the sigmoid function.

Like linear regression, gradient descent is typically used to optimize the values of the coefficients (each input value or column) by iteratively minimizing the loss of the model during training.

The decision boundary is the acceptable threshold at which a probability can be mapped to a discrete class e.g. pass/fail or vegan/vegetarian/omnivore.

The cost function in logistic regression is more complex than linear regression. For example, mean squared error would yield a non-convex function with many local minimums, making it difficult to optimize with gradient descent. Cross entropy, also called log loss is the cost function used with logistic regression.

Regularization is a technique used to prevent overfitting by penalizing signals that provide too much explanatory power to a single feature. Regularization is extremely important in logistic regression.

Accuracy, a model evaluation metric, is used to measure how accurate a model's predictions are -- this is expressed as the number of true classifications divided by the total.

Linear vs Logistic Regression

Linear regression predictions are continuous (e.g. test scores from 0-100).

Logistic regression predictions classify items where only specific values or classes are allowed (e.g. binary classification or multiclass classification). The model provides a probability score (confidence) with each prediction.

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