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Logistic regression

Regressione logistica

Logistic regression is a statistical model used for classification, that is, for predicting which category an observation belongs to, typically in two-class problems like spam versus not spam, or customer churn versus retention. Despite the name containing regression, it does not estimate a continuous value but a probability between 0 and 1.

Definition

How it works

The model combines the input variables into a weighted sum, exactly like linear regression, but then applies a function called the sigmoid, which squashes the result into a range between 0 and 1, interpretable as the probability of belonging to the positive class. A threshold, often 0.5, turns that probability into a binary decision. The weights are estimated by maximizing the likelihood of the observed data, usually through gradient descent.

Applications

It is among the most widely used models in production for its speed, interpretability and reliability: spam filters, credit card fraud detection, customer churn prediction, binary medical diagnosis and credit scoring. It often serves as a solid baseline before trying more complex models like trees or neural networks, and in many regulated contexts it remains the preferred choice precisely because every coefficient can be explained.

History & etymology

The name comes from the logistic function, first described in the mid-nineteenth century by the Belgian mathematician Pierre François Verhulst to model population growth, which slows as it approaches a limit instead of growing forever. The same S-shaped curve turned out to be a perfect fit for modeling probabilities, and it was adopted in statistics during the twentieth century under the name logistic regression, underlining its kinship with linear regression while describing a different phenomenon, the probability of class membership.

How it's used in Grace

Grace's 7 evaluation dimensions use principles similar to logistic regression to turn multiple criteria into a 0-100 score: knowing how an estimated probability works helps you interpret your results better.

Related terms

• Linear regression
• Classification
• Confusion matrix
• Precision and Recall
• ROC curve and AUC

More in Fondamenti AI

• LLM (Large Language Model)
• Token
• Context Window
• Temperature
• AI Hallucination
• Fine-tuning
• RAG (Retrieval Augmented Generation)
• Embedding

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