# Akaike information criterion

## Summary

The Akaike Information Criterion (AIC) is a frequentist model selection criterion typically used to regularize maximum likelihood estimators. The AIC provides a relative estimate of the quality of the tested models (so it is necessary to report the AIC differences between models), but the AIC will not indicate if all tested models poorly describe the data. The quality score is a relative estimate of the kl-divergence between the given model and the true model.

## Context

This concept has the prerequisites:

- maximum likelihood (The AIC is often used to regularize maximum likelihood estimation.)
- generalization (The AIC is a way of improving generalization.)
- KL divergence (The AIC is minimized for the model that minimizes the kl-divergence between the model and the true model (even though the true model is not known).)

## Goals

- Know the definition of the AIC.

- How is the AIC justified in terms of performance on held-out data?

## Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Ratio Tests (2004)

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## See also

- Bayesian Information Criterion (BIC) is a different model selection criterion with different theoretical underpinnings, and practically, AIC does not penalize the number of parameters as severely as BIC
- Mathematical justification of the AIC .