Akaike information criterion

Index: The Book of Statistical Proofs ▷ Model Selection ▷ Classical information criteria ▷ Akaike information criterion ▷ Definition

Definition: Let $m$ be a generative model with likelihood function $p(y \vert \theta, m)$ and maximum likelihood estimates

\[\label{eq:MLE} \hat{\theta} = \operatorname*{arg\,max}_\theta \log p(y | \theta, m) \; .\]

Then, the Akaike information criterion (AIC) of this model is defined as

\[\label{eq:AIC} \mathrm{AIC}(m) = -2 \log p(y | \hat{\theta}, m) + 2 \, k\]

where $k$ is the number of free parameters estimated via \eqref{eq:MLE}.

Sources:

Akaike H (1974): "A New Look at the Statistical Model Identification"; in: IEEE Transactions on Automatic Control, vol. AC-19, no. 6, pp. 716-723; URL: https://ieeexplore.ieee.org/document/1100705; DOI: 10.1109/TAC.1974.1100705.

Metadata: ID: D23 | shortcut: aic | author: JoramSoch | date: 2020-02-25, 12:31.