An information-theoretic criterion for statistical model selection, defined by the formula AIC = 2k − 2ln(L), where k is the number of estimated parameters in the model and L is the maximized likelihood. The criterion estimates the relative information loss when a given model is used to represent the process that generated the data; lower AIC values indicate less estimated loss. It balances goodness-of-fit (via log-likelihood) against model complexity (via the penalty term 2k), automating the trade-off between underfitting and overfitting. Computed by evaluating each candidate model's log-likelihood at its maximum-likelihood estimates, counting its free parameters, and applying the formula. Published by Hirotugu Akaike in 1974 as derived from Kullback–Leibler divergence, it persists through statistical textbooks, software implementations (R, Python, MATLAB), and research practice across disciplines including econometrics, ecology, signal processing, and machine learning. [formal: AIC | substrate: mind | horizon: a moment | explicit: yes | epoch: 2.10]
Accepted ontology entry
akaike-information-criterion
An information-theoretic criterion for statistical model selection, defined by the formula AIC = 2k − 2ln(L), where k is the number of estimated parameters in the model and L is the maximized likelihood. The criterion estimates the relativ…
Definition
Why it is in scope
An information-theoretic measure for model selection that estimates the relative quality of statistical models for a given dataset by balancing goodness-of-fit against model complexity. Human-made: derived from information theory by Hirotugu Akaike (1974), defined by the formula 2k − 2ln(L), and maintained through statistical practice, software packages, and academic literature across disciplines.
Names and aliases
- akaike-information-criterionen · CANONICAL
Relations from this entry
- cmsftujnv00f0qszgpolboiajDERIVED_FROM →
AIC was derived from information-theoretic considerations: Akaike showed that minimizing the estimated Kullback–Leibler divergence between the true model and a candidate model leads to the AIC formula. Information theory (Shannon, 1948; extended to KL divergence by Kullback and Leibler, 1951) existed before AIC (1974) and directly fed into its derivation. Historical direction: information theory came first and fed into AIC.
- information-criterionINSTANCE_OF →
AIC is a specific member of the information-criterion family: its formula 2k − 2·logL is one fit-vs-complexity scoring rule of the family, distinguished by its penalty function (2k per free parameter). Law 9 specific→general: a competent speaker calls AIC 'an information criterion'. Nearest kind (Law 11e): the family itself — no intermediate rung exists, so the leap is the first true connection.
- statistical-modelDEPENDS_ON →
AIC estimates the relative information loss of a statistical model — it is defined as −2·log-likelihood + 2k, where k is the number of parameters in the model. Remove statistical models and AIC has no definition. Constitutive dependency.
- cms7xukk2007xh6s8dqyihtf7INSTANCE_OF →
AIC is a specific kind of model selection criterion. A competent speaker would call AIC 'a model selection method.' The specific→general direction is correct for INSTANCE_OF. It is one of several model selection criteria (along with BIC, MDL, etc.), each implementing a different trade-off between fit and complexity.
- cms7xukk2007xh6s8dqyihtf7SERVES →
AIC is built for the sake of model selection: it was explicitly designed as a criterion for selecting among statistical models by estimating relative information loss. For whose sake? Model selection. Servant (AIC) → master (model-selection). Law 8d.
- cmsm0cr9y00331q137lslor2hDEPENDS_ON →
AIC = 2k - 2log(L) requires a statistical model: k is the number of free parameters, L is the maximum likelihood from fitting the model. Remove the statistical model and AIC ceases to operate — no model to count parameters from, no likelihood to evaluate. AIC is a model-comparison tool, not a standalone formula.
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Record identity
- Created
- Sep 2, 2026, 10:36 PM UTC
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- 6a96d2791ff82c9ba0847080f59fb2d023fc695d6f2b5d817d6b66147835ad7f