An information criterion is a scoring rule that compares fitted statistical models by trading goodness-of-fit against model complexity: it maps a fitted model to a single number, lower values indicating the preferred model, combining the model's maximized log-likelihood with a penalty on the number of free parameters k — AIC = 2k − 2·logL, BIC = k·log(n) − 2·logL, with MDL in the same family via coding theory. Its parameters are the model's maximized log-likelihood, the number of free parameters k, and (for BIC-type members) the sample size n; the choice of penalty function is what distinguishes one member of the family from another. It persists as named, standardized formulas in the statistical and machine-learning literature, in textbooks, and in software implementations (R's AIC/BIC functions, statsmodels, scikit-learn scoring), so that models fitted in different places remain comparable on a shared yardstick. [formal: criterium informationis | substrate: mind | horizon: generations | explicit: yes | epoch: 0.11]
Accepted ontology entry
information-criterion
An information criterion is a scoring rule that compares fitted statistical models by trading goodness-of-fit against model complexity: it maps a fitted model to a single number, lower values indicating the preferred model, combining the m…
Definition
Why it is in scope
A human-made family of statistical scoring rules that trade goodness-of-fit against model complexity, built to persist as the standard comparison yardstick of model-selection practice.
Names and aliases
- information-criterionen · CANONICAL
Relations from this entry
- cms7xukk2007xh6s8dqyihtf7SERVES →
Law 8d 'for whose sake?': the information criteria were built explicitly as rules for choosing among candidate models — Akaike (1973) introduced AIC as a model-selection device via his information-theoretic extension of maximum likelihood, and Schwarz (1978) introduced BIC for the same end. Its designed purpose is to make model-selection operational: a shared yardstick for comparing fitted models. Servant (criterion) points at master (model-selection); the purpose is by design and sustained practice, not incidental benefit.
- statistical-modelDEPENDS_ON →
Law 8 removal test, operational not meta: an information criterion scores a fitted statistical model — its input is a model with a maximized log-likelihood and a count of free parameters. Remove statistical models NOW and there is nothing to score: the scoring, comparing, and selecting operations have no object and stop operating, not merely stop being sayable (Law 2b). Not identity (Law 8c): a criterion is not a model, it is a rule that operates on models; the model is an essential argument of the function, as in the parallel AIC and log-likelihood cases.
Relations to this entry
- akaike-information-criterion← INSTANCE_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.
Record identity
- Created
- Sep 3, 2026, 1:00 PM UTC
- Content hash
- d99485053f5fedcf5d7dcb5fbefe33420eb55d85ede16e02066e11c9ed314b7d