Estimating the Dimension of a Model¶
Schwarz, G. (1978). Estimating the Dimension of a Model. The Annals of Statistics, 6(2), 461-464.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Clustering
- Every commitment of the prime is explicit. Similarity is chosen, not given: change the covariance structure (spherical versus full) and the same points cluster differently, which is the labels-as-output invariant operating — the grouping is produced by the procedure, not presupposed. The partition is a hypothesis: the fit asserts the data are a discrete mixture of \(k\) Gaussians rather than one continuous density, a claim the analyst tests with a held-out likelihood or an information criterion (BIC) that penalises \(k\).
This sourceIntroduces the Bayesian Information Criterion (BIC), used to select the number of mixture components / clusters by penalizing complexity.
- Every commitment of the prime is explicit. Similarity is chosen, not given: change the covariance structure (spherical versus full) and the same points cluster differently, which is the labels-as-output invariant operating — the grouping is produced by the procedure, not presupposed. The partition is a hypothesis: the fit asserts the data are a discrete mixture of \(k\) Gaussians rather than one continuous density, a claim the analyst tests with a held-out likelihood or an information criterion (BIC) that penalises \(k\).
- Overfitting
This sourceBIC (Bayesian Information Criterion) as alternative to AIC.
- Parsimony (Occam's Razor)
Verification¶
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Registry ID ref:3478c3dd194a · see in the full table