Label switching
Topic of Mixtures and the EM algorithm, part of Statistical learning
Label switching
| Type | Topic |
| Taught in | Mixtures and the EM algorithm |
| Part | Statistical learning |
Renaming the components of a mixture changes the parameter vector and leaves the density unchanged, so a fitted mixture is identified only up to a permutation of labels. Comparing component parameters across fits, or across MCMC draws, needs a rule for matching labels.
In Mixtures and the EM algorithm
Label switching. Renaming components changes the parameter vector and leaves the density unchanged. Finite Gaussian mixtures with distinct components and positive weights are identifiable up to this permutation. Coincident components or zero weights introduce further non-identifiability (McLachlan and Peel, 2000). Before comparing component parameters across fits, decide how to match labels. Ordering means can help in one dimension. The order becomes unstable when means are close.
Used in
See also
Finite mixture model · Posterior membership · Complete-data likelihood · EM for a normal mixture · Monotonicity of EM · Likelihood of a normal mixture · What the stationary equations suggest · E and M steps