Groups And Symmetries In Statistical Models
summary
Draws a precise bridge between invariant theory and maximum likelihood for Gaussian models: for reductive groups unstable ↔ likelihood unbounded, semistable ↔ likelihood bounded, polystable ↔ MLE exists, and stability implies uniqueness (complex case gives full equivalence). Introduces RDAGs (colored DAGs), constructs augmented sample matrices and gives an explicit linear‑algebra algorithm: MLE exists iff the child row is not in the span of the other rows, uniqueness iff all color blocks have full rank. Identifies a group for RDAGs under transitivity plus the butterfly criterion; non‑reductive cases need extra care but the methods compute MLEs and connect to geodesically‑convex scaling algorithms.
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