Local computations of the iterative proportional scaling procedure for hierarchical models

Xu, Ping‐Feng; Sun, Jubo; Shan, Na

doi:10.1016/j.csda.2015.10.009

Cited by 2 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The IPS algorithm is widely used in survey statistics, such as in [9,27,43], and has been researched in connection to optimal transport problems in its more restricted form as Sinkhorn's algorithm [6,37]. Partition models include hierarchical models, which have been the subject of much study in connection with the IPS algorithm [21,25,42]. Maximum likelihood estimation for log-linear models and its relationship to algebraic and combinatorial objects is also of interest in algebraic statistics.…”

Section: Introductionmentioning

confidence: 99%

Rational partition models under iterative proportional scaling

Coons¹,

Langer²,

Ruddy³

2022

Preprint

View full text Add to dashboard Cite

In this work we investigate partition models, the subset of log-linear models for which one can perform the iterative proportional scaling (IPS) algorithm to numerically compute the maximum likelihood estimate (MLE). Partition models include families of models such as hierarchical models and balanced, stratified staged trees. We define a sufficient condition, called the Generalized Running Intersection Property (GRIP), on the matrix representation of a partition model under which IPS algorithm produces the exact MLE in one cycle. Additionally we connect the GRIP to the toric fiber product and to previous results for hierarchical models and balanced, stratified staged trees. This leads to a characterization of balanced, stratified staged trees in terms of the GRIP.

show abstract