A. Roverato, M. Studeny:
A graphical representation of equivalence classes
of AMP chain graphs.
Journal of Machine Learning Research
7 (2006), pp. 1045-1078.
This papers deals with chain graph models under alternative AMP
interpretation. A new representative of na AMP Markov equivalence
class, called the largest deflagged graph, is proposed. The
representative is based on revealed internal structure of the AMP
Markov equivalence class. More specifically, the AMP Markov equivalence
class decomposes into finer strong equivalence classes and there
exists a distinguished strong equivalence class among those forming the
AMP Markov equivalence class. The largest deflagged graph is the largest
chain graph in that distinguished strong equivalence class. A composed
graphical procedure to get the largest deflagged graph on the basis
of any AMP Markov equivalent chain graph is presented.
- chain graph
- AMP Markov equivalence
- largest deflagged graph
- strong equivalence
- deflagging procedure
- component merging procedure
pdf version of the paper (308kB) is available.
The paper partially builds on the following papers:
- S. A. Andersson, D. Madigan, M. D. Perlman:
Alternative Markov properties for chain graphs. Scandinavian Journal of
Statistics 28 (2001), pp. 33-85.
- A. Roverato: A unified approach to the characterisation of
equivalence classes of DAGs, chain graphs with no flags and chain
graphs. Scandinavian Journal of Statistics 32 (2005), pp. 295-312.