The Living Thing / Notebooks : Chain graphs

Partially directed random fields, for some kind of definition thereof? The classic chain graph of the 80s allows you to have cycling sets of mutually influencing variables, connected by directed acyclic influence. It looks like the CPDAGs of Maathuis et al, and I’m curious what the precise relationship is.

BoSt95
Bouckaert, R. R., & Studený, M. (1995) Chain graphs: Semantics and expressiveness. In C. Froidevaux & J. Kohlas (Eds.), Symbolic and Quantitative Approaches to Reasoning and Uncertainty (pp. 69–76). Springer Berlin Heidelberg
Bunt96
Buntine, W. L.(1996) A guide to the literature on learning probabilistic networks from data. IEEE Transactions on Knowledge and Data Engineering, 8(2), 195–210. DOI.
Bunt13
Buntine, W. L.(2013) Chain Graphs for Learning. arXiv:1302.4933 [Cs].
DaLa93
Dawid, A. P., & Lauritzen, S. L.(1993) Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models. The Annals of Statistics, 21(3), 1272–1317. DOI.
Drto09
Drton, M. (2009) Discrete chain graph models. Bernoulli, 15(3), 736–753. DOI.
Laur92
Lauritzen, S. L.(1992) Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models. Journal of the American Statistical Association, 87(420), 1098–1108. DOI.
LaRi02
Lauritzen, S. L., & Richardson, T. S.(2002) Chain graph models and their causal interpretations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(3), 321–348. DOI.
LaWe89
Lauritzen, S. L., & Wermuth, N. (1989) Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative. The Annals of Statistics, 17(1), 31–57. DOI.
Stud97a
Studený, M. (1997a) A recovery algorithm for chain graphs. International Journal of Approximate Reasoning, 17(2–3), 265–293. DOI.
Stud97b
Studený, M. (1997b) On Recovery Algorithm for Chain Graphs.
StBo98
Studený, M., & Bouckaert, R. R.(1998) On chain graph models for description of conditional independence structures. The Annals of Statistics, 26(4), 1434–1495. DOI.
WeLa90
Wermuth, N., & Lauritzen, S. L.(1990) On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models. Journal of the Royal Statistical Society. Series B (Methodological), 52(1), 21–50.
XiJR12
Xing, E. P., Jordan, M. I., & Russell, S. (2012) A Generalized Mean Field Algorithm for Variational Inference in Exponential Families. arXiv:1212.2512 [Cs, Stat].