A few weeks ago I was playing with the Good Regulator and John’s Gooder version and incidentally I also found myself pulling out some simple graphical manipulation rules. Your ‘Markov re-rooting’ came into play, and also various of the ‘Bookkeeping’ rules. You have various more exciting rules here too, thanks!
I also ended up noticing a kind of ‘good regulator motif’ as I tried expanded the setting with a few temporal steps and partial observability and so forth. Basically, doing some bookkeeping and coarse-graining, you can often find a simple GR structure within a larger ‘regulator-like’ structure, and conclude things from that. I might publish it at some point but it’s not too exciting yet. I do think the overall move of finding motifs in manipulated graphs is solid, and I have a hunch there’s a cool mashup of Bayes-net algebra and Gooder Regulator waiting to be found!
I love the Frankenstein rule. FYI, the orderings you’re talking about which are ‘consistent’ with the graphs are called topological orderings, and every DAG has (at least) one. So you could concisely phrase some of your conditions along the lines of ‘shared topological order’ or ‘mutually-consistent topological ordering’.
BTW causal graphs are usually restricted to be DAGs, right? (i.e., the ‘causes’ relation is acyclic and antisymmetric.) So in this setting where we are peering at various fragments which are assumed to correspond to some ‘overall mega-distribution’, it might come in handy to assume the overall distribution has some acyclic presentation—then there’s always a(t least one) topo ordering available to be invoked.
Oh yeah, I don’t know how common it is, but when manipulating graphs, if there’s a topo order, I seem to strongly prefer visualising things with that order respected on the page (vertically or horizontally). So your images committed a few minor crimes according to that aesthetic. I can also imagine that some other aesthetics would strongly prefer writing things the way you did though, e.g. with M←X→N. (My preference would put M and N slightly lower, as you did with the M, Xi graph.)
This is really great!
A few weeks ago I was playing with the Good Regulator and John’s Gooder version and incidentally I also found myself pulling out some simple graphical manipulation rules. Your ‘Markov re-rooting’ came into play, and also various of the ‘Bookkeeping’ rules. You have various more exciting rules here too, thanks!
I also ended up noticing a kind of ‘good regulator motif’ as I tried expanded the setting with a few temporal steps and partial observability and so forth. Basically, doing some bookkeeping and coarse-graining, you can often find a simple GR structure within a larger ‘regulator-like’ structure, and conclude things from that. I might publish it at some point but it’s not too exciting yet. I do think the overall move of finding motifs in manipulated graphs is solid, and I have a hunch there’s a cool mashup of Bayes-net algebra and Gooder Regulator waiting to be found!
I love the Frankenstein rule. FYI, the orderings you’re talking about which are ‘consistent’ with the graphs are called topological orderings, and every DAG has (at least) one. So you could concisely phrase some of your conditions along the lines of ‘shared topological order’ or ‘mutually-consistent topological ordering’.
BTW causal graphs are usually restricted to be DAGs, right? (i.e., the ‘causes’ relation is acyclic and antisymmetric.) So in this setting where we are peering at various fragments which are assumed to correspond to some ‘overall mega-distribution’, it might come in handy to assume the overall distribution has some acyclic presentation—then there’s always a(t least one) topo ordering available to be invoked.
Oh yeah, I don’t know how common it is, but when manipulating graphs, if there’s a topo order, I seem to strongly prefer visualising things with that order respected on the page (vertically or horizontally). So your images committed a few minor crimes according to that aesthetic. I can also imagine that some other aesthetics would strongly prefer writing things the way you did though, e.g. with M←X→N. (My preference would put M and N slightly lower, as you did with the M, Xi graph.)