I suppose another way to look at this is the overlapping components are the blanket states in some kind of time dependent markov blanket setup, right?
In the scenario you created you could treat x1,x2,x3as the some shielded state at time step t, so it. Then x5,x6,x7 are states outside of the blanket, so et (which group of states is i and which is e don’t really matter, so long as they are on either side of the blanket). y1,y2,y3,y4[1]become it+1, and y5,y6,y7,y8 become et+1.
Then x4 becomes the blanket bt such that
I(it+1,et+1|bt)≈0
and
P(it+1,et+1|it,et,bt)=P(it+1|it,bt)⋅P(et+1|et,bt)
With all that implies. In fact you can just as easily have three shielded states, or four, using this formulation.
(the setup for this is shamelessly ripped off from @Gunnar_Zarncke ’s unsupervised agent detection work)
I suppose another way to look at this is the overlapping components are the blanket states in some kind of time dependent markov blanket setup, right?
In the scenario you created you could treat x1,x2,x3as the some shielded state at time step t, so it. Then x5,x6,x7 are states outside of the blanket, so et (which group of states is i and which is e don’t really matter, so long as they are on either side of the blanket). y1,y2,y3,y4 [1]become it+1, and y5,y6,y7,y8 become et+1.
Then x4 becomes the blanket bt such that
I(it+1,et+1|bt)≈0
and
P(it+1,et+1|it,et,bt)=P(it+1|it,bt)⋅P(et+1|et,bt)
With all that implies. In fact you can just as easily have three shielded states, or four, using this formulation.
(the setup for this is shamelessly ripped off from @Gunnar_Zarncke ’s unsupervised agent detection work)
Did you miss an arrow going to y4 ?