While most examples in the literature utilize static Markov blankets in which time does not affect whether or not nodes are assigned to object, blanket, and environment this is not a necessary feature of Markov Blankets. They can move and model exchanges of matter between object and environment. In a dynamic setting, every single node has a markov blanket and the intersection of the blankets associated with each any set of nodes also forms a markov blanket (even if that blanket is disconnected). For this reason, the Markov blankets alone dont define objects. Rather it is the statistics of the blanket (or rather p(b,t)) that define an object. Blankets simply specify the set of possible domains over which the distribution that defines an object’s phenotype may be defined.
I don’t understand. The fact that every single node has a Markov blanket seems unrelated. The claim that the intersection of any two blankets is a blanket doesn’t seem true? For example, I can have a network:
a → b → c
| | |
v v v
d → e → f
| | |
v v v
g → h → i
It seems like the intersection of the blankets for ‘a’ and ‘c’ don’t form a blanket.
While most examples in the literature utilize static Markov blankets in which time does not affect whether or not nodes are assigned to object, blanket, and environment this is not a necessary feature of Markov Blankets. They can move and model exchanges of matter between object and environment. In a dynamic setting, every single node has a markov blanket and the intersection of the blankets associated with each any set of nodes also forms a markov blanket (even if that blanket is disconnected). For this reason, the Markov blankets alone dont define objects. Rather it is the statistics of the blanket (or rather p(b,t)) that define an object. Blankets simply specify the set of possible domains over which the distribution that defines an object’s phenotype may be defined.
I don’t understand. The fact that every single node has a Markov blanket seems unrelated. The claim that the intersection of any two blankets is a blanket doesn’t seem true? For example, I can have a network:
a → b → c
| | |
v v v
d → e → f
| | |
v v v
g → h → i
It seems like the intersection of the blankets for ‘a’ and ‘c’ don’t form a blanket.