The terminology sepset is used quite often in the Probabilistic graphical models and causality. What does it mean and what is its relevance ?


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The term sepset is used in connection with cluster graphs. A cluster graph is a graph with nodes $C$ including a subset of variables $\{X_1, \dots, X_n\}$.

A sepset $S_{ij}$ is the subset of variables between nodes $C_i$ and $C_j$ that are in the intersection of the scopes of both nodes (scope simply means the list of variables node $C$ depends on. I.e., $S_{ij} \subseteq (Scope(C_i) \bigcap Scope(C_j)).$

If $C_i = \phi(A, B, C)$ and $C_j = \phi(B, C, D)$, then possible sepsets are:

  • $S_{ij}^1 = \{\}$ - this means there is no edge between $C_i, C_j$
  • $S_{ij}^2 = \{B\}$
  • $S_{ij}^3 = \{C\}$
  • $S_{ij}^4 = \{B,C\}$

The relevance of sepsets is that they determine e.g. in belief propagation whether a node $C_i$ sends a message to $C_j$ about a given variable (they only send a message containing information about a variable if it is in $S_{ij}$).

  • $\begingroup$ Would you please define "scope of a node". It isn't clear how it differs from a neighbourhood. $\endgroup$
    – Galen
    Sep 23, 2021 at 13:23
  • $\begingroup$ The scope of the node is the set of variables included in that node. E.g. if a node $X$ is described by potential $\phi(A, B)$, then the scope is $\{A,B\}$. Whereas the neighborhood is the set of the nodes connected to $X$. $\endgroup$ Sep 24, 2021 at 10:58

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