- E. Xing. 2014. 15 : Mean Field Approximation and Topic Models. Abstract: The mean parameter μα associated with a sufficient φα is defined by the expectation μα = Ep[φα(X)], for α ∈ I We then define the set M := {μ ∈ R|∃p s.t.Ep[φα(X)] = μα,∀α ∈ I} corresponding to all realizable mean parameters. Further, for an exponential family with sufficient statistics φ defined on graph G, the set of realizable mean parameter set is : M(G;φ) := {μ ∈ R|∃p s.t.Ep[φ(X)] = μ} More generally, consider an exponential family with a collection φ = (φα, α ∈ I) of sufficient statistics associated with the cliques of G = (V,E). Given a subgraph F , let I(F ) be the subset of sufficient statistics associated with subgraph F . Then the set of all distributions associated with F is a sub-family of full φ-exponential family. It is parameterized by the subspace of canonical parameters: Ω(F ) := {θ ∈ Ω|θα = 0,∀α ∈ I − I(F )}
