Agreement-Based Learning
نویسندگان
چکیده
Assume submodels are in exponential family: pm(x, z; θm) = exp { θ m ( φm(x)φ Z(z) ) −Am(θm) } for x ∈ X , z ∈ Zm and 0 otherwise Reformulation of Product EM: Aggregate parameters: b = ∑ m bm, bm = φ X m(x) θm E-step: compute expected sufficient statistics μ = E(b,∩mZm) def = Eq(z;b)φ(z) with support ∩mZm M-step: set θm to match moments φ X m(x)μ Exponential family formulation Two sources of intractability in the E-step: • Domain Z = ∩mZm is unwieldy (e.g., matchings) • Parameters b result in high tree-width graph New objective function: • A function of sufficient statistics μm and parameters θm for each submodel m = 1, . . . ,M • See paper for some preliminary bounds Algorithm: Aggregate parameters: b = ∑ m bm E-step: compute statistics μm = E(b′,Z ′) Aggregate statistics: μ̄ = 1 M ∑ m μm M-step: set θm to match moments φ X m(x)μ̄
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