(1) cannot be decoupled for eachŷ i and is usually formulated as an ILP problem (Roth and Yih, 2004;Chambers and Jurafsky, 2008;.
let I r (ij) ∈ {0, 1} be the indicator function of relation r for event i and event j and f r (ij) ∈ [0, 1] be the corresponding soft-max score.