Laplace's formula defines the determinant as a linear combination of matrix cofactors of an arbitrary row j: It should be clear that any c j,k is constant with respect to the cell [A] j,i (since it is formed by removing row j of A) and that other entries of A are constant with respect to the cell [A] j,i .
moving to the nonprojective case, there are two difficulties: (a) we must marginalize over nonprojective trees and (b) we must define a generative model over (X, Y).