Material for “ Learning the Network Structure of Heterogeneous Data via Pairwise Exponential Markov Random Fields ”
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چکیده
where (b) holds by applying chain rule successively, and (c) holds because conditioning reduces entropy. Note that, for a known exponential family distribution, H(Xr | Br(X)) is constant. For examples in a Gaussian, Dirichlet, Gamma, Wishart, Xr is also a function of Br(Xr), meaning H(Xr | Br(X)) = 0. For a Laplacian distribution, H(Xr | Br(X)) = H(Sign(Xr)) = 1. Therefore, we can conclude that H(X) = H(bnode(X)) + C0 where C0 = ∑p r=1 H(Xr | Br(X)) is the constant determined by the types of nodes.
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تاریخ انتشار 2017