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It is proved that an unbounded gap between the update maps can coexist with vanishing predictive KL for every fixed finite $K\ge2$ in a stationary symmetric Gaussian HMM, and isolates two missing links between internal update gaps and predictive cost.
HiTOC is proposed, a Hierarchical Topological Ordering framework for Causal discovery that constructs the global causal structure via layer-wise integration of local orderings over induced subsets by Markov Blanket and achieves state-of-the-art performance in both accuracy and scalability, particularly in high-dimensio...
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