Recursive-Head Geometry and Order-Free Efficient Inference in Finite-State Nested Markov Models
有限状态嵌套 Markov 模型的递归头几何与无序有效推断
Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither…