The computation of first order moments on junction trees
This is an incremental review paper for researchers in probabilistic graphical models, comparing computational efficiency of existing moment computation methods.
The paper reviews existing methods for computing first order moments on junction trees, comparing approaches that treat it as a vertices problem using Shafer-Shenoy algorithm with memory scaling by edge-set cardinality, versus normalization-based algorithms (Lauritzen-Nilsson and Mauá et al.) with memory scaling by leaf-set cardinality.
We review some existing methods for the computation of first order moments on junction trees using Shafer-Shenoy algorithm. First, we consider the problem of first order moments computation as vertices problem in junction trees. In this way, the problem is solved using the memory space of an order of the junction tree edge-set cardinality. After that, we consider two algorithms, Lauritzen-Nilsson algorithm, and Mauá et al. algorithm, which computes the first order moments as the normalization problem in junction tree, using the memory space of an order of the junction tree leaf-set cardinality.