A Sufficiently Fast Algorithm for Finding Close to Optimal Junction Trees
This provides a faster algorithm for approximate junction tree construction, which is incremental for improving inference efficiency in Bayesian networks and related graphical models.
The paper tackles the problem of finding near-optimal junction trees for graphs, developing an algorithm with worst-case complexity O(c^k n^a) that guarantees the logarithm of the heaviest clique's state space size is within a constant factor of optimal, and yields polynomial inference for Bayesian networks when k = O(log n).
An algorithm is developed for finding a close to optimal junction tree of a given graph G. The algorithm has a worst case complexity O(c^k n^a) where a and c are constants, n is the number of vertices, and k is the size of the largest clique in a junction tree of G in which this size is minimized. The algorithm guarantees that the logarithm of the size of the state space of the heaviest clique in the junction tree produced is less than a constant factor off the optimal value. When k = O(log n), our algorithm yields a polynomial inference algorithm for Bayesian networks.