2012/10/19 by Jeff A. Bilmes, Jeff Bilmes, Chris Bartels +2
Computer Science · #Algorithms and Data Compression #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Topic Modeling #cs.AI
paper · pdf · doi:10.48550/arxiv.1212.2448
Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003)
arxiv created 2012/10/19 · openalex publication_date 2012/10/19 · arxiv updated 2012/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties of the underlying directed graph, we find it useful to view triangulation and elimination using properties only of the resulting undirected graph, obtained after the moralization step. We first briefly introduce the Graphical model toolkit (GMTK) and its notion of dynamic graphical models, one that slightly extends the standard notion of a DBN. We next introduce the 'boundary algorithm', a method to find the best boundary between partitions in a dynamic model. We find that using this algorithm, the notions of forward- and backward-interface become moot - namely, the size and fill-in of the best forward- and backward- interface are identical. Moreover, we observe that finding a good partition boundary allows for constrained elimination orders (and therefore graph triangulations) that are not possible using standard slice-by-slice constrained eliminations. More interestingly, with certain boundaries it is possible to obtain constrained elimination schemes that lie outside the space of possible triangulations using only unconstrained elimination. Lastly, we report triangulation results on invented graphs, standard DBNs from the literature, novel DBNs used in speech recognition research systems, and also random graphs. Using a number of different triangulation quality measures (max clique size, state-space, etc.), we find that with our boundary algorithm the triangulation quality can dramatically improve.