Pre-processing for Triangulation of Probabilistic Networks

The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001

An Introduction to Clique Minimal Separator Decomposition

International audienceThis paper is a review which presents and explains the decomposition of graphs by clique minimal separators. The pace is leisurely, we give many examples and figures. Easy algorithms are provided to implement this decomposition. The historical and theoretical background is given, as well as sketches of proofs of the structural results involved

Stochastic kinetic models: Dynamic independence, modularity and graphs

The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition $[A,D,B]$ of the vertices, the graphical separation $A\perp B|D$ in the undirected KIG has an intuitive chemical interpretation and implies that $A$ is locally independent of $B$ given $A\cup D$. It is proved that this separation also results in global independence of the internal histories of $A$ and $B$ conditional on a history of the jumps in $D$ which, under conditions we derive, corresponds to the internal history of $D$. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Graphical decomposition methods are developed for the identification and efficient computation of nested modularizations. Application to an SKM of the red blood cell advances understanding of this biochemical system.Comment: Published in at http://dx.doi.org/10.1214/09-AOS779 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entropy characterization of commutative partitions.

Lo Ying Hang.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 80-81).Abstracts in English and Chinese.Chapter Chapter 1 --- Introduction --- p.1Chapter Chapter 2 --- Background --- p.4Chapter Chapter 3 --- Commutative Partition Pair Analysis --- p.9Chapter Chapter 4 --- Entropy Inequalities for Partition Pair --- p.19Chapter Chapter 5 --- Entropy Characterization of Commutative Partition Pair --- p.32Chapter Chapter 6 --- Ordered Commutative Partitions --- p.43Chapter Chapter 7 --- Running Intersection Property for Partitions --- p.45Chapter Chapter 8 --- Entropy Characterization of Ordered Commutative Partitions --- p.53Chapter Chapter 9 --- Significance and Application --- p.72Chapter Chapter 10 --- Future Plan --- p.78Chapter Chapter 11 --- Conclusion --- p.79Bibliography --- p.8

BAYESIAN FRAMEWORKS FOR PARSIMONIOUS MODELING OF MOLECULAR CANCER DATA

In this era of precision medicine, clinicians and researchers critically need the assistance of computational models that can accurately predict various clinical events and outcomes (e.g,, diagnosis of disease, determining the stage of the disease, or molecular subtyping). Typically, statistics and machine learning are applied to ‘omic’ datasets, yielding computational models that can be used for prediction. In cancer research there is still a critical need for computational models that have high classification performance but are also parsimonious in the number of variables they use. Some models are very good at performing their intended classification task, but are too complex for human researchers and clinicians to understand, due to the large number of variables they use. In contrast, some models are specifically built with a small number of variables, but may lack excellent predictive performance. This dissertation proposes a novel framework, called Junction to Knowledge (J2K), for the construction of parsimonious computational models. The J2K framework consists of four steps: filtering (discretization and variable selection), Bayesian network generation, Junction tree generation, and clique evaluation. The outcome of applying J2K to a particular dataset is a parsimonious Bayesian network model with high predictive performance, but also that is composed of a small number of variables. Not only does J2K find parsimonious gene cliques, but also provides the ability to create multi-omic models that can further improve the classification performance. These multi-omic models have the potential to accelerate biomedical discovery, followed by translation of their results into clinical practice