### Ilya Korsunsky

Computational Biology PhD Student

New York University

March 4, 2014

Novel Causal Score for Learning Conjunctive Bayesian Networks

Cancer is a complex disease that involves the interplay of many genes
and regulatory factors. Despite this complexity, each specific type of
cancer is thought to progress through a sequence of stages, defined by
genomic events. Various mathematical models to capture this progression
have been proposed. In particular, graphical approaches have been used
to model the progression as a path, as a tree, and various types of
directed acyclic graphs (DAG). The most recent work considered
conjunctive Bayesian networks (CBNs). These model progression through a
DAG, in which an event only occurs when all of its causes have occurred.
The CBNs are learned with the standard statistical approach of maximum
likelihood, under the constraints of monotonicity and conjuntivity. We
learn the same model but consider an alternate score based in the
philosophical foundations of causality and in the monotonicity of the
progression events. Just like log likelihood, our score decomposes into a
sum of scores for each node. However, our score distinguishes between
edge directions and is thus better suited to this particular type of
Bayesian network. We learn the resulting network using GOBNILP, a
Bayesian network learning software that optimizes an arbitrary
decomposable score by formulating the problem as an integer program and
solving it to optimality through linear relaxation and plane cutting.