21 research outputs found
Towards a Multi-Subject Analysis of Neural Connectivity
Directed acyclic graphs (DAGs) and associated probability models are widely
used to model neural connectivity and communication channels. In many
experiments, data are collected from multiple subjects whose connectivities may
differ but are likely to share many features. In such circumstances it is
natural to leverage similarity between subjects to improve statistical
efficiency. The first exact algorithm for estimation of multiple related DAGs
was recently proposed by Oates et al. 2014; in this letter we present examples
and discuss implications of the methodology as applied to the analysis of fMRI
data from a multi-subject experiment. Elicitation of tuning parameters requires
care and we illustrate how this may proceed retrospectively based on technical
replicate data. In addition to joint learning of subject-specific connectivity,
we allow for heterogeneous collections of subjects and simultaneously estimate
relationships between the subjects themselves. This letter aims to highlight
the potential for exact estimation in the multi-subject setting.Comment: to appear in Neural Computation 27:1-2
Advances in Learning Bayesian Networks of Bounded Treewidth
This work presents novel algorithms for learning Bayesian network structures
with bounded treewidth. Both exact and approximate methods are developed. The
exact method combines mixed-integer linear programming formulations for
structure learning and treewidth computation. The approximate method consists
in uniformly sampling -trees (maximal graphs of treewidth ), and
subsequently selecting, exactly or approximately, the best structure whose
moral graph is a subgraph of that -tree. Some properties of these methods
are discussed and proven. The approaches are empirically compared to each other
and to a state-of-the-art method for learning bounded treewidth structures on a
collection of public data sets with up to 100 variables. The experiments show
that our exact algorithm outperforms the state of the art, and that the
approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table
A Score-and-Search Approach to Learning Bayesian Networks with Noisy-OR Relations
A Bayesian network is a probabilistic graphical model that consists of a
directed acyclic graph (DAG), where each node is a random variable and attached
to each node is a conditional probability distribution (CPD). A Bayesian
network can be learned from data using the well-known score-and-search
approach, and within this approach a key consideration is how to simultaneously
learn the global structure in the form of the underlying DAG and the local
structure in the CPDs. Several useful forms of local structure have been
identified in the literature but thus far the score-and-search approach has
only been extended to handle local structure in form of context-specific
independence. In this paper, we show how to extend the score-and-search
approach to the important and widely useful case of noisy-OR relations. We
provide an effective gradient descent algorithm to score a candidate noisy-OR
using the widely used BIC score and we provide pruning rules that allow the
search to successfully scale to medium sized networks. Our empirical results
provide evidence for the success of our approach to learning Bayesian networks
that incorporate noisy-OR relations.Comment: Accepted to Probabilistic Graphical Models, 202