32,785 research outputs found
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
Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior
In recent years a number of methods have been developed for automatically
learning the (sparse) connectivity structure of Markov Random Fields. These
methods are mostly based on L1-regularized optimization which has a number of
disadvantages such as the inability to assess model uncertainty and expensive
cross-validation to find the optimal regularization parameter. Moreover, the
model's predictive performance may degrade dramatically with a suboptimal value
of the regularization parameter (which is sometimes desirable to induce
sparseness). We propose a fully Bayesian approach based on a "spike and slab"
prior (similar to L0 regularization) that does not suffer from these
shortcomings. We develop an approximate MCMC method combining Langevin dynamics
and reversible jump MCMC to conduct inference in this model. Experiments show
that the proposed model learns a good combination of the structure and
parameter values without the need for separate hyper-parameter tuning.
Moreover, the model's predictive performance is much more robust than L1-based
methods with hyper-parameter settings that induce highly sparse model
structures.Comment: Accepted in the Conference on Uncertainty in Artificial Intelligence
(UAI), 201
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