21 research outputs found
Learning Bounded Treewidth Bayesian Networks with Thousands of Variables
We present a method for learning treewidth-bounded Bayesian networks from
data sets containing thousands of variables. Bounding the treewidth of a
Bayesian greatly reduces the complexity of inferences. Yet, being a global
property of the graph, it considerably increases the difficulty of the learning
process. We propose a novel algorithm for this task, able to scale to large
domains and large treewidths. Our novel approach consistently outperforms the
state of the art on data sets with up to ten thousand variables
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
Learning tractable multidimensional Bayesian network classifiers
Multidimensional classification has become one of the most relevant topics in view of the many
domains that require a vector of class values to be assigned to a vector of given features. The
popularity of multidimensional Bayesian network classifiers has increased in the last few years
due to their expressive power and the existence of methods for learning different families of these
models. The problem with this approach is that the computational cost of using the learned models
is usually high, especially if there are a lot of class variables. Class-bridge decomposability means
that the multidimensional classification problem can be divided into multiple subproblems for these
models. In this paper, we prove that class-bridge decomposability can also be used to guarantee
the tractability of the models. We also propose a strategy for efficiently bounding their inference
complexity, providing a simple learning method with an order-based search that obtains tractable
multidimensional Bayesian network classifiers. Experimental results show that our approach is
competitive with other methods in the state of the art and ensures the tractability of the learned
models
Learning low inference complexity Bayesian networks
One of the main research topics in machine learning nowa-
days is the improvement of the inference and learning processes in proba-
bilistic graphical models. Traditionally, inference and learning have been
treated separately, but given that the structure of the model conditions
the inference complexity, most learning methods will sometimes produce
ineficient inference models. In this paper we propose a new representa-
tion for discrete probability distributions that allows eficiently evaluat-
ing the inference complexity of the models during the learning process.
We use this representation to create procedures for learning low infer-
ence complexity Bayesian networks. Experimental results show that the
proposed methods obtain tractable models that improve the accuracy of
the predictions provided by approximate inference in models obtained
with a well-known Bayesian network learner
Exact Learning of Bounded Tree-width Bayesian Networks
Abstract Inference in Bayesian networks is known to be NP-hard, but if the network has bounded treewidth, then inference becomes tractable. Not surprisingly, learning networks that closely match the given data and have a bounded tree-width has recently attracted some attention. In this paper we aim to lay groundwork for future research on the topic by studying the exact complexity of this problem. We give the first non-trivial exact algorithm for the NP-hard problem of finding an optimal Bayesian network of tree-width at most w, with running time 3 n n w+O (1) , and provide an implementation of this algorithm. Additionally, we propose a variant of Bayesian network learning with "super-structures", and show that finding a Bayesian network consistent with a given super-structure is fixedparameter tractable in the tree-width of the super-structure