262 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
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
Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The
assumption that an infinite sequence of data points is exchangeable is at the
core of Bayesian statistics. However, finite exchangeability as a statistical
property that renders probabilistic inference tractable is less
well-understood. We develop a theory of finite exchangeability and its relation
to tractable probabilistic inference. The theory is complementary to that of
independence and conditional independence. We show that tractable inference in
probabilistic models with high treewidth and millions of variables can be
understood using the notion of finite (partial) exchangeability. We also show
that existing lifted inference algorithms implicitly utilize a combination of
conditional independence and partial exchangeability.Comment: In Proceedings of the 28th AAAI Conference on Artificial Intelligenc
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
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