19,074 research outputs found
Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes
We investigate approximating joint distributions of random processes with
causal dependence tree distributions. Such distributions are particularly
useful in providing parsimonious representation when there exists causal
dynamics among processes. By extending the results by Chow and Liu on
dependence tree approximations, we show that the best causal dependence tree
approximation is the one which maximizes the sum of directed informations on
its edges, where best is defined in terms of minimizing the KL-divergence
between the original and the approximate distribution. Moreover, we describe a
low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure
Approximate Discrete Probability Distribution Representation using a Multi-ResolutionBinary Tree
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiples random variables. The problem of efficient representation of probability distributions is central in term of computational efficiency in the field of probabilistic reasoning. The main problem arises when dealing with joint probability distributions over a set of random variables: they are always represented using huge probability arrays. In this paper, a new method based on a binary-tree representation
is introduced in order to store efficiently very large joint distributions. Our approach approximates any multidimensional joint distributions using an adaptive discretization of the space. We make the assumption that the lower is the probability mass of a particular region of feature space, the larger is the discretization step. This assumption leads to a very optimized representation in term of time and memory. The other advantages of our approach are the ability to refine dynamically the distribution every time it is needed leading to a more accurate representation of the probability
distribution and to an anytime representation of the distribution
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
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