Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact and approximate inference in graphical models: variable
  elimination and beyond   Probabilistic graphical models offer a powerful framework to account for the
dependence structure between variables, which is represented as a graph.
However, the dependence between variables may render inference tasks
intractable. In this paper we review techniques exploiting the graph structure
for exact inference, borrowed from optimisation and computer science. They are
built on the principle of variable elimination whose complexity is dictated in
an intricate way by the order in which variables are eliminated. The so-called
treewidth of the graph characterises this algorithmic complexity: low-treewidth
graphs can be processed efficiently. The first message that we illustrate is
therefore the idea that for inference in graphical model, the number of
variables is not the limiting factor, and it is worth checking for the
treewidth before turning to approximate methods. We show how algorithms
providing an upper bound of the treewidth can be exploited to derive a 'good'
elimination order enabling to perform exact inference. The second message is
that when the treewidth is too large, algorithms for approximate inference
linked to the principle of variable elimination, such as loopy belief
propagation and variational approaches, can lead to accurate results while
being much less time consuming than Monte-Carlo approaches. We illustrate the
techniques reviewed in this article on benchmarks of inference problems in
genetic linkage analysis and computer vision, as well as on hidden variables
restoration in coupled Hidden Markov Models.

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The categories of this paper are: math
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin