Continuously indexed Potts models on unoriented graphs

Loic Landrieu 1, 2 Guillaume Obozinski 3, 2
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
2 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
Abstract : This paper introduces an extension to undirected graphical models of the classical continuous time Markov chains. This model can be used to solve a transductive or unsupervised multi-class classi- fication problem at each point of a network de- fined as a set of nodes connected by segments of different lengths. The classification is performed not only at the nodes, but at every point of the edge connecting two nodes. This is achieved by constructing a Potts process indexed by the con- tinuum of points forming the edges of the graph. We propose a homogeneous parameterization which satisfies Kolmogorov consistency, and show that classical inference and learning algo- rithms can be applied. We then apply our model to a problem from geo- matics, namely that of labelling city blocks auto- matically with a simple typology of classes (e.g. collective housing) from simple properties of the shape and sizes of buildings of the blocks. Our experiments shows that our model outperform standard MRFs and a discriminative model like logistic regression.
Type de document :
Communication dans un congrès
UAI 20114 - 30th Conference on Uncertainty in Artificial Intelligence, Jul 2014, Quebec, Canada. pp.459-468, 2014
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https://hal-enpc.archives-ouvertes.fr/hal-01060957
Contributeur : Loic Landrieu <>
Soumis le : jeudi 4 septembre 2014 - 16:24:32
Dernière modification le : jeudi 5 juillet 2018 - 14:23:40
Document(s) archivé(s) le : vendredi 5 décembre 2014 - 10:40:06

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  • HAL Id : hal-01060957, version 1

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Loic Landrieu, Guillaume Obozinski. Continuously indexed Potts models on unoriented graphs. UAI 20114 - 30th Conference on Uncertainty in Artificial Intelligence, Jul 2014, Quebec, Canada. pp.459-468, 2014. 〈hal-01060957〉

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