Inference for determinantal point processes ...
Document type :
Communication dans un congrès avec actes
Title :
Inference for determinantal point processes without spectral knowledge
Author(s) :
Bardenet, Remi [Auteur correspondant]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Centre National de la Recherche Scientifique [CNRS]
Titsias, Michalis [Auteur]
Athens University of Economics and Business [AUEB]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Centre National de la Recherche Scientifique [CNRS]
Titsias, Michalis [Auteur]
Athens University of Economics and Business [AUEB]
Conference title :
Neural Information Processing Systems (NIPS)
City :
Montréal
Country :
Canada
Start date of the conference :
2015-12-07
Book title :
Proceedings of the Neural Information Processing Systems Conference
HAL domain(s) :
Mathématiques [math]/Statistiques [math.ST]
English abstract : [en]
Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel K. DPPs possess desirable properties, such as exact ...
Show more >Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel K. DPPs possess desirable properties, such as exact sampling or analyticity of the moments, but learning the parameters of kernel K through likelihood-based inference is not straightforward. First, the kernel that appears in the likelihood is not K, but another kernel L related to K through an often intractable spectral decomposition. This issue is typically bypassed in machine learning by directly parametrizing the kernel L, at the price of some interpretability of the model parameters. We follow this approach here. Second, the likelihood has an intractable normalizing constant, which takes the form of a large determinant in the case of a DPP over a finite set of objects, and the form of a Fredholm determinant in the case of a DPP over a continuous domain. Our main contribution is to derive bounds on the likelihood of a DPP, both for finite and continuous domains. Unlike previous work, our bounds are cheap to evaluate since they do not rely on approximating the spectrum of a large matrix or an operator. Through usual arguments, these bounds thus yield cheap variational inference and moderately expensive exact Markov chain Monte Carlo inference methods for DPPs.Show less >
Show more >Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel K. DPPs possess desirable properties, such as exact sampling or analyticity of the moments, but learning the parameters of kernel K through likelihood-based inference is not straightforward. First, the kernel that appears in the likelihood is not K, but another kernel L related to K through an often intractable spectral decomposition. This issue is typically bypassed in machine learning by directly parametrizing the kernel L, at the price of some interpretability of the model parameters. We follow this approach here. Second, the likelihood has an intractable normalizing constant, which takes the form of a large determinant in the case of a DPP over a finite set of objects, and the form of a Fredholm determinant in the case of a DPP over a continuous domain. Our main contribution is to derive bounds on the likelihood of a DPP, both for finite and continuous domains. Unlike previous work, our bounds are cheap to evaluate since they do not rely on approximating the spectrum of a large matrix or an operator. Through usual arguments, these bounds thus yield cheap variational inference and moderately expensive exact Markov chain Monte Carlo inference methods for DPPs.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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