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Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling

Rémi Gribonval 1, 2 Gilles Blanchard 3 Nicolas Keriven 4 Yann Traonmilin 5 
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
2 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The principle of compressive statistical learning is to compress a training collection, in one pass, into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. We explicitly describe and analyze random feature functions which empirical averages preserve the needed information for compressive clustering and compressive Gaussian mixture modeling with fixed known variance, and establish sufficient sketch sizes given the problem dimensions.
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https://hal.inria.fr/hal-02536818
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Submitted on : Monday, August 16, 2021 - 5:03:19 PM
Last modification on : Friday, August 5, 2022 - 2:54:52 PM

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Rémi Gribonval, Gilles Blanchard, Nicolas Keriven, Yann Traonmilin. Statistical Learning Guarantees for Compressive Clustering and Compressive Mixture Modeling. Mathematical Statistics and Learning, EMS Publishing House, 2021, 3 (2), pp.165-257. ⟨10.4171/msl/21⟩. ⟨hal-02536818v3⟩

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