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Compressive Statistical Learning with Random Feature Moments

Rémi Gribonval 1, 2 Gilles Blanchard 3, 4, 5 Nicolas Keriven 1, 6 Yann Traonmilin 1, 7
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
4 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We describe a general framework --compressive statistical learning-- for resource-efficient large-scale learning: the training collection is compressed 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. A near-minimizer of the risk is computed from the sketch through the solution of a nonlinear least squares problem. We investigate sufficient sketch sizes to control the generalization error of this procedure. The framework is illustrated on compressive PCA, compressive clustering, and compressive Gaussian mixture Modeling with fixed known variance. The latter two are further developed in a companion paper.
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https://hal.inria.fr/hal-01544609
Contributor : Rémi Gribonval <>
Submitted on : Tuesday, March 23, 2021 - 9:41:34 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:51 PM

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  • HAL Id : hal-01544609, version 4
  • ARXIV : 1706.07180

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Rémi Gribonval, Gilles Blanchard, Nicolas Keriven, Yann Traonmilin. Compressive Statistical Learning with Random Feature Moments. Mathematical Statistics and Learning, EMS Publishing House, In press. ⟨hal-01544609v4⟩

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