Compressive Gaussian Mixture Estimation

Anthony Bourrier 1, 2 Rémi Gribonval 2 Patrick Pérez 1
2 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : When fitting a probability model to voluminous data, memory and computational time can become prohibitive. In this paper, we propose a framework aimed at fitting a mixture of isotropic Gaussians to data vectors by computing a low-dimensional sketch of the data. The sketch represents empirical moments of the underlying probability distribution. Deriving a reconstruction algorithm by analogy with compressive sensing, we experimentally show that it is possible to precisely estimate the mixture parameters provided that the sketch is large enough. Our algorithm provides good reconstruction and scales to higher dimensions than previous probability mixture estimation algorithms, while consuming less memory in the case of numerous data. It also provides a privacy-preserving data analysis tool, since the sketch doesn't disclose information about individual datum it is based on.
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Anthony Bourrier, Rémi Gribonval, Patrick Pérez. Compressive Gaussian Mixture Estimation. ICASSP - 38th International Conference on Acoustics, Speech, and Signal Processing, May 2013, Vancouver, Canada. pp.6024-6028. ⟨hal-00799896⟩

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