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Book Sections Year : 2015

Compressive Gaussian Mixture Estimation


When performing a learning task on voluminous data, memory and computational time can become prohibitive. In this chapter, we propose a framework aimed at estimating the parameters of a density mixture on training data in a compressive manner by computing a low-dimensional sketch of the data. The sketch represents empirical moments of the underlying probability distribution. Instantiating the framework on the case where the densities are isotropic Gaussians, we derive a reconstruction algorithm by analogy with compressed sensing. We experimentally show that it is possible to precisely estimate the mixture parameters provided that the sketch is large enough, while consuming less memory in the case of numerous data. The considered framework also provides a privacy-preserving data analysis tool, since the sketch does not disclose information about individual datum it is based on.

Dates and versions

hal-01181063 , version 1 (28-07-2015)



Anthony Bourrier, Rémi Gribonval, Patrick Pérez. Compressive Gaussian Mixture Estimation. Holger Boche; Robert Calderbank; Gitta Kutyniok; Jan Vybíral. Compressed Sensing and its Applications - MATHEON Workshop 2013, Birkhäuser Basel, pp.239--258, 2015, Applied and Numerical Harmonic Analysis, 978-3-319-16041-2. ⟨10.1007/978-3-319-16042-9_8⟩. ⟨hal-01181063⟩
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