Tensor decomposition for learning Gaussian mixtures from moments
This work addresses a fundamental challenge in machine learning for data modeling, offering a novel approach to Gaussian mixture recovery with potential applications in various domains.
The paper tackles the problem of recovering Gaussian mixture models from data by using symmetric tensor decomposition on empirical moments, proving identifiability for certain tensors and presenting a linear algebra-based algorithm. Experimental results demonstrate its effectiveness compared to state-of-the-art methods.
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gaussian mixture models from datasets. We investigate symmetric tensor decomposition methods for tackling this problem, where the tensor is built from empirical moments of the data distribution. We consider identifiable tensors, which have a unique decomposition, showing that moment tensors built from spherical Gaussian mixtures have this property. We prove that symmetric tensors with interpolation degree strictly less than half their order are identifiable and we present an algorithm, based on simple linear algebra operations, to compute their decomposition. Illustrative experimentations show the impact of the tensor decomposition method for recovering Gaussian mixtures, in comparison with other state-of-the-art approaches.