Learning mixtures of spherical Gaussians: moment methods and spectral decompositions
This work addresses the challenge of efficient parameter estimation in Gaussian mixture models for machine learning and statistics, representing an incremental improvement by relaxing assumptions.
The authors tackled the problem of estimating parameters in mixtures of spherical Gaussians by developing a moment-based estimator that is computationally efficient and statistically consistent, achieving this without requiring minimum separation assumptions needed by prior methods.
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, without additional minimum separation assumptions needed by previous computationally efficient estimation procedures. Thus computational and information-theoretic barriers to efficient estimation in mixture models are precluded when the mixture components have means in general position and spherical covariances. Some connections are made to estimation problems related to independent component analysis.