Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations
This work addresses a foundational challenge in machine learning for statisticians and data scientists, offering a practical solution for mixture models with overlapping components.
The authors tackled the problem of consistently estimating identifiable nonparametric mixture models from grouped observations, proposing an algorithm that outperforms existing methods, especially when mixture components overlap significantly.
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap. This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations. Our analysis leverages an oracle inequality for weighted kernel density estimators of the distribution on groups, together with a general result showing that consistent estimation of the distribution on groups implies consistent estimation of mixture components. A practical implementation is provided for paired observations, and the approach is shown to outperform existing methods, especially when mixture components overlap significantly.