On strong identifiability and convergence rates of parameter estimation in finite mixtures

By Nhat Ho, XuanLong Nguyen. 2016

65 citations recorded by the source corpus.

Abstract: This paper studies identifiability and convergence behaviors for parameters of multiple types, including matrix-variate ones, that arise in finite mixtures, and the effects of model fitting with extra mixing components. We consider several notions of strong identifiability in a matrix-variate setting, and use them to establish sharp inequalities relating the distance of mixture densities to the Wasserstein distances of the corresponding mixing measures. Characterization of identifiability is given for a broad range of mixture models commonly employed in practice, including locationcovariance mixtures and location-covariance-shape mixtures, for mixtures of symmetric densities, as well as some asymmetric ones. Minimax lower bounds and rates of convergence for the maximum likelihood estimates are established for such classes, which are also confirmed by simulation studies.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/22ea3c2b0ec1c9d709f824ba1a6c1966d37ac609

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Aritra Guha
2. Nhat Ho
3. XuanLong Nguyen

In Statistics and Probability

1. Aritra Guha
2. Nhat Ho
3. XuanLong Nguyen
4. Qiang Liu
5. Fernando Perez-Cruz
6. Barnab'as P'oczos

Citations in the corpus

• On posterior contraction of parameters and interpretability in Bayesian mixture modeling (2019, methodology): “The uniform Lipschitz condition can be formulated as follows [22].”