Corpus ID: 237364674

# Uniform Consistency in Nonparametric Mixture Models

@inproceedings{Aragam2021UniformCI,
title={Uniform Consistency in Nonparametric Mixture Models},
author={Bryon Aragam and Ruiyi Yang},
year={2021}
}
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to uniform results. The… Expand

#### References

SHOWING 1-10 OF 68 REFERENCES
Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering
• Mathematics, Computer Science
• The Annals of Statistics
• 2020
This work establishes general conditions under which families of nonparametric mixture models are identifiable by introducing a novel framework for clustering overfitted \emph{parametric} (i.e. misspecified) mixture models, and applies these results to partition-based clustering, generalizing the well-known notion of a Bayes optimal partition from classical model- based clustering to non parametric settings. Expand
Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations
• Computer Science, Mathematics
• NeurIPS
• 2020
This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations, and the approach is shown to outperform existing methods, especially when mixture components overlap significantly. Expand
Nonparametric inference in multivariate mixtures
• Mathematics
• 2005
We consider mixture models in which the components of data vectors from any given subpopulation are statistically independent, or independent in blocks. We argue that if, under this condition ofExpand
A Universal Approximation Theorem for Mixture-of-Experts Models
• Mathematics, Medicine
• Neural Computation
• 2016
The theorem presented allows MoE users to be confident in applying such models for estimation when data arise from nonlinear and nondifferentiable generative processes. Expand
Nonparametric modal regression
• Mathematics
• 2016
Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usualExpand
Learning Mixtures of Linear Regressions with Nearly Optimal Complexity
• Computer Science, Mathematics
• COLT
• 2018
This paper proposes a fixed parameter tractable algorithm for the MLR problem under general conditions, which achieves global convergence and the sample complexity scales nearly linearly in the dimension. Expand
Approximate nonparametric maximum likelihood for mixture models: A convex optimization approach to fitting arbitrary multivariate mixing distributions
• Computer Science
• Comput. Stat. Data Anal.
• 2018
A class of flexible, scalable, and easy to implement approximate NPML methods is studied for problems with multivariate mixing distributions, and the empirical results demonstrate the relative effectiveness of using multivariate (as opposed to univariate) mixing distributions for NPML-based approaches. Expand
EM Converges for a Mixture of Many Linear Regressions
• Mathematics, Computer Science
• AISTATS
• 2020
The results imply exact recovery as $\sigma \rightarrow 0$, in contrast to most previous local convergence results for EM, where the statistical error scaled with the norm of parameters. Expand
Convergence rates of parameter estimation for some weakly identifiable finite mixtures
• Mathematics
• 2015
We establish minimax lower bounds and maximum likelihood convergence rates of parameter estimation for mean-covariance multivariate Gaussian mixtures, shape-rate Gamma mixtures, and some variants ofExpand
SEMIPARAMETRIC ESTIMATION OF A TWO-COMPONENT MIXTURE MODEL
• Mathematics
• 2006
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However,Expand