• Corpus ID: 251018185

Tight bounds on the hardness of learning simple nonparametric mixtures

@inproceedings{Aragam2022TightBO,
  title={Tight bounds on the hardness of learning simple nonparametric mixtures},
  author={Bryon Aragam and Wai Ming Tai},
  year={2022}
}
We study the problem of learning nonparametric distributions in a finite mixture, and establish tight bounds on the sample complexity for learning the component distributions in such models. Namely, we are given i.i.d. samples from a pdf f where 

Figures and Tables from this paper

References

SHOWING 1-10 OF 75 REFERENCES

Tight Bounds for Learning a Mixture of Two Gaussians

TLDR
The main results are upper and lower bounds giving a computationally efficient moment-based estimator with an optimal convergence rate, thus resolving a problem introduced by Pearson (1894).

A spectral algorithm for learning mixture models

Learning mixtures of Gaussians

  • S. Dasgupta
  • Computer Science
    40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
  • 1999
TLDR
This work presents the first provably correct algorithm for learning a mixture of Gaussians, which returns the true centers of the Gaussian to within the precision specified by the user with high probability.

Learning mixtures of arbitrary distributions over large discrete domains

TLDR
It is shown that efficient learning is possible exactly at the information-theoretically least-possible aperture of 2k-1, and it is proved that such a dependence is unavoidable when one considers general mixtures.

Learning Mixtures of Tree Graphical Models

TLDR
A novel method is proposed for estimating the mixture components with provable guarantees of discrete graphical models, where the class variable is hidden and each mixture component can have a potentially different Markov graph structure and parameters over the observed variables.

ASYMPTOTIC BEHAVIOR OF THE Lp-NORMS AND THE ENTROPY FOR GENERAL ORTHOGONAL POLYNOMIALS

The limit behavior of the sequence of Lp-norms of orthogonal polynomials is studied. Orthogonal polynomials on both a finite interval and the entire real line are considered. As a corollary,

Rates of convergence for the cluster tree

TLDR
Finite-sample convergence rates for the algorithm and lower bounds on the sample complexity of this estimation problem are given.

The Spectral Method for General Mixture Models

TLDR
A general property of spectral projection for arbitrary mixtures is proved and it is shown that the resulting algorithm is efficient when the components of the mixture are logconcave distributions in R n whose means are separated.

Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering

TLDR
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.

Settling the Polynomial Learnability of Mixtures of Gaussians

  • Ankur MoitraG. Valiant
  • Computer Science
    2010 IEEE 51st Annual Symposium on Foundations of Computer Science
  • 2010
TLDR
This paper gives the first polynomial time algorithm for proper density estimation for mixtures of k Gaussians that needs no assumptions on the mixture, and proves that such a dependence is necessary.
...