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We show, by an explicit construction, that a mixture of univariate Gaussian densities with variance $1$ and means in $[-A,A]$ can have $\Omega(A^2)$ modes.
On the Information Capacity of Peak and Average Power Constrained Gaussian Channels
J. G. Smith · 1969
Earlier work this paper cites.
The information capacity of amplitude- and variance-constrained scalar Gaussian channels
J. G. Smith · 1971
Earlier work this paper cites.
Using kernel density estimates to investigate multimodality
B. W. Silverman · 1981
Earlier work this paper cites.
On the number of modes of a Gaussian mixture
M. Carreira-Perpiñan and C. Williams · 2003
Cited alongside, same era.
Local maxima in the likelihood of gaussian mixture models: Structural results and algorithmic consequences
Chi Jin, Yuchen Zhang, Sivaraman Balakrishnan, Martin Wainwright, and Michael Jordan · 2016
Cited alongside, same era.
Maximum number of modes of Gaussian mixtures
Carlos Améndola, Alexander Engström, and Christian Haase · 2019
Cited alongside, same era.
The capacity achieving distribution for the amplitude constrained additive Gaussian channel: An upper bound on the number of mass points
A. Dytso, S. Yagli, H. V. Poor, and S. Shamai (Shitz) · 2020
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Self-regularizing property of nonparametric maximum likelihood estimator in mixture models
Yury Polyanskiy and Yihong Wu · 2020
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