ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

How many modes can a mixture of Gaussians with uniformly bounded means have?

Kashyap, N and Krishnapur, M (2022) How many modes can a mixture of Gaussians with uniformly bounded means have? In: Information and Inference, 11 (2). pp. 423-434.

Full text not available from this repository.
Official URL: https://doi.org/10.1093/imaiai/iaab009


We show, by an explicit construction, that a mixture of univariate Gaussian densities with variance 1 and means in -A,A can have \varOmega (A2) modes. This disproves a recent conjecture of Dytso et al. (2020, IEEE Trans. Inf. Theory, 66, 2006-2022) who showed that such a mixture can have at most O(A²) modes and surmised that the upper bound could be improved to O(A). Our result holds even if an additional variance constraint is imposed on the mixing distribution. Extending the result to higher dimensions, we exhibit a mixture of Gaussians in \mathbbRd, with identity covariances and means inside -A,Ad, that has \varOmega (A2d) modes. © 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Item Type: Journal Article
Publication: Information and Inference
Publisher: Oxford University Press
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Gaussian mixtures; modes
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 28 Jul 2022 05:34
Last Modified: 28 Jul 2022 05:34
URI: https://eprints.iisc.ac.in/id/eprint/75012

Actions (login required)

View Item View Item