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.Abstract
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 |
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