The Number of Modes in a Gaussian Mixture with Centres in a Bounded Interval
Navin Kashyap (IISc)
| Speaker |
Navin Kashyap (IISc)
|
|---|---|
| When |
Jan 25, 2022
from 04:00 PM to 05:00 PM |
| Where | zoom meeting |
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Abstract: We consider the problem of determining the maximum number of modes (i.e., local maxima) possible in a mixture of univariate Gaussian densities with variance 1 and means within a bounded interval [-A,A]. Denoting this maximum number by m(A), we show that m(A) =\Theta(A^2), meaning that m(A) grows quadratically in A. Our motivation for this study comes from a 50-year-old open problem (it's still open!) in information theory, which we will also describe.
The talk is based on joint work with Manjunath Krishnapur.