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math.ST2026
Unconditional Finiteness of the Number of Critical Points of Gaussian Mixture Densities
Akifumi Okuno
By slightly adapting Wang's recent important argument for the homoscedastic setting, we prove that every finite heteroscedastic Gaussian mixture has only finitely many critical poi…
math.ST2026
At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture
Yutaro Kabata, Hirotaka Matsumoto, Akifumi Okuno
A Gaussian mixture density can have more modes than components. It has been conjectured that the maximum number of modes of a -variate -component Gaussian mixture density is…
math.ST2026
On Mixtures of Three Homoscedastic Gaussian Densities: An Unconditional Sharper Bound on the Number of Modes
Akifumi Okuno, Yutaro Kabata
It is known that a mixture of three homoscedastic multivariate Gaussian densities whose centers form an equilateral triangle can have four modes, owing to the emergence of a ``ghos…