13 citations · 33 across the 25 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…
Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regression
Akifumi Okuno, Masaaki Imaizumi
We study a minimax risk of estimating inverse functions on a plane, while keeping an estimator is also invertible. Learning invertibility from data and exploiting an invertible est…
Dependence of variance on covariate design in nonparametric link regression
Akifumi Okuno, Keisuke Yano
This paper discusses a design-dependent nature of variance in nonparametric link regression aiming at predicting a mean outcome at a link, i.e., a pair of nodes, based on currently…