13 citations · 33 across the 25 of their papers we have counts for
25 papers
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…
Selecting New Measurement Locations to Diversify Traffic-Pattern Coverage: A Real-World Evaluation for Total Traffic Volume Estimation
Masaaki Inoue, Akifumi Okuno, Shintaro Fukushima
Accurate measurement of traffic volumes and flows is vital for modern intelligent transportation. However, despite recent technological advances in sensor devices, it is still expe…
Algebraic Approach to Ridge-Regularized Mean Squared Error Minimization in Minimal ReLU Neural Network
Ryoya Fukasaku, Yutaro Kabata, Akifumi Okuno
This paper investigates a perceptron, a simple neural network model, with ReLU activation and a ridge-regularized mean squared error (RR-MSE). Our approach leverages the fact that…
An integrated perspective of robustness in regression through the lens of the bias-variance trade-off
Akifumi Okuno
This paper presents an integrated perspective on robustness in regression. Specifically, we examine the relationship between traditional outlier-resistant robust estimation and rob…