6 papers
Tropical Fréchet Means: a polyhedral approach to exact optimization
Kamillo Ferry, Bo Lin, Carlos Améndola +2
The Fréchet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fréchet means…
Bandwidth Selection of Density Estimators over Treespaces
Ruriko Yoshida, Zhiwen Wang
A kernel density estimator (KDE) is one of the most popular non-parametric density estimators. In this paper we focus on a best bandwidth selection method for use in an analogue of…
Covariance Decomposition for Distance Based Species Tree Estimation
Georgios Aliatimis, Ruriko Yoshida, Burak Boyaci +1
In phylogenomics, species-tree methods must contend with two major sources of noise; stochastic gene-tree variation under the multispecies coalescent model (MSC) and finite-sequenc…
Projected Gradient Descent Method for Tropical Principal Component Analysis over Tree Space
Ruriko Yoshida
In 2019, Yoshida et al. developed tropical Principal Component Analysis (PCA), that is, an analogue of the classical PCA in the setting of tropical geometry and applied it to visua…
Inference for max-linear Bayesian networks with noise
Mark Adams, Kamillo Ferry, Ruriko Yoshida
Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in t…
Tropical Bisectors and Carlini-Wagner Attacks
Gillian Grindstaff, Julia Lindberg, Daniela Schkoda +2
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against s…