4 papers
On the Uniqueness of Fréchet Means for Polytope Norms
Roan Talbut, Andrew McCormack, Anthea Monod
Fréchet means are a popular type of average for non-Euclidean datasets, defined as those points which minimise the average squared distance to a set of data points. We consider th…
Tropical Gradient Descent
Roan Talbut, Anthea Monod
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interes…
Tropical Fermat-Weber Points over Spaces of -Ultrametrics
Shelby Cox, John Sabol, Roan Talbut +1
We extend reconstruction methods for phylogenetic trees to ultrametrics of arbitrary matroids and study the stability of these data analysis methods in the combinatorial spirit of…
Probability Metrics for Tropical Spaces of Different Dimensions
Roan Talbut, Daniele Tramontano, Yueqi Cao +2
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that…