10 papers
Variance Inequalities for Transformed Fréchet Means in Hadamard Spaces
Christof Schötz
The Fréchet mean (or barycenter) generalizes the expectation of a random variable to metric spaces by minimizing the expected squared distance to the random variable. Similarly, t…
Quadruple Inequalities: Between Cauchy-Schwarz and Triangle
Christof Schötz
We prove a set of inequalities that interpolate the Cauchy-Schwarz inequality and the triangle inequality. Every nondecreasing, convex function with a concave derivative induces su…
Transformed Fréchet Means for Robust Estimation in Hadamard Spaces
Christof Schötz
We establish finite-sample error bounds in expectation for transformed Fréchet means in Hadamard spaces under minimal assumptions. Transformed Fréchet means provide a unifying fr…
Matters Arising: Spatial correlation in economic analysis of climate change
Christof Schötz
Climate change poses substantial risks to the global economy. Kotz, Levermann and Wenz (Nature, 2024) statistically analyzed economic and climate data, finding significant projecte…
Strong Laws of Large Numbers for Generalizations of Fréchet Mean Sets
Christof Schötz
A Fréchet mean of a random variable with values in a metric space is an element of the metric space that minimizes . This mini…
Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Data
Christof Schötz, Niklas Boers
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. This study shows that learning f…