15 citations · 37 across the 14 of their papers we have counts for
18 papers
Weighted Power Fréchet Means in Metric Spaces with Curvature Bounded Above
Christof Schötz
We establish non-asymptotic risk bounds for power Fréchet means in geodesic metric spaces with curvature bounded above. The observations form weighted, possibly infinite sequences…
The trapezoid comparison inequality in metric spaces with curvature bounded above
Christof Schötz
Among four points of a CAT(0) space, the planar symmetric trapezoids are configurations on which Ptolemy's and Reshetnyak's inequalities are both equalities. We show that the symme…
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 fram…
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…
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…
Rethinking Climate Econometrics: Data Cleaning, Flexible Trend Controls, and Predictive Validation
Christof Schötz, Jan Hassel, Christian Otto
We assess empirical models in climate econometrics using modern statistical learning techniques. Existing approaches are prone to outliers, ignore sample dependencies, and lack pri…
Generating time-consistent dynamics with discriminator-guided image diffusion models
Philipp Hess, Maximilian Gelbrecht, Christof Schötz +4
Realistic temporal dynamics are crucial for many video generation, processing and modelling applications, e.g. in computational fluid dynamics, weather prediction, or long-term cli…
Lower Bounds for Nonparametric Estimation of Ordinary Differential Equations
Christof Schötz, Maximilian Siebel
We noisily observe solutions of an ordinary differential equation at given times, where lives in a -dimensional state space. The model function is unknow…
Machine Learning for Predicting Chaotic Systems
Christof Schötz, Alistair White, Maximilian Gelbrecht +1
Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial c…
Nonparametric Estimation of Ordinary Differential Equations: Snake and Stubble
Christof Schötz
We study nonparametric estimation in dynamical systems described by ordinary differential equations (ODEs). Specifically, we focus on estimating the unknown function $f \colon \mat…
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, th…
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…
Deep learning for bias-correcting CMIP6-class Earth system models
Philipp Hess, Stefan Lange, Christof Schötz +1
The accurate representation of precipitation in Earth system models (ESMs) is crucial for reliable projections of the ecological and socioeconomic impacts in response to anthropoge…
Nonparametric Regression in Nonstandard Spaces
Christof Schötz
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fréchet regression, where the val…
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 minim…
Arbitrary Rates of Convergence for Projected and Extrinsic Means
Christof Schötz
We study central limit theorems for the projected sample mean of independent and identically distributed observations on subsets of the Euclidean p…
Convergence Rates for the Generalized Fréchet Mean via the Quadruple Inequality
Christof Schötz
For sets and , the generalized Fréchet mean of a random variable , which has values in , is any minimizer of $q\mapsto \m…
Low temperature dipolar echo in amorphous dielectrics: Significance of relaxation and decoherence free two level systems
Alexander L. Burin, John M. Leveritt, Gudrun Fickenscher +6
The nature of dielectric echoes in amorphous solids at low temperatures is investigated. It is shown that at long delay times the echo amplitude is determined by a small subset of…