13 citations · 49 across the 16 of their papers we have counts for
18 papers
Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
Shayan Hundrieser, Insung Kong, Johannes Schmidt-Hieber
We introduce Hyper Input Convex Neural Networks (HyCNNs), a novel neural network architecture designed for learning convex functions. HyCNNs combine the principles of Maxout networ…
On the Universal Representation Property of Spiking Neural Networks
Shayan Hundrieser, Philipp Tuchel, Insung Kong +1
Inspired by biology, spiking neural networks (SNNs) process information via discrete spikes over time, offering an energy-efficient alternative to the classical computing paradigm…
Sharp Convergence Rates of Empirical Unbalanced Optimal Transport for Spatio-Temporal Point Processes
Marina Struleva, Shayan Hundrieser, Dominic Schuhmacher +1
We statistically analyze empirical plug-in estimators for unbalanced optimal transport (UOT) formalisms, focusing on the Kantorovich-Rubinstein distance, between general intensity…
Optimal Transport Based Testing in Factorial Designs
Michel Groppe, Linus Niemöller, Shayan Hundrieser +4
We introduce a general framework for testing statistical hypotheses in factorial designs for probability measures supported on discrete spaces. The suggested methodology is based o…
Local Poisson Deconvolution for Discrete Signals
Shayan Hundrieser, Tudor Manole, Danila Litskevich +1
We analyze the statistical problem of recovering an atomic signal, modeled as a discrete uniform distribution , from a binned Poisson convolution model. This question is motivat…
A Lower Bound for Estimating Fréchet Means
Shayan Hundrieser, Benjamin Eltzner, Stephan F. Huckemann
Fréchet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fréchet means can be estimated from independent and identi…
Lower Complexity Adaptation for Empirical Entropic Optimal Transport
Michel Groppe, Shayan Hundrieser
Entropic optimal transport (EOT) presents an effective and computationally viable alternative to unregularized optimal transport (OT), offering diverse applications for large-scale…
Convergence of Empirical Optimal Transport in Unbounded Settings
Thomas Staudt, Shayan Hundrieser
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbou…
Weak Limits for Empirical Entropic Optimal Transport: Beyond Smooth Costs
Alberto González-Sanz, Shayan Hundrieser
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require on…
Empirical Optimal Transport under Estimated Costs: Distributional Limits and Statistical Applications
Shayan Hundrieser, Gilles Mordant, Christoph Alexander Weitkamp +1
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of di…
Unbalanced Kantorovich-Rubinstein distance, plan, and barycenter on finite spaces: A statistical perspective
Shayan Hundrieser, Florian Heinemann, Marcel Klatt +2
We analyze statistical properties of plug-in estimators for unbalanced optimal transport quantities between finitely supported measures in different prototypical sampling models. S…
A Unifying Approach to Distributional Limits for Empirical Optimal Transport
Shayan Hundrieser, Marcel Klatt, Thomas Staudt +1
We provide a unifying approach to central limit type theorems for empirical optimal transport (OT). In general, the limit distributions are characterized as suprema of Gaussian pro…
Empirical Optimal Transport between Different Measures Adapts to Lower Complexity
Shayan Hundrieser, Thomas Staudt, Axel Munk
The empirical optimal transport (OT) cost between two probability measures from random data is a fundamental quantity in transport based data analysis. In this work, we derive nove…
On the Uniqueness of Kantorovich Potentials
Thomas Staudt, Shayan Hundrieser, Axel Munk
Kantorovich potentials denote the dual solutions of the renowned optimal transportation problem. Uniqueness of these solutions is relevant from both a theoretical and an algorithmi…
Limit Distributions and Sensitivity Analysis for Empirical Entropic Optimal Transport on Countable Spaces
Shayan Hundrieser, Marcel Klatt, Axel Munk
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal…
The Statistics of Circular Optimal Transport
Shayan Hundrieser, Marcel Klatt, Axel Munk
Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to…
Finite Sample Smeariness on Spheres
Benjamin Eltzner, Shayan Hundrieser, Stephan F. Huckemann
Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fréchet means of underlying rather unsuspicious random variables can behave as…
Finite Sample Smeariness of Fréchet Means and Application to Climate
Shayan Hundrieser, Benjamin Eltzner, Stephan F. Huckemann
Fréchet means on non-Euclidean spaces may exhibit nonstandard asymptotic rates rendering quantile-based asymptotic inference inapplicable. We show here that this affects, among oth…