Related papers: Geodesic Optimal Transport Regression
A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean data. Circular data is a classic example, but so is data in…
Fr\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis…
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…
This work presents a non-parametric spatio-temporal model for mapping human activity by mobile autonomous robots in a long-term context. Based on Variational Gaussian Process Regression, the model incorporates prior information of spatial…
This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables.…
Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean…
Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which…
Extrinsic Gaussian process regression methods, such as wrapped Gaussian process, have been developed to analyze manifold data. However, there is a lack of intrinsic Gaussian process methods for studying complex data with manifold-valued…
While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…
Trajectory planning tasks for non-holonomic or collaborative systems are naturally modeled by state spaces with non-Euclidean metrics. However, existing proofs of convergence for sample-based motion planners only consider the setting of…
Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…
In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying…