相关论文: Geodesic Optimal Transport Regression

Regression discontinuity designs have been widely used in observational studies to estimate causal effects of an intervention or treatment at a cutoff point. We propose a generalization of regression discontinuity designs to handle complex…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…

This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…

Modern-day problems in statistics often face the challenge of exploring and analyzing complex non-Euclidean object data that do not conform to vector space structures or operations. Examples of such data objects include covariance matrices,…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

We consider the optimal transport problem between zero mean Gaussian stationary random fields both in the aperiodic and periodic case. We show that the solution corresponds to a weighted Hellinger distance between the multivariate and…

We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in…

A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual…

We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…