A Gaussian Process Regression Model for Distribution Inputs

  title={A Gaussian Process Regression Model for Distribution Inputs},
  author={F. Bachoc and F. Gamboa and Jean-Michel Loubes and N. Venet},
  journal={IEEE Transactions on Information Theory},
Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide a probabilistic understanding of these kernels and characterize the corresponding… Expand
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Sliced Wasserstein Kernels for Probability Distributions
  • S. Kolouri, Yang Zou, G. Rohde
  • Computer Science, Mathematics
  • 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
  • 2016
This work provides a new perspective on the application of optimal transport flavored distances through kernel methods in machine learning tasks and provides a family of provably positive definite kernels based on the Sliced Wasserstein distance. Expand
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This paper provides theoretical guarantees for a remarkably simple algorithmic alternative to solve the distribution regression problem: embed the distributions to a reproducing kernel Hilbert space, and learn a ridge regressor from the embeddings to the outputs. Expand
Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions
Estimation algorithms are presented, how to apply them for machine learning tasks on distributions are described, and empirical results on synthetic data, real word images, and astronomical data sets are shown. Expand
Kernel Mean Embedding of Distributions: A Review and Beyonds
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Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and includes detailed algorithms for supervised-learning problem for both regression and classification. Expand
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This paper presents a new technique for computing the barycenter of a set of distance or kernel matrices, which define the interrelationships between points sampled from individual domains, and provides a fast iterative algorithm for the resulting nonconvex optimization problem. Expand
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This paper develops theory and methods for distribution-free versions of distribution regression and proves that when the eective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate. Expand
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This article considers the estimation of structured correlation matrices in infinitely differentiable Gaussian random field models. The problem is essentially motivated by the stochastic modeling ofExpand