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Found 15 papers, 5 papers with code
Diffeomorphic Measure Matching with Kernels for Generative Modeling
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs), inspired by ideas from diffeomorphic matching and image registration.
Conditional Optimal Transport on Function Spaces
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference.
Nonlinear Filtering with Brenier Optimal Transport Maps
This paper is concerned with the problem of nonlinear filtering, i. e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations.
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods.
Kernel Methods are Competitive for Operator Learning
We present a general kernel-based framework for learning operators between Banach spaces along with a priori error analysis and comprehensive numerical comparisons with popular neural net (NN) approaches such as Deep Operator Net (DeepONet) [Lu et al.] and Fourier Neural Operator (FNO) [Li et al.].
Bayesian Posterior Perturbation Analysis with Integral Probability Metrics
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention.
A Kernel Approach for PDE Discovery and Operator Learning
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods.
An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms
This paper presents a variational representation of the Bayes' law using optimal transportation theory.
Solving and Learning Nonlinear PDEs with Gaussian Processes
The main idea of our method is to approximate the solution of a given PDE as the maximum a posteriori (MAP) estimator of a Gaussian process conditioned on solving the PDE at a finite number of collocation points.
Posterior Consistency of Semi-Supervised Regression on Graphs
Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices.
Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps.
Model Reduction and Neural Networks for Parametric PDEs
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces.
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised learning algorithms.
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data.
Geometric structure of graph Laplacian embeddings
More precisely, we assume that the data is sampled from a mixture model supported on a manifold $\mathcal{M}$ embedded in $\mathbb{R}^d$, and pick a connectivity length-scale $\varepsilon>0$ to construct a kernelized graph Laplacian.
