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Found 24 papers, 10 papers with code
Universal Generalization Guarantees for Wasserstein Distributionally Robust Models
Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts.
Generalized Sobolev Transport for Probability Measures on a Graph
In connection with the OW, we show that one only needs to simply solve a univariate optimization problem to compute the GST, unlike the complex two-level optimization problem in OW.
Sliced Wasserstein with Random-Path Projecting Directions
From the RPD, we derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i. e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW).
Scalable Counterfactual Distribution Estimation in Multivariate Causal Models
We consider the problem of estimating the counterfactual joint distribution of multiple quantities of interests (e. g., outcomes) in a multivariate causal model extended from the classical difference-in-difference design.
Optimal Transport for Measures with Noisy Tree Metric
It is known that such OT problem (i. e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying tree structure over supports of input measures.
Few-Shot Object Detection via Synthetic Features with Optimal Transport
Our overarching goal is to train a generator that captures the data variations of the base dataset.
Scalable Unbalanced Sobolev Transport for Measures on a Graph
We show that the proposed unbalanced Sobolev transport (UST) admits a closed-form formula for fast computation, and it is also negative definite.
Dynamic Flows on Curved Space Generated by Labeled Data
The scarcity of labeled data is a long-standing challenge for many machine learning tasks.
Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics
In this work, we consider probability measures supported on a graph metric space and propose a novel Sobolev transport metric.
Adversarial Regression with Doubly Non-negative Weighting Matrices
In this paper, we propose a novel and coherent scheme for kernel-reweighted regression by reparametrizing the sample weights using a doubly non-negative matrix.
Gradient flows on the feature-Gaussian manifold
The scarcity of labeled data is a long-standing challenge for cross-domain machine learning tasks.
Nonsmooth Implicit Differentiation for Machine Learning and Optimization
In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus.
Nonsmooth Implicit Differentiation for Machine-Learning and Optimization
In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus.
Point-set Distances for Learning Representations of 3D Point Clouds
From this study, we propose to use sliced Wasserstein distance and its variants for learning representations of 3D point clouds.
Entropy Partial Transport with Tree Metrics: Theory and Practice
In this work, we consider an \textit{entropy partial transport} (EPT) problem for nonnegative measures on a tree having different masses.
Adaptive Tree Wasserstein Minimization for Hierarchical Generative Modeling
In this work, we consider OT over tree metrics, which is more general than the sliced Wasserstein and includes the sliced Wasserstein as a special case, and we propose a fast minimization algorithm in $O(n)$ for the optimal Wasserstein-1 transport plan between two distributions in the tree structure.
Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search
Building upon tree-Wasserstein (TW), which is a negative definite variant of OT, we develop a novel discrepancy for neural architectures, and demonstrate it within a Gaussian process surrogate model for the sequential NAS settings.
Flow-based Alignment Approaches for Probability Measures in Different Spaces
By leveraging a tree structure, we propose to align \textit{flows} from a root to each support instead of pair-wise tree metrics of supports, i. e., flows from a support to another, in GW.
Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes
We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance.
LSMI-Sinkhorn: Semi-supervised Mutual Information Estimation with Optimal Transport
To estimate the mutual information from data, a common practice is preparing a set of paired samples $\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n \stackrel{\mathrm{i. i. d.
Topological Bayesian Optimization with Persistence Diagrams
In this paper, we propose the topological Bayesian optimization, which can efficiently find an optimal solution from structured data using \emph{topological information}.
Tree-Sliced Variants of Wasserstein Distances
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions.
Safe Grid Search with Optimal Complexity
Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task.
Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams
To deal with it, an emerged approach is to use kernel methods, and an appropriate geometry for PDs is an important factor to measure the similarity of PDs.
