Related papers: Transductive Generalization via Optimal Transport …
To achieve full autonomous driving, a good understanding of the surrounding environment is necessary. Especially predicting the future states of other traffic participants imposes a non-trivial challenge. Current SotA-models already show…
Unsupervised graph alignment finds the node correspondence between a pair of attributed graphs by only exploiting graph structure and node features. One category of recent studies first computes the node representation and then matches…
In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…
To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1…
Generative models aim to learn the distribution of datasets, such as images, so as to be able to generate samples that statistically resemble real data. However, learning the underlying probability distribution can be very challenging and…
Learning generic representations with deep networks requires massive training samples and significant computer resources. To learn a new specific task, an important issue is to transfer the generic teacher's representation to a student…
We analyze two algorithms for approximating the general optimal transport (OT) distance between two discrete distributions of size $n$, up to accuracy $\varepsilon$. For the first algorithm, which is based on the celebrated Sinkhorn's…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
Graph Convolution Networks (GCN) are widely used in learning graph representations due to their effectiveness and efficiency. However, they suffer from the notorious over-smoothing problem, in which the learned representations of densely…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
Graph neural network (GNN) is effective to model graphs for distributed representations of nodes and an entire graph. Recently, research on the expressive power of GNN attracted growing attention. A highly-expressive GNN has the ability to…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of…
We propose a learning framework for graph kernels, which is theoretically grounded on regularizing optimal transport. This framework provides a novel optimal transport distance metric, namely Regularized Wasserstein (RW) discrepancy, which…
Graph neural networks (GNNs) have emerged as a powerful model to capture critical graph patterns. Instead of treating them as black boxes in an end-to-end fashion, attempts are arising to explain the model behavior. Existing works mainly…
Graph Convolutional Networks (GCNs) have been shown to be a powerful concept that has been successfully applied to a large variety of tasks across many domains over the past years. In this work we study the theory that paved the way to the…