相关论文: Linear Partial Gromov-Wasserstein Embedding

The GW approximation is a well-known method to improve electronic structure predictions calculated within density functional theory. In this work, we have implemented a computationally efficient GW approach that calculates central…

We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…

The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…

The $GW$ approximation is a widely used method for computing electron addition and removal energies of molecules and solids. The computational effort of conventional $GW$ algorithms increases as $O(N^4)$ with the system size $N$, hindering…

Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…

The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision…

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal…

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…

When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To…

Variational approximation, such as mean-field (MF) and tree-reweighted (TRW), provide a computationally efficient approximation of the log-partition function for a generic graphical model. TRW provably provides an upper bound, but the…

In many real-world contexts, such as social or transport networks, data exhibit both structural connectivity and node-level attributes. For example, roads in a transport network can be characterized not only by their connectivity but also…

Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class of models, which have attracted great attention in various applications. However, this framework has two main drawbacks: (i) Wasserstein-1 (or Earth-Mover)…

We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

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…

Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential…

GW approximation is one of the most popular parameter-free many-body methods that goes beyond the limitations of the standard density functional theory (DFT) to determine the excitation spectra for moderately correlated materials and in…

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…

This study examines how the GW approximation, one of the techniques covered by Green's functions and on many-body approximations (GFMBA), fares compared to the treatment of the Hubbard model solved using an exact diagonalization (ED)…