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Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications. However, finding these directions usually requires an iterative optimization procedure over the space of…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency "Coulomb" matrix, used in kernel ridge regression based supervised learning. Resulting quantum machine learning models…
While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on…
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neural network architectures. Recent works have experimentally shown that two different solutions found…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
This paper addresses the significant challenge in open-set object detection (OSOD): the tendency of state-of-the-art detectors to erroneously classify unknown objects as known categories with high confidence. We present a novel approach…
We propose a stable, parallel approach to train Wasserstein Conditional Generative Adversarial Neural Networks (W-CGANs) under the constraint of a fixed computational budget. Differently from previous distributed GANs training techniques,…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we…
Object density reconstruction from projections containing scattered radiation and noise is of critical importance in many applications. Existing scatter correction and density reconstruction methods may not provide the high accuracy needed…
Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…
The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the…
We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing…
In generative modeling, the Wasserstein distance (WD) has emerged as a useful metric to measure the discrepancy between generated and real data distributions. Unfortunately, it is challenging to approximate the WD of high-dimensional…