Related papers: Sulcal Pattern Matching with the Wasserstein Dista…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
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…
We propose a novel technique for training deep networks with the objective of obtaining feature representations that exist in a Euclidean space and exhibit strong clustering behavior. Our desired features representations have three traits:…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…
We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides…
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space. In…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^1$ Wasserstein distance. We show that measure satisfying certain self-similarity conditions…
Whole-brain surface extraction is an essential topic in medical imaging systems as it provides neurosurgeons with a broader view of surgical planning and abnormality detection. To solve the problem confronted in current deep learning skull…
The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…
Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement…
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…
This paper targets the task with discrete and periodic class labels ($e.g.,$ pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore…
We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…
We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…
The classification of random objects within metric spaces without a vector structure has attracted increasing attention. However, the complexity inherent in such non-Euclidean data often restricts existing models to handle only a limited…
Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…
Using statistical learning methods to analyze stochastic simulation outputs can significantly enhance decision-making by uncovering relationships between different simulated systems and between a system's inputs and outputs. We focus on…