Related papers: Wasserstein Variational Inference
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…
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric…
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…
Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…
We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG)…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…
Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…
The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive…
We propose a novel Wasserstein method with a distillation mechanism, yielding joint learning of word embeddings and topics. The proposed method is based on the fact that the Euclidean distance between word embeddings may be employed as the…
Imitation Learning describes the problem of recovering an expert policy from demonstrations. While inverse reinforcement learning approaches are known to be very sample-efficient in terms of expert demonstrations, they usually require…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…
Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two…
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…
A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a…
In this paper, we address the classification of instances each characterized not by a singular point, but by a distribution on a vector space. We employ the Wasserstein metric to measure distances between distributions, which are then used…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
Controlling the $\mathcal W_\infty$ Wasserstein distance by the $\mathcal W_p$ Wasserstein distance is interesting both for theorical and numerical applications. A first paper on this problem was written several years ago [3]. Some year…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…