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This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self-assignment flow takes a pairwise data affinity matrix as input data…

Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy…

Domain adaptation is an essential task in transfer learning to leverage data in one domain to bolster learning in another domain. In this paper, we present a new semi-supervised manifold alignment technique based on a two-step approach of…

Predicting how distributions over discrete variables vary over time is a common task in time series forecasting. But whereas most approaches focus on merely predicting the distribution at subsequent time steps, a crucial piece of…

The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…

Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…

Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…

The problem of domain adaptation on an unlabeled target dataset using knowledge from multiple labelled source datasets is becoming increasingly important. A key challenge is to design an approach that overcomes the covariate and target…

Predicting the future behavior of human road users is an important aspect for the development of risk-aware autonomous vehicles. While many models have been developed towards this end, effectively capturing and predicting the variability…

In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework. In the embedding spaces,…

We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning…

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…

One of the central problems in machine learning is domain adaptation. Unlike past theoretical work, we consider a new model for subpopulation shift in the input or representation space. In this work, we propose a provably effective…

Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…

We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…

Domain Translation is the problem of finding a meaningful correspondence between two domains. Since in a majority of settings paired supervision is not available, much work focuses on Unsupervised Domain Translation (UDT) where data samples…

Optimal Transport (OT) has proven effective for domain adaptation (DA) by aligning distributions across domains with differing statistical properties. Building on the approach of Courty et al. (2016), who mapped source data to the target…