Related papers: Diffeomorphic Registration using Sinkhorn Divergen…
Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint…
In this paper, we study the Entropic Martingale Optimal Transport (EMOT) problem on \mathbb{R}. The investigation of the EMOT problem arises in the calibration problem of the Stochastic Volatility Models, where martingale constraints…
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…
We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…
Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a…
A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this…
Although machine learning models trained on massive data have led to break-throughs in several areas, their deployment in privacy-sensitive domains remains limited due to restricted access to data. Generative models trained with privacy…
Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC)…
In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
Multi-contrast magnetic resonance (MR) image registration is useful in the clinic to achieve fast and accurate imaging-based disease diagnosis and treatment planning. Nevertheless, the efficiency and performance of the existing registration…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…
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…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
In computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has become a central tool for modeling smooth, invertible transformations between shapes such as curves or landmarks. In this paper, we extend…
We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees. Leveraging an entropic version of Brenier's theorem, we show that our…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
We present a method based on optimal transport to remove arbitrage opportunities within a finite set of option prices. The method is notably intended for regulatory stress-tests, which require applying significant local distortions to…