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Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
We investigate the small regularization limit of entropic optimal transport when the cost function is the Euclidean distance in dimensions $d > 1$, and the marginal measures are absolutely continuous with respect to the Lebesgue measure.…
This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which…
Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, potentially leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates…
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measured in Wasserstein distance, which are applicable to a wide…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
Modal split prediction in transportation networks has the potential to support network operators in managing traffic congestion and improving transit service reliability. We focus on the problem of hourly prediction of the fraction of…
We study the regularity of optimal transport maps between convex domains with quadratic cost. For nondegenerate $C^{\alpha}$-densities, we prove $C^{1, 1-\varepsilon}$-regularity of the potentials up to the boundary. If in addition the…
In this paper, we address the fusion problem in wireless sensor networks, where the cross-correlation between the estimates is unknown. To solve the problem within the Bayesian framework, we assume that the covariance matrix has a prior…
Microbial communities analysis is drawing growing attention due to the rapid development of high-throughput sequencing techniques nowadays. The observed data has the following typical characteristics: it is high-dimensional, compositional…
Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known…
Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
We will study variations in Sobolev spaces of optimal transport maps with the standard Gaussian measure as the reference measure. Some dimension free inequalities will be obtained. As application, we construct solutions to Monge-Ampere…
It is well known that martingale transport plans between marginals $\mu\neq\nu$ are never given by Monge maps -- with the understanding that the map is over the first marginal $\mu$, or forward in time. Here, we change the perspective, with…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
Domain adaptation and generative modelling have collectively mitigated the expensive nature of data collection and labelling by leveraging the rich abundance of accurate, labelled data in simulation environments. In this work, we study the…
The inverse reflector problem arises in geometrical nonimaging optics: Given a light source and a target, the question is how to design a reflecting free-form surface such that a desired light density distribution is generated on the…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…