Related papers: Optimal transport for model calibration
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…
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…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in…
Transportation occupies one-third of the amount in the logistics costs, and accordingly transportation systems largely influence the performance of the logistics system. This work presents an adaptive data-driven innovative modular approach…
This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping…
The vertical alignment optimization problem in road design seeks the optimal vertical alignment of a road at minimal cost, taking into account earthwork while meeting all safety and design requirements. In recent years, modelling techniques…
We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
Traffic congestion has lead to an increasing emphasis on management measures for a more efficient utilization of existing infrastructure. In this context, this paper proposes a novel framework that integrates real-time optimization of…
We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the…
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…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
Selecting input features of top relevance has become a popular method for building self-explaining models. In this work, we extend this selective rationalization approach to text matching, where the goal is to jointly select and align text…