Related papers: Neural Optimal Transport with General Cost Functio…
We present a primal--dual memory efficient algorithm for solving a relaxed version of the general transportation problem. Our approach approximates the original cost function with a differentiable one that is solved as a sequence of…
Fast and efficient path generation is critical for robots operating in complex environments. This motion planning problem is often performed in a robot's actuation or configuration space, where popular pathfinding methods such as A*, RRT*,…
We study optimal transport between two high-dimensional distributions $\mu,\nu$ in $R^n$ from an algorithmic perspective: given $x \sim \mu$, find a close $y \sim \nu$ in $poly(n)$ time, where $n$ is the dimension of $x,y$. Thus, running…
Trajectory data mining is crucial for smart city management. However, collecting large-scale trajectory datasets is challenging due to factors such as commercial conflicts and privacy regulations. Therefore, we urgently need trajectory…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
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…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…
Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better…
Autonomous exploration is a complex task where the robot moves through an unknown environment with the goal of mapping it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of…
Neural representations for 3D meshes are emerging as an effective solution for compact storage and efficient processing. Existing methods often rely on neural overfitting, where a coarse mesh is stored and progressively refined through…
We introduce a novel model based on the discrete optimal transport problem that incorporates congestion costs and replaces traditional constraints with weighted penalization terms. This approach better captures real-world scenarios…
Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through…
Personalized Route Recommendation (PRR) aims to generate user-specific route suggestions in response to users' route queries. Early studies cast the PRR task as a pathfinding problem on graphs, and adopt adapted search algorithms by…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
Recent advances in label assignment in object detection mainly seek to independently define positive/negative training samples for each ground-truth (gt) object. In this paper, we innovatively revisit the label assignment from a global…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
We develop an inferential toolkit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end we introduce conditional…
This work proposes a way to align statistical modeling with decision making. We provide a method that propagates the uncertainty in predictive modeling to the uncertainty in operational cost, where operational cost is the amount spent by…
We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which…
When predicting observations across space and time, the spatial layout of errors impacts a model's real-world utility. For instance, in bike sharing demand prediction, error patterns translate to relocation costs. However, commonly used…