Related papers: PLOT: Progressive Localization via Optimal Transpo…
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…
Trajectory prediction and planning in autonomous driving are highly challenging due to the complexity of predicting surrounding agents' movements and planning the ego agent's actions in dynamic environments. Existing methods encode map and…
In this paper, we present a motion planning framework for multi-modal vehicle dynamics. Our proposed algorithm employs transcription of the optimization objective function, vehicle dynamics, and state and control constraints into sparse…
Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical…
UAVs equipped with a single depth camera encounter significant challenges in dynamic obstacle avoidance due to limited field of view and inevitable blind spots. While active vision strategies that steer onboard cameras have been proposed to…
Generalization across domains requires stable structure that links the source and target distributions. Building on causal transportability theory, we study a sequential prediction setting in which the target predictor can be represented as…
Long-horizon planning for robot manipulation is a challenging problem that requires reasoning about the effects of a sequence of actions on a physical 3D scene. While traditional task planning methods are shown to be effective for…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
Missing data in single-cell sequencing datasets poses significant challenges for extracting meaningful biological insights. However, existing imputation approaches, which often assume uniformity and data completeness, struggle to address…
We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning…
The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
Current research in Visual Navigation reveals opportunities for improvement. First, the direct adoption of RNNs and Transformers often overlooks the specific differences between Embodied AI and traditional sequential data modelling,…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
Accurate trajectory prediction has long been a major challenge for autonomous driving (AD). Traditional data-driven models predominantly rely on statistical correlations, often overlooking the causal relationships that govern traffic…
Differentiable causal discovery has made significant advancements in the learning of directed acyclic graphs. However, its application to real-world datasets remains restricted due to the ubiquity of latent confounders and the requirement…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
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…