Related papers: Synchronized Optimal Transport for Joint Modeling …

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal…

Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…

Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes $n$ and $m$ in $\mathbb{R}^d$, entropic OT (EOT)…

We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…

Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal…

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…

Single-cell RNA-sequencing captures a temporal slice, or a snapshot, of a cell differentiation process. A major bioinformatical challenge is the inference of differentiation trajectories from a single snapshot, and methods that account for…

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e.,…

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…

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous…

We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…

We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…

The control of traffic signals is fundamental and critical to alleviate traffic congestion in urban areas. However, it is challenging since traffic dynamics are complicated in real-world scenarios. Because of the high complexity of the…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…

Understanding the spatial dynamics of cars within urban systems is essential for optimizing infrastructure management and resource allocation. Recent empirical approaches for analyzing traffic patterns have gained traction due to their…

Standard representational similarity methods align each layer of a network to its best match in another independently, producing asymmetric results, lacking a global alignment score, and struggling with networks of different depths. These…

Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being…

Discrete ordinates $S_N$ transport solvers on unstructured meshes pose a challenge to scale due to complex data dependencies, memory access patterns and a high-dimensional domain. In this paper, we review the performance bottlenecks within…

While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…