Related papers: Randomized Optimal Transport on a Graph: framework…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

We propose an efficient novel path sampling-based framework designed to accelerate the investigation of rare events in complex molecular systems. A key innovation is the shift from sampling restricted path ensemble distributions, as in…

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…

Grogan et al [11,12] have recently proposed a solution to colour transfer by minimising the Euclidean distance L2 between two probability density functions capturing the colour distributions of two images (palette and target). It was shown…

In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy…

We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially completely disordered quantum systems, comparable to the systems which are sometimes referred to as Lifshitz…

In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the…

This paper proposes a generalised framework for density estimation in large networks with measurable spatiotemporal variance in edge weights. We solve the stochastic shortest path problem for a large network by estimating the density of the…

Efficient sampling from high-dimensional and multimodal unnormalized probability distributions is a central challenge in many areas of science and machine learning. We focus on Boltzmann generators (BGs) that aim to sample the Boltzmann…

This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two…

This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this…

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…

In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately…

Sample-based trajectory optimisers are a promising tool for the control of robotics with non-differentiable dynamics and cost functions. Contemporary approaches derive from a restricted subclass of stochastic optimal control where the…

We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Stochastic Optimal Transport (SOT) with a hard terminal distribution and soft, application-driven path costs. A low-dimensional guidance…

We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the…

Systematics contaminate observables, leading to distribution shifts relative to theoretically simulated signals-posing a major challenge for using pre-trained models to label such observables. Since systematics are often poorly understood…

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…

Bayesian optimization (BO) is a powerful framework for estimating parameters of expensive simulation models, particularly in settings where the likelihood is intractable and evaluations are costly. In stochastic models every simulation is…

A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…