Related papers: Sinkhorn-Flow: Predicting Probability Mass Flow in…
Many problems in machine learning can be formulated as solving entropy-regularized optimal transport on the space of probability measures. The canonical approach involves the Sinkhorn iterates, renowned for their rich mathematical…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over a dynamical system, which is challenging due to its high computational…
Motivated by the need for accurate traffic flow prediction in transportation management, we propose a functional data method to analyze traffic flow patterns and predict future traffic flow. In this study we approach the problem by sampling…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
Continuous diffusion models are commonly acknowledged to display a deterministic probability flow, whereas discrete diffusion models do not. In this paper, we aim to establish the fundamental theory for the probability flow of discrete…
Predicting the future behavior of human road users is an important aspect for the development of risk-aware autonomous vehicles. While many models have been developed towards this end, effectively capturing and predicting the variability…
We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…
We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…
Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational…