相关论文: Causal transport on path space

In this work we prove that the unique 1-convex solution of the Monge problem contructed from the solution of the Monge-Kantorovitch problem between the Wiener measure and a target measure which has a log-concave density w.r.to the Wiener…

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs…

We present a range of applications of localisation for constrained transports for pairs of probability measures in order with respect to a lattice cone. These examples comprise irreducible convex paving for martingale transports in…

We construct solutions to Monge-Amp\`ere equations whose Monge-Amp\`ere measures contain singular components supported on low codimensional sets. We also study the regularity of such solutions. To motivate our construction, we present…

The origins of the large differences observed to the rates with which the diverse particles are conveyed along axonal microtubules are still a matter of debate in the literature. There is evidence that certain neurodegenerative diseases may…

We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…

Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin…

It is shown that continuous causal isomorphisms on two-dimensional Minkowski spacetime can be characterized by the invariance of wave equations.

We will study variations in Sobolev spaces of optimal transport maps with the standard Gaussian measure as the reference measure. Some dimension free inequalities will be obtained. As application, we construct solutions to Monge-Ampere…

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…

In this short note, we show that given a cost function $c$, any coupling $\pi$ of two probability measures where the second is a discrete measure can be associated to a certain bipartite graph containing a perfect matching, based on the…

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dL is a geodesic Borel distance which makes (X,dL) a non branching geodesic space. We show that under the assumption that geodesics are…

In this paper we study the bicausal optimal transport problem for Markov chains, an optimal transport formulation suitable for stochastic processes which takes into consideration the accumulation of information as time evolves. Our analysis…

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…

We consider the incorporation of causal knowledge about the presence or absence of (possibly indirect) causal relations into a causal model. Such causal relations correspond to directed paths in a causal model. This type of knowledge…

In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…

For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…

We experimentally study the transport prop- erties of dipolar and fundamental modes on one di- mensional (1D) coupled waveguide arrays. By carefully modulating a wide optical beam, we are able to effec- tively excite dipolar or fundamental…