Related papers: Distributionally Robust Martingale Optimal Transpo…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
This paper studies a variant of ramified/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a firm looks for an allocation of productions over factories, a distribution of sales…
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…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…
We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations…
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…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which…
This paper presents consideration of the Semi-Relaxed Sinkhorn (SR-Sinkhorn) algorithm for the semi-relaxed optimal transport (SROT) problem, which relaxes one marginal constraint of the standard OT problem. For evaluation of how the…
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of…
Recently, Neural Topic Models (NTMs) inspired by variational autoencoders have obtained increasingly research interest due to their promising results on text analysis. However, it is usually hard for existing NTMs to achieve good document…
In this article, we develop a semigroup-theoretic framework for the analytic characterisation of martingales with path-dependent terminal conditions. Our main result establishes that a measurable adapted process of the form \[ V(t) -…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…