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We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $\Omega\subset\mathbb{R}^d$, where $d>1$. Extending beyond compactly…
We propose the Block Coordinate Descent Network Simplex (BCDNS) method for solving large-scale discrete Optimal Transport (OT) problems. BCDNS integrates the Network Simplex (NS) algorithm with a block coordinate descent (BCD) strategy,…
Next location prediction is a key task in human mobility analysis, crucial for applications like smart city resource allocation and personalized navigation services. However, existing methods face two significant challenges: first, they…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…
Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper bounds; however, unless the covariates…
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport…
We introduce a unified framework for contextual and causal Bayesian optimisation, which aims to design intervention policies maximising the expectation of a target variable. Our approach leverages both observed contextual information and…
Future wireless networks will need to improve adaptive resource allocation and decision-making to handle the increasing number of intelligent devices. Unmanned aerial vehicles (UAVs) are being explored for their potential in real-time…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
In this work we propose a framework to address the issue of state dependent nonlinear equality-constrained state estimation using Bayesian filtering. This framework is constructed specifically for a linear approximation of Bayesian…
We introduce \textbf{BO4Mob}, a new benchmark framework for high-dimensional Bayesian Optimization (BO), driven by the challenge of origin-destination (OD) travel demand estimation in large urban road networks. Estimating OD travel demand…
Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…
This paper presents a variational representation of the Bayes' law using optimal transportation theory. The variational representation is in terms of the optimal transportation between the joint distribution of the (state, observation) and…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…