Study investigates duality and dual optimizers for various transport problems.
problem Existence and characterization of dual optimizers for adapted transport problems.
method Minimal assumptions, including causal and bicausal settings, are considered.
result No-arbitrage assumption leads to multicausal couplings and equivalent robust superhedging price computation.
COT-GAN generates sequential data with a causal optimal transport approach.
problem Generating sequential data with temporal causality constraints.
method Adversarial training with Causal Optimal Transport (COT) and entropic penalization.
result COT-GAN effectively learns time-dependent data distributions and generates stable time series data.
PLOT uses optimal transport to find neural site handles for causal abstraction.
problem Finding the relevant neural site for causal analysis is computationally challenging.
method PLOT employs optimal transport to localize causal variables from neural network outputs.
result PLOT efficiently finds intervention handles for causal abstraction in neural networks.
New curvature measure for causal sets derived from optimal transport.
problem Capturing Ricci curvature in causal sets.
method Using Lorentzian optimal transport, novel curvature defined along maximal chains.
result Recovery of timelike Ricci curvature from order-theoretic data.
New method uses optimal transport for better covariate matching in causal effect estimation.
problem Estimating causal effects in observational studies with high-dimensional covariates.
method Multimarginal unbalanced optimal transport for interpretable matching.
result Method provides interpretable weights and competitive performance with k-nearest neighbors.
This work clarifies different transport map constructions and their causal interpretations.
problem Identifying distinct transport map constructions and their equivalence.
method Comparative analysis of three transport map constructions: cyclically monotone, quantile-preserving, and triangular monotone.
result Conditions for equivalence of different transport map constructions.
We establish a foundation for multivariate counterfactual identification using dynamic optimal transport.
problem Addressing the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data.
method Establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings, with tools from dynamic optimal transport.
result Characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map, ensuring consistent inference.
COTA learns abstraction maps from data without complete SCM knowledge.
problem Learning causally consistent representations at different resolutions.
method Multi-marginal Optimal Transport (OT) with do-calculus constraints and interventional cost.
result COTA outperforms non-causal and independent formulations on synthetic and real-world problems.
A new method corrects bias in causal inference by balancing covariate distributions.
problem Bias in causal effect estimates due to covariate imbalance.
method Causal Optimal Transport, a nonparametric approach targeting distributional balance.
result Causal Optimal Transport outperforms other methods in misspecified models.
Paper introduces geometry-aware normalizing flows for improved causal inference.
problem Disparity between sample and population distributions in causal inference.
method Integrates continuous normalizing flows with parametric submodels, employing Wasserstein gradient flows and optimal transport.
result Significantly reduces parameter estimation bias and variance in finite-sample settings.
New method uses nested optimal transport for financial time series evaluation.
problem Lack of consensus metric for evaluating generative models in finance.
method Nested optimal transport distance for time-causal tasks, with a parallelizable algorithm.
result Substantial speedups and robustness to financial tasks.
Paper develops methods to estimate generalization error across domains.
problem Uncertainty in predicting unseen data distributions.
method Partial identification and transportability theory, Neural Causal Models.
result First general estimation technique for transportability problems.
This work evaluates risks over time using robust measures and neural networks.
problem Distributionally robust risk evaluation over temporal data.
method Characterizes alternative measures using causal optimal transport, approximates test functions by neural networks, and proves sample complexity.
result Framework outperforms classic counterparts in portfolio selection problems.
Bayesian method identifies causal sets across populations without graph knowledge.
problem Transporting causal information across populations without causal graph knowledge.
method Combines observational and experimental data to identify s-admissible backdoor sets.
result Proves asymptotic convergence and corrects transportability bias in simulations.
The paper explores how to apply causal knowledge across different datasets to improve learning.
problem How to apply causal knowledge across different datasets to improve learning.
method Investigates the structural causal bandit with transportability, fusing priors from source environments to enhance learning in the deployment setting.
result Achieves a sub-linear regret bound with an explicit dependence on informativeness of prior data, potentially outperforming standard bandit approaches.
Conditional COT-GAN predicts sequences using past data and kernel smoothing.
problem Predicting sequences given past data.
method Conditional COT-GAN with kernel smoothing.
result Improved convergence results for sequence prediction.
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
Enhances MOT with causality constraints for better option pricing.
problem Limited applicability of traditional martingale optimal transport (MOT) for option pricing.
method Integrates causality constraints into MOT and proposes McCormick relaxations for computational tractability.
result Empirically, McCormick MOT yields significant price reductions for basket and digital options compared to classic MOT.
Clarifies definitions of global hyperbolicity in various spaces.
problem Clarifying terminology in recent literature on global hyperbolicity.
method Comparing definitions in Lorentzian length spaces, optimal transport, and topological preordered spaces.
result The causal relation is a closed order and preserves compactness in all cases.
A new framework for robust and coherent counterfactual transports.
problem Estimating joint distributions over counterfactual outcomes in personalized decision-making and treatment risk assessment.
method Counterfactual cocycles that use algebraic structure to provide coherence and identifiability guarantees, bridging the gap between bijective SCMs and OT methods.
result Counterfactual cocycles provide state-of-the-art performance and noise-robustness across synthetic benchmarks and a real-world study.
Method predicts how probability distributions evolve over time.
problem Predicting how systems described by probability distributions evolve under different conditions.
method Wasserstein Parallel Transport
result Wasserstein Parallel Transport provides counterfactual comparisons of distributional dynamics.
A novel framework synthesizes treatment data across sites using optimal transport.
problem Estimating treatment effects across different sites with varying conditions.
method Distributional causal inference, Optimal Transport for alignment of control group distributions.
result Synthetic treatment group data aligns with true target distribution under general conditions.
The paper establishes general results in Lorentzian optimal transport theory.
problem Establishing strong duality and optimality conditions in Lorentzian optimal transport.
method Providing non-trivial assumptions on measures, characterizing optimality, and proving regularity results.
result Regularity results for c-convex functions and (weak) Kantorovich potentials do not extend to the Lorentzian setting, but under suitable assumptions, they are locally semconvex. New method identifies SDE drift and diffusion from temporal data.
problem Learning SDE parameters from temporal data, especially in noisy or incomplete data.
method Entropy-regularized optimal transport, APPEX algorithm.
result Can almost always recover drift and diffusion from temporal marginals.
Proposes ESCFR to estimate treatment effects from biased data.
problem Treatment selection bias in observational data.
method Stochastic optimal transport with relaxed mass-preserving and proximal factual outcome regularizers.
result Significantly better performance in estimating treatment effects.
CAST predicts distribution-valued time series by stabilizing and transporting simplex-supported successors.
problem Forecasting distribution-valued time series with structural failure modes.
method CAST (Causal Anchored Simplex Transport) uses successors retrieved from causal context, stabilized with a persistence anchor, and locally transported on ordered supports.
result CAST outperforms baselines on eleven public and simulated benchmarks, achieving best average rank on both one-step KL and autoregressive rollout JSD.
New framework optimizes decisions under uncertainty considering causal and continuous data.
problem Optimizing decisions under uncertain distributions with causal and continuous data structures.
method Developed a framework using Causal Sinkhorn DRO with Soft Regression Forest decision rules.
result Framework provides interpretable and tractable decision rules for optimizing under uncertainty.
Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on …
This paper addresses external validity bias in causal inference.
problem Estimating causal effects in a target population.
method Synthesis of approaches for generalizability and transportability, including tests for heterogeneity of treatment effects and differences between study and target populations.
result Framework for addressing external validity bias in causal inference.
TC-VAE generates robust financial time series data with causal constraints.
problem Generating realistic financial time series data with causal relationships.
method TC-VAE with causality constraint, RealNVP prior, and Wasserstein distance.
result TC-VAE loss controls discrepancy between market and generated distributions.
Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.
problem Synthetic curvature bounds for Lorentzian spaces.
method Optimal transport, convexity analysis of entropy functionals.
result Synthetic notion of timelike Ricci curvature lower bounds.
Synthetic framework for null hypersurfaces in non-smooth spacetimes.
problem Analyzing null hypersurfaces in non-smooth spacetimes.
method Develops synthetic null hypersurfaces using optimal transport and Lorentzian geometry.
result Synthetic null energy condition stabilizes under convergence and applies to low-regularity spacetimes.
Defines tangent spaces on causal sets using partial derivatives and metrics.
problem Defining geometric structures on causal sets.
method Using partial derivatives and metrics to define tangent spaces, connection, curvature, parallel transport, and geodesics.
result Approaches expected values for a flat spacetime as density increases.
Causal analysis reveals regional discrepancies in TOPCAT trial results.
problem Inconclusive results in TOPCAT trial for heart failure treatment.
method Causal discovery methods with domain knowledge integration.
result Significant causal effects shown for some subgroups globally.
Modeling multiple Hawkes processes with shared dynamics using graphons.
problem Modeling multiple multivariate point processes with shared dynamics.
method Leverage graphons to model an uncountable event type space, learn graphon-based Hawkes process model by minimizing hierarchical optimal transport distance.
result Infer underlying relations and simulate event sequences with similar dynamics.
New method for fair regression using optimal transport.
problem Learning fair regression models under counterfactual fairness constraints.
method Causal uncertainty view, optimal transport, post-processing method.
result High-probability fairness guarantees with O(n−1/3) decay. New measure captures differences across entire distributions of counterfactual outcomes.
problem Capturing differences across entire distributions of counterfactual outcomes.
method Entropic optimal transport measure, statistical functional, smooth transformation of embeddings.
result Established first-order and second-order pathwise differentiability.
New method distinguishes cause from effect using causal velocity.
problem Inferring causal direction from bivariate data.
method Parametrization of bivariate SCMs in terms of causal velocity, using tools from measure transport.
result Method extends beyond known model classes and requires no assumptions on noise distributions.
Unified method for inference on partially identified causal effects using covariates.
problem Partial identification of causal effects due to unobserved joint potential outcomes.
method Model-agnostic approach using duality theory for optimal transport problems.
result Uniformly valid inference for a wide class of estimands, even with inaccurate nuisance parameter estimates.
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
Unified framework for constructing kernels for transport equations and Koopman eigenfunctions.
problem Constructing kernels for transport equations and Koopman eigenfunctions.
method Three methods: variational principle, Green's function, and resolvent operator.
result Kernels constructed via these methods are identical under mild assumptions.
Generates counterfactuals in target domain from source domain observations.
problem Cross-domain learning with domain shifts and lack of parallel datasets.
method Unsupervised, Neural Causal Models, Joint Causal Graphs, Effect-Intrinsic vs Domain-Intrinsic Variables.
result Framework generates counterfactuals that closely match ground truth.
Introduces statistical optimal transport for probabilistic lectures.
problem No specific problem stated; focuses on introduction.
method Lecture-based introduction to statistical optimal transport.
result Provides an introduction to statistical optimal transport.
We present FlipTest, a black-box technique for uncovering discrimination in classifiers. FlipTest is motivated by the intuitive question: had an individual been of a different protected status, would the model have treated them differently? Rather than relying on causal information to answer this question, FlipTest lev…
NOT learns optimal transport plans, kernel costs improve performance.
problem NOT algorithm learns non-optimal plans with weak quadratic costs.
method Introduced kernel weak quadratic costs to improve NOT's performance.
result Kernel costs provide improved theoretical and practical guarantees.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
Extends optimal transport to dynamic and martingale settings.
problem Dynamic and martingale relaxation of optimal transport problems.
method Extends Benamou-Brenier formula to weak optimal transport and introduces barycentric optimal transport.
result Relates barycentric optimal transport to martingale Benamou-Brenier formula.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.