Causal Optimal Coupling for Gaussian Input-Output Distributional Data
We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint reflecting the temporal structure of the system. We formulate this problem as a Schr"odinger Bridge, which seeks the coupling closest - in Kullback-Leibler divergence - to a given prior while enforcing both marginal and causality constraints. For the case of Gaussian marginals and general time-dependent quadratic cost functions, we derive a fully tractable characterization of the Sinkhorn iterations that converges to the optimal solution. Beyond its theoretical contribution, the proposed framework provides a principled foundation for applying causal optimal transport methods to system identification from distributional data.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space
The Optimal Transport (OT) problem with squared Euclidean cost consists in finding a coupling between two input measures that maximizes correlation. Consequently, the optimal coupling is often singular with respect to th…
PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction
Causal abstraction offers a principled framework for mechanistic interpretability, aligning a high-level causal model with the low-level computation realized by a neural network through counterfactual intervention analys…
A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings
We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent f…
Bayesian InferenceClassificationEEGElectroencephalogram (EEG)+1Dynamic Causal Bayesian Optimization
This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety o…
Bayesian OptimizationCausal InferenceDecision MakingSequential Decision MakingCausal Beam Selection for Reliable Initial Access in AI-driven Beam Management
Efficient and reliable beam alignment is a critical requirement for mmWave multiple-input multiple-output (MIMO) systems, especially in 6G and beyond, where communication must be fast, adaptive, and resilient to real-wor…
Beam Prediction