Partial identification with entropy regularized optimal transport

@misc{costa2026partial,
  title = {{Partial identification with entropy regularized optimal transport}},
  author = {Bruno N. Costa and Florian F. Gunsilius},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40156},
  eprint = {2609.40156},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40156},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Partial identification with entropy regularized optimal transport
AU  - Bruno N. Costa
AU  - Florian F. Gunsilius
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40156
UR  - https://arxiv.org/abs/2609.40156
AB  - In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In such cases, one can only identify sets which are guaranteed to contain the true parameters. These are often characterized through linear programs that optimize over models compatible with the observed data. These programs can be infinite-dimensional in the optimizer and the number of constraints. We provide a unified way to characterize and solve such optimization problems by phrasing them as optimal transport problems on path spaces. This allows us to regularize the problem with an entropy penalty, recasting it as a multi-marginal entropic optimal transport problem, which can be solved efficiently via Sinkhorn iterations. In addition, it allows us to establish convergence of the regularized value to the sharpest bound, derive consistency rates for a plug-in estimator, and obtain asymptotic distribution for approximate bounds. The method is general and accommodates settings ranging from instrumental variable models with continuous variables to welfare estimation in heterogeneous demand models. We verify the statistical and computational properties in simulations and provide an application to demand estimation.
ER  -