Uncertainty Quantification under Noisy Constraints, with Applications to Raking
<|reference_start|>Uncertainty Quantification under Noisy Constraints, with Applications to Raking: We consider statistical inference problems under uncertain equality constraints, and provide asymptotically valid uncertainty estimates for inferred parameters. The proposed approach leverages the implicit function theorem and primal-dual optimality conditions for a particular problem class. The motivating application is multi-dimensional raking, where observations are adjusted to match marginals; for example, adjusting estimated deaths across race, county, and cause in order to match state all-race all-cause totals. We review raking from a convex optimization perspective, providing explicit primal-dual formulations, algorithms, and optimality conditions for a wide array of raking applications, which are then leveraged to obtain the uncertainty estimates. Empirical results show that the approach obtains, at the cost of a single solve, nearly the same uncertainty estimates as computationally intensive Monte Carlo techniques that pass thousands of observed and of marginal draws through the entire raking process.<|reference_end|>
@article{ducellier2024uncertainty,
    title={Uncertainty Quantification under Noisy Constraints, with Applications to
  Raking},
    author={Ariane Ducellier (1), Alexander Hsu (1 and 2), Parkes Kendrick (1),
  Bill Gustafson (1), Laura Dwyer-Lindgren (1), Christopher Murray (1), Peng
  Zheng (1) and Aleksandr Aravkin (1 and 2) ((1) Institute for Health Metrics
  and Evaluation, Seattle, WA (2) Department of Applied Mathematics, University
  of Washington, Seattle, WA)},
    journal={arXiv preprint arXiv:2407.20520},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.20520},
    primaryClass={stat.ME cs.NA math.NA stat.AP stat.CO}
}