Borrowing Strength in Distributionally Robust Optimization via Hierarchical Dirichlet Processes
<|reference_start|>Borrowing Strength in Distributionally Robust Optimization via Hierarchical Dirichlet Processes: This paper presents a novel optimization framework to address key challenges presented by modern machine learning applications: High dimensionality, distributional uncertainty, and data heterogeneity. Our approach unifies regularized estimation, distributionally robust optimization (DRO), and hierarchical Bayesian modeling in a single data-driven criterion. By employing a hierarchical Dirichlet process (HDP) prior, the method effectively handles multi-source data, achieving regularization, distributional robustness, and borrowing strength across diverse yet related data-generating processes. We demonstrate the method's advantages by establishing theoretical performance guarantees and tractable Monte Carlo approximations based on Dirichlet process (DP) theory. Numerical experiments validate the framework's efficacy in improving and stabilizing both prediction and parameter estimation accuracy, showcasing its potential for application in complex data environments.<|reference_end|>
@article{bariletto2024borrowing,
    title={Borrowing Strength in Distributionally Robust Optimization via
  Hierarchical Dirichlet Processes},
    author={Nicola Bariletto, Khai Nguyen, Nhat Ho},
    journal={arXiv preprint arXiv:2405.13160},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.13160},
    primaryClass={stat.ML cs.LG}
}