Regularization and approximation: statistical inference, model selection, and large data

正则化和近似：统计推断、模型选择和大数据

• 批准号: RGPIN-2021-02618
• 负责人: McDonald, Daniel
• 金额: $ 1.97万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=742109
• 关键词: Regularization; approximation; statistical; inference; model

Extracting information from large data requires computational tractability and statistical efficiency. These are typically achieved through approximation or regularization, either of which heuristically balances fidelity to the data with scientific goals like parsimony, smoothness, sparsity, or interpretability. My long-term objective is to enable fundamental scientific progress by developing and characterizing the connections between computational approximation and statistical regularization, thereby facilitating improved inference. In particular, my research program investigates how statistically optimal decisions depend on the amount of regularization or approximation and their structures, both of which must be tied to the scientific questions at stake and calibrated according to the data. Research in computer science has focused on improving algorithms to enable computation with a minimum of approximation. Meanwhile, statisticians have developed regularization techniques in order to take advantage of simple structures that, if representative of the truth, will improve inference and prediction. My work seeks to bridge the gap between these perspectives. My research program aims to deepen the theoretical links between approximation algorithms and inference for estimation and prediction by: (1) developing and justifying approximation techniques for dependent data; (2) enabling application through reasoned tuning parameter selection; (3) precisely characterizing the effect of approximations in nonparametric statistics; and (4) ensuring scientific applicability through synergistic development and collaboration with domain experts.

从大数据中提取信息需要计算的易处理性和统计的效率。这些通常是通过近似或正则化来实现的，这两种方法都可以启发式地平衡数据的保真度与简约性、平滑性、稀疏性或可解释性等科学目标。我的长期目标是通过开发和表征计算近似与统计正则化之间的联系来实现基础科学进步，从而促进改进的推理。特别是，我的研究项目调查统计上的最佳决策如何取决于正则化或近似的数量及其结构，这两者都必须与所涉及的科学问题联系起来并根据数据进行校准。计算机科学研究的重点是改进算法，以最小化近似值进行计算。与此同时，统计学家开发了正则化技术，以便利用简单的结构，如果这些结构代表事实，将改善推理和预测。我的工作旨在弥合这些观点之间的差距。我的研究计划旨在通过以下方式加深近似算法与估计和预测推理之间的理论联系：（1）开发并证明相关数据的近似技术； (2) 通过合理的调整参数选择来启用应用； (3) 精确表征非参数统计中的近似效应； (4) 通过与领域专家的协同开发和合作，确保科学适用性。