Statistical Queries and Statistical Algorithms: Foundations and Applications
This is an incremental work that synthesizes existing knowledge for researchers in theoretical machine learning and related fields.
This paper provides a comprehensive survey of the statistical query model, covering its foundational theory and connections to learnability concepts, along with detailed applications in optimization, evolvability, and differential privacy.
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to various notions of learnability. We also give a detailed summary of some of the applications of statistical queries to other areas, including to optimization, to evolvability, and to differential privacy.