Statistical Queries and Statistical Algorithms: Foundations and Applications

Over 20 years ago, Kearns [1998] introduced statistical queries as a framework for designing machine learning algorithms that are tolerant to noise. The statistical query model restricts a learning algorithm to ask certain types of queries to an oracle that responds with approximately correct answers. This framework has has proven useful, not only for designing noise-tolerant algorithms, but also for its connections to other noise models, for its ability to capture many of our current techniques, and for its explanatory power about the hardness of many important problems. Researchers have also found many connections between statistical queries and a variety of modern topics, including to evolvability, differential privacy, and adaptive data analysis. Statistical queries are now both an important tool and remain a foundational topic with many important questions. The aim of this survey is to illustrate these connections and bring researchers to the forefront of our understanding of this important area.