Program Analysis for Adaptive Data Analysis

Abstract

Data analyses are usually designed to identify some property of the population from which the data are drawn, generalizing beyond the specific data sample. For this reason, data analyses are often designed to produce a low generalization error, so that the result of an analysis on sample data does not differ too much from the result one would achieve over the entire population. An adaptive data analysis can be seen as a process composed of multiple queries interrogating some data, where the choice of which query to run next may rely on the results of previous queries. The generalization error of each individual query can be controlled using well-established statistical techniques. However, when queries are arbitrarily composed, errors can propagate through the chain of queries and lead to high generalization error. To address this issue, several techniques guarantee bounds not only on single queries but also on composed analyses. The choice of technique often depends on the chain of queries that an adaptive data analysis can generate. In this work, we consider adaptive data analyses implemented as while-like programs and design a program analysis to help identify which technique to use to control their generalization errors. More specifically, we formalize the intuitive notion of adaptivity as a quantitative property of programs. Based on this definition, we design a program analysis for soundly approximating this quantity. The analysis represents the data analysis as a weighted dependency graph, where weights upper-bound how often variables can be reached, and uses a path-search strategy to upper-bound adaptivity. We implement our program analysis and show that it can analyze several concrete data analyses with different adaptivity structures.