The Everlasting Database: Statistical Validity at a Fair Price
This addresses the issue of invalid statistical inferences due to adaptivity for researchers and practitioners in fields like machine learning and science, offering a novel solution with provable guarantees.
The paper tackles the problem of adaptivity in data analysis, such as test-set overfitting in ML, by proposing a mechanism that answers an arbitrarily long sequence of potentially adaptive statistical queries while guaranteeing statistical validity without assumptions on query generation. It ensures that the cost for M non-adaptive queries is O(log M) and for adaptive queries is O(sqrt M) with high probability.
The problem of handling adaptivity in data analysis, intentional or not, permeates a variety of fields, including test-set overfitting in ML challenges and the accumulation of invalid scientific discoveries. We propose a mechanism for answering an arbitrarily long sequence of potentially adaptive statistical queries, by charging a price for each query and using the proceeds to collect additional samples. Crucially, we guarantee statistical validity without any assumptions on how the queries are generated. We also ensure with high probability that the cost for $M$ non-adaptive queries is $O(\log M)$, while the cost to a potentially adaptive user who makes $M$ queries that do not depend on any others is $O(\sqrt{M})$.