The Everlasting Database: Statistical Validity at a Fair Price

Blake Woodworth
Vitaly Feldman
Saharon Rosset
Nathan Srebro
NeurIPS (2018)

Abstract

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 $O(\sqrt{M})$.