Researchers from the Apple Machine Learning Research division have presented a new concept addressing the problem of verifying claims about unknown data distributions. In the described scenario, one party has access to a limited number of samples, while another, potentially untrusted party, claims to have performed a complex analysis and draws conclusions about the properties of this data.

The authors constructed interactive proof systems that allow the first party to efficiently verify the second party's claims. The key advantage of the proposed approach is that verification requires significantly fewer computational resources than independently conducting the initial deep analysis.

The developed system applies to general distribution properties that can be defined using bounded-depth circuits. This theoretical achievement opens possibilities for creating protocols where trust in big data processing results is ensured mathematically rather than by the executor's reputation.