Streaming Verification in Data Analysis

TL;DR

This paper develops streaming interactive proof protocols for data analysis tasks such as clustering, shape fitting, matrix multiplication, and eigenvector verification, optimizing communication and space complexity.

Contribution

It introduces new streaming interactive proof protocols for data analysis problems, including improved methods for matrix multiplication and eigenvector verification.

Findings

Protocols use polylogarithmic rounds and communication.

Constant round protocols for special cases with easy verification.

Protocols for matrix multiplication and eigenvector verification operate in the annotated data streaming model.

Abstract

Streaming interactive proofs (SIPs) are a framework to reason about outsourced computation, where a data owner (the verifier) outsources a computation to the cloud (the prover), but wishes to verify the correctness of the solution provided by the cloud service. In this paper we present streaming interactive proofs for problems in data analysis. We present protocols for clustering and shape fitting problems, as well as an improved protocol for rectangular matrix multiplication. The latter can in turn be used to verify $k$ eigenvectors of a (streamed) $n \times n$ matrix. In general our solutions use polylogarithmic rounds of communication and polylogarithmic total communication and verifier space. For special cases (when optimality certificates can be verified easily), we present constant round protocols with similar costs. For rectangular matrix multiplication and eigenvector verification, our protocols work in the more restricted annotated data streaming model, and use sublinear (but not polylogarithmic) communication.