Streaming Verification in Data Analysis

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.