Average-Case Communication Complexity of Statistical Problems [article]

Cyrus Rashtchian, David P. Woodruff, Peng Ye, Hanlin Zhu
2021 arXiv   pre-print
We study statistical problems, such as planted clique, its variants, and sparse principal component analysis in the context of average-case communication complexity. Our motivation is to understand the statistical-computational trade-offs in streaming, sketching, and query-based models. Communication complexity is the main tool for proving lower bounds in these models, yet many prior results do not hold in an average-case setting. We provide a general reduction method that preserves the input
more » ... stribution for problems involving a random graph or matrix with planted structure. Then, we derive two-party and multi-party communication lower bounds for detecting or finding planted cliques, bipartite cliques, and related problems. As a consequence, we obtain new bounds on the query complexity in the edge-probe, vector-matrix-vector, matrix-vector, linear sketching, and 𝔽_2-sketching models. Many of these results are nearly tight, and we use our techniques to provide simple proofs of some known lower bounds for the edge-probe model.
arXiv:2107.01335v1 fatcat:bq4332fg3ndnfn2j4e5l4c5qne