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 distribution 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 $\mathbb{F}_2$-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.

翻译：我们研究的是统计问题,如种植区、其变种和在平均情况通信复杂度背景下的稀少主要组成部分分析。 我们的动机是了解流、草图和基于查询的模式中的统计-计算取舍。 通信的复杂性是证明这些模型中较低界限的主要工具, 但许多先前的结果在平均情况中并不存在。 我们提供了一个一般的减少方法, 以保存输入分布, 涉及随机图或带有种植结构的矩阵的问题。 然后, 我们从两党和多党的通信中得出较低界限, 以探测或找到种植区、 两党的晶体和相关问题。 因此, 我们获得了边缘- Probe、 矢量- 矩阵- 摄取、 矩阵- 摄取、 线性绘图和 $\mathbb{F ⁇ 2$- setzetching 模型中的查询复杂性的新界限。 许多这些结果几乎是紧凑的, 我们用我们的方法为边缘- 模型提供一些已知较低界限的简单证据。