2015/07/01 by Gérard Biau, Kevin Bleakley, Biau, Gérard +3
Computer Science · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Methodology (stat.ME) #Privacy-Preserving Technologies in Data #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1507.00171
openalex publication_date 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The statistical analysis of massive and complex data sets will require the\ndevelopment of algorithms that depend on distributed computing and\ncollaborative inference. Inspired by this, we propose a collaborative framework\nthat aims to estimate the unknown mean \θ of a random variable X. In\nthe model we present, a certain number of calculation units, distributed across\na communication network represented by a graph, participate in the estimation\nof \θ by sequentially receiving independent data from X while\nexchanging messages via a stochastic matrix A defined over the graph. We give\nprecise conditions on the matrix A under which the statistical precision of\nthe individual units is comparable to that of a (gold standard) virtual\ncentralized estimate, even though each unit does not have access to all of the\ndata. We show in particular the fundamental role played by both the non-trivial\neigenvalues of A and the Ramanujan class of expander graphs, which provide\nremarkable performance for moderate algorithmic cost.\n