Parameter Estimation in a Stochastic System Model for PageRank

The PageRank algorithm is used by Google as a way of hierarchically indexing web pages in order to provide relevant and reputable search results. Fundamentally, this algorithm relies on the hypertextual nature of the World Wide Web; indeed, the PageRank vector can be computed based simply on the hyperlink structure of every page in the web. In this paper, we consider a model for PageRank whose dynamics are described by a stochastic system and we establish strong consistency of the least squares estimator of an unknown parameter in this system. Furthermore, motivated by recent work on distributed randomized methods for computing PageRank, we show that the least squares estimator remains strongly consistent within a distributed framework.