A general decision framework for structuring computation using Data   Directional Scaling to process massive similarity matrices
  As datasets grow it becomes infeasible to process them completely with a desired model. For giant datasets, we frame the order in which computation is performed as a decision problem. The order is designed so that partial computations are of value and early stopping yields useful results. Our approach comprises two related tools: a decision framework to choose the order to perform computations, and an emulation framework to enable estimation of the unevaluated computations. The approach is applied to the problem of computing similarity matrices, for which the cost of computation grows quadratically with the number of objects. Reasoning about similarities before they are observed introduces difficulties as there is no natural space and hence comparisons are difficult. We solve this by introducing a computationally convenient form of multidimensional scaling we call `data directional scaling'. High quality estimation is possible with massively reduced computation from the naive approach, and can be scaled to very large matrices. The approach is applied to the practical problem of assessing genetic similarity in population genetics. The use of statistical reasoning in decision making for large scale problems promises to be an important tool in applying statistical methodology to Big Data. 
Daniel John Lawson and Niall M Adams
stat.CO