It has long been a recognized problem that many datasets contain significant levels of missing numerical data. A potentially critical predicate for application of machine learning methods to datasets involves addressing this problem. However, this is a challenging task. In this paper, we apply a recently developed multi-level stochastic optimization approach to the problem of imputation in massive medical records. The approach is based on computational applied mathematics techniques and is highly accurate. In particular, for the Best Linear Unbiased Predictor (BLUP) this multi-level formulation is exact, and is significantly faster and more numerically stable. This permits practical application of Kriging methods to data imputation problems for massive datasets. We test this approach on data from the National Inpatient Sample (NIS) data records, Healthcare Cost and Utilization Project (HCUP), Agency for Healthcare Research and Quality. Numerical results show that the multi-level method significantly outperforms current approaches and is numerically robust. It has superior accuracy as compared with methods recommended in the recent report from HCUP. Benchmark tests show up to 75% reductions in error. Furthermore, the results are also superior to recent state of the art methods such as discriminative deep learning

SimRank-based similarity joins, which mainly include threshold-based and top- k similarity joins, are important types of all-pair SimRank queries. Although a line of related algorithms have been proposed recently, they still fall short of providing approximation guarantee and suffer from scalability issues on medium and large graphs. Meanwhile, we also lack an extensive analysis of existing techniques in terms of accuracy and efficiency. Motivated by these challenges, we first conduct detailed analysis of state-of-the-art algorithms and provide additional theoretical results. Second, to address the limitations of existing techniques, we propose simple yet effective algorithm frameworks for both queries to theoretically guarantee the approximation bound, and present a more efficient all-pair algorithm inspired by randomized local push of Personalized PageRank. Next, we analyze the algorithmic complexity of threshold-based and top- k similarity joins by leveraging a reasonable assumption of SimRank distribution. Through extensive experiments, we find that our proposed methods far exceed existing ones with respect to query efficiency, approximation guarantee and practical accuracy, while our theoretical analysis nicely matches the empirical study.