Parallel Statistical Computing in Theory: Lecture Notes on Large-Scale Parallel Statistics

This monograph collects theoretical foundations for parallel statistical computing. It presents classical time-series analysis, a comprehensive toolkit of non-asymptotic concentration inequalities, and the theory behind parallel matrix-completion algorithms. Topics include ARIMA/SARIMA modelling, transfer-function and intervention analysis, entropy and logarithmic Sobolev inequalities, hypercontractivity, as well as ALS, CCD++ and parallel SGD for low-rank matrix recovery. Designed for graduate-level teaching and self-study, it bridges probabilistic theory and large-scale statistical algorithms.