Abstract
Due to recent emergence of many big data problems, Monte Carlo methods tend to become powerful tools for analyzing big data sets. In this chapter, we first review the fundamental principles of Monte Carlo methods. Then, we describe several popular variance reduction techniques, including stratified sampling, control variates, antithetic variates, and importance sampling, to improve Monte Carlo sampling efficiency. Finally, application examples of estimation of sum, Monte Carlo linear solver, image recovery, matrix multiplication, and low-rank approximation are shown as case studies to demonstrate the effectiveness of Monte Carlo methods in data analysis.
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