3. Statistical Leveraging Methods in Big Data

With the advance in science and technologies in the past decade, big data becomes ubiquitous in all fields. The exponential growth of big data significantly outpaces the increase of storage and computational capacity of high performance computers. The challenge in analyzing big data calls for innovative analytical and computational methods that make better use of currently available computing power. An emerging powerful family of methods for effectively analyzing big data is called statistical leveraging. In these methods, one first takes a random subsample from the original full sample, then uses the subsample as a surrogate for any computation and estimation of interest. The key to success of statistical leveraging methods is to construct a data-adaptive sampling probability distribution, which gives preference to those data points that are influential to model fitting and statistical inference. In this chapter, we review the recent development of statistical leveraging methods. In particular, we focus on various algorithms for constructing subsampling probability distribution, and a coherent theoretical framework for investigating their estimation property and computing complexity. Simulation studies and real data examples are presented to demonstrate applications of the methodology.