Scalable and Numerically Stable Descriptive Statistics in SystemML

With the exponential growth in the amount of data that is being generated in recent years, there is a pressing need for applying machine learning algorithms to large data sets. SystemML is a framework that employs a declarative approach for large scale data analytics. In SystemML, machine learning algorithms are expressed as scripts in a high-level language, called DML, which is syntactically similar to R. DML scripts are compiled, optimized, and executed in the SystemML runtime that is built on top of MapReduce. As the basis of virtually every quantitative analysis, descriptive statistics provide powerful tools to explore data in SystemML. In this paper, we describe our experience in implementing descriptive statistics in SystemML. In particular, we elaborate on how to overcome the two major challenges: (1) achieving numerical stability while operating on large data sets in a distributed setting of MapReduce, and (2) designing scalable algorithms to compute order statistics in MapReduce. By empirically comparing to algorithms commonly used in existing tools and systems, we demonstrate the numerical accuracy achieved by SystemML. We also highlight the valuable lessons we have learned in this exercise.