  Statistical Machine Learning (SML) refers to a body of algorithms and methods
by which computers are allowed to discover important features of input data
sets which are often very large in size. The very task of feature discovery
from data is essentially the meaning of the keyword `learning' in SML.
Theoretical justifications for the effectiveness of the SML algorithms are
underpinned by sound principles from different disciplines, such as Computer
Science and Statistics. The theoretical underpinnings particularly justified by
statistical inference methods are together termed as statistical learning
theory.
  This paper provides a review of SML from a Bayesian decision theoretic point
of view -- where we argue that many SML techniques are closely connected to
making inference by using the so called Bayesian paradigm. We discuss many
important SML techniques such as supervised and unsupervised learning, deep
learning, online learning and Gaussian processes especially in the context of
very large data sets where these are often employed. We present a dictionary
which maps the key concepts of SML from Computer Science and Statistics. We
illustrate the SML techniques with three moderately large data sets where we
also discuss many practical implementation issues. Thus the review is
especially targeted at statisticians and computer scientists who are aspiring
to understand and apply SML for moderately large to big data sets.
