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In recent years, a growing number of organizations have been allocating vast amount
of resources to construct and maintain databases and data warehouses. In scientific
endeavours, data refers to carefully collected observations about some phenomenon
under study. In business, data capture information about economic trends, critical
markets, competitors and customers. In manufacturing, data record machinery
performances and production rates in different conditions. There are essentially
two reasons why people gather increasing volumes of data: first, they think some
valuable assets are implicitly coded within them, and computer technology enables
effective data storage at reduced costs.
The idea of extracting useful knowledge from volumes of data is common to many
disciplines, from statistics to physics, from econometrics to system identification
and adaptive control. The procedure for finding useful patterns in data is known
by different names in different communities, viz., knowledge extraction, pattern
analysis, data processing. More recently, the set of computational techniques and
tools to support the modelling of large amount of data is being grouped under the
more general label of machine learning [46].
The need for programs that can learn was stressed by Alan Turing who ar-
gued that it may be too ambitious to write from scratch programs for tasks that
even human must learn to perform. This handbook aims to present the statistical
foundations of machine learning intended as the discipline which deals with the au-
tomatic design of models from data. In particular, we focus on supervised learning
problems (Figure 1.1), where the goal is to model the relation between a set of input
variables, and one or more output variables, which are considered to be dependent
on the inputs in some manner.
Since the handbook deals with artificial learning methods, we do not take into
consideration any argument of biological or cognitive plausibility of the learning
methods we present. Learning is postulated here as a problem of statistical estima-
tion of the dependencies between variables on the basis of empirical data.
The relevance of statistical analysis arises as soon as there is a need to extract
useful information from data records obtained by repeatedly measuring an observed
phenomenon. Suppose we are interested in learning about the relationship between
two variables x (e.g. the height of a child) and y (e.g. the weight of a child)
which are quantitative observations of some phenomenon of interest (e.g. obesity
during childhood). Sometimes, the a priori knowledge that describes the relation
between x and y is available. In other cases, no satisfactory theory exists and all
that we can use are repeated measurements of x and y. In this book our focus is the
second situation where we assume that only a set of observed data is available. The
reasons for addressing this problem are essentially two. First, the more complex
is the input/output relation, the less effective will be the contribution of a human
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