Keywords

Machine learningMathematical ModelTraining Data

Institute(s)

Cambridge University Press

Year

2022

Abstract

Machine learning is about learning, reasoning, and acting based on data. This
is done by constructing computer programs that process the data, extract useful
information, make predictions regarding unknown properties, and suggest actions to
take or decisions to make. What turns data analysis into machine learning is that the
process is automated and that the computer program is learnt from data. This means
that generic computer programs are used, which are adapted to application-specific
circumstances by automatically adjusting the settings of the program based on
observed, so-called training data. It can therefore be said that machine learning
is a way of programming by example. The beauty of machine learning is that it is
quite arbitrary what the data represents, and we can design general methods that are
useful for a wide range of practical applications in different domains. We illustrate
this via a range of examples below.
The ‘generic computer program’ referred to above corresponds to a mathematical
model of the data. That is, when we develop and describe different machine
learning methods, we do this using the language of mathematics. The mathematical
model describes a relationship between the quantities involved, or variables, that
correspond to the observed data and the properties of interest (such as predictions,
actions, etc.) Hence, the model is a compact representation of the data that, in a
precise mathematical form, captures the key properties of the phenomenon we are
studying. Which model to make use of is typically guided by the machine learning
engineer’s insights generated when looking at the available data and the practitioner’s
general understanding of the problem. When implementing the method in practice,
this mathematical model is translated into code that can be executed on a computer.
However, to understand what the computer program actually does, it is important
also to understand the underlying mathematics.

Author(s)

Andreas LindholmNiklas WahlströmFredrik LindstenThomas B. Schön