Machine learningMathematical ModelTraining Data
Cambridge University Press
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.
Andreas LindholmNiklas WahlströmFredrik LindstenThomas B. Schön