Our security system is only one of many possible tasks for a learning system. Others
may be for example to predict the amount of snow that will fall tonight given the current
weather conditions, or to predict the average house price in an area given some demographic
information (in fact, exactly this, the house pricing problem, is tackled in chapter 4). We
need a general mathematical framework that will encompass all of these and enable us to
discuss them in a formal manner; we develop this in the following section.