In other words, a milk production value can only be understood in the context of the cow which produced the milk, and the cow is further linked to a specific herd owned by a given farmer. Causal relationships denote that x causes y, and so in a system that is trying to predict y, for example, we know that we have to include x in order to do this prediction meaningfully. In many applications a whole causal chain exists. For example, in the dairy data there exists a chain from the farmer, herd and cow identifiers through measured attributes such as milk production down to the attribute that records whether a particular cow was retained or sold by the farmer. Rules which fail to establish this chain or which attempt to break it are meaningless.
Functional relationships occur in many databases.
In database theory attempts are made to locate these dependencies for the purposes of normalisation. In our application the meaning of a functional dependency is that if x is discovered in part of a rule then there is no need to consider y. Many machine learning schemes will often attempt to rediscover functional dependencies that are already known. This data has to be specified in a meaningful way so that only true outliers are discovered and removed from consideration. This attribute is often continuous in the raw data, and must be discretized by making use of distribution and standard deviation information to form appropriate discrete blocks of data values.