Science and common sense both tell us that the facts about the world are not directly observable but can be inferred from observations about the effects of actions. What people infer about the world is not just relations among observations but relations among entities that are much more stable than observations. For example, 3-dimensional objects are more stable than the image on a person's retina, the information directly obtained from feeling an object or on an image scanned into a computer. Likewise the fact that a customer has children is more stable than the fact that a particular basket includes Roll-ups. The fact that a customer has diabetes is more stable than a particular pattern of food purchases that may allow inferring that he has diabetes. The phenomenal facts, partly because they are more stable than observations, are more predictive of future behavior than simple observational facts.
The extreme positivist philosophical view that science concerns relations among observations still influences the design of learning programs, and that's what data miners are. However, science never worked that way, neither do babies and neither should data mining programs. All obtain and use representations of the objects and use observations only as a means to that end.
Data mining involves computer programs that infer relations among different kinds of data in large databases. The goal has been to infer useful relations that might not have been noticed or at least could not have been confirmed among this data. We use the standard example of a supermarket chain with a database of all the cash register receipts for some long time period--many gigabytes of data. The company wants to mine this database for information useful for improving its business.
Data-mining can be made to do more than just find relations among data. Data amounts to observations of the world, and it is possible to infer relations among entities in the world from the data. Such relations are likely to be as useful to know about as are relations among the entities directly represented in the data. In the supermarket chain example, there are people, groups of people, their homes with pantries, refrigerators and freezers and facts about what they cook and what they eat. It should even be possible to infer the existence of entities in the world, such as previously unidentified groups of people with distinct eating and purchasing habits. Another example is to identify bellwether groups; what they buy today, many more will buy tomorrow.
Moreover, the information will usually admit a more compact description in terms of the underlying phenomena than in terms of the data.
Although all common sense level knowledge of the world is potentially relevant to data mining, formalizing common sense has proved to be a difficult AI problem, and progress has been slow. Nevertheless, we can expect that certain phenomena will be related to the information in databases in a straightforward enough way so that information about them can be found by data miners.