Machine Learning - DISCo

and (b) classify the observed training examples in a single inference step.
Thus, the learned rules can be seen as a reformulation of the domain theory
into a set of special-case rules capable of classifying instances of the target
concept in a single inference step.
0 EBL as "just" restating what the learner already "knows." In one sense, the
learner in our SafeToStack example begins with full knowledge of the Safe-
ToStack concept. That is, if its initial domain theory is sufficient to explain
any observed training examples, then it is also sufficient to predict their
classification in advance. In what sense, then, does this qualify as learning?
One answer is that in many tasks the difference between what one knows
in principle and what one can efficiently compute in practice may be great,
and in such cases this kind of "knowledge reformulation" can be an important
form of learning. In playing chess, for example, the rules of the game
constitute a perfect domain theory, sufficient in principle to play perfect
chess. Despite this fact, people still require considerable experience to learn
how to play chess well. This is precisely a situation in which a complete,
perfect domain theory is already known to the (human) learner, and further
learning is "simply" a matter of reformulating this knowledge into a form
in which it can be used more effectively to select appropriate moves. A beginning
course in Newtonian physics exhibits the same property-the basic
laws of physics are easily stated, but students nevertheless spend a large
part of a semester working out the consequences so they have this knowledge
in more operational form and need not derive every problem solution
from first principles come the final exam. PROLOG-EBG performs this type
of reformulation of knowledge-its learned rules map directly from observable
instance features to the classification relative to the target concept, in a
way that is consistent with the underlying domain theory. Whereas it may
require many inference steps and considerable search to classify an arbitrary
instance using the original domain theory, the learned rules classify
the observed instances in a single inference step.
Thus, in its pure form EBL involves reformulating the domain theory to
produce general rules that classify examples in a single inference step. This kind
of knowledge reformulation is sometimes referred to as knowledge compilation,
indicating that the transformation is an efficiency improving one that does not
alter the correctness of the system's knowledge.
11.3.1 Discovering New Features
One interesting capability of PROLOG-EBG is its ability to formulate new features
that are not explicit in the description of the training examples, but that are needed
to describe the general rule underlying the training example. This capability is
illustrated by the algorithm trace and the learned rule in the previous section. In
particular, the learned rule asserts that the essential constraint on the Volume and
Density of x is that their product is less than 5. In fact, the training examples