Machine Learning - DISCo

which enable the user to specify the predicate and function symbols to be
considered, and the types and formats of arguments for each.
2. PROGOL uses a sequential covering algorithm to learn a set of expressions
from H that cover the data. For each example (xi, f (xi)) that is not yet
covered by these learned expressions, it first searches for the most specific
hypothesis hi within H such that (B A hi A xi) l- f (xi). More precisely, it
approximates this by calculating the most specific hypothesis among those
that entail f (xi) within k applications of the resolution rule (where k is a
user-specified parameter).
3. PROGOL then performs a general-to-specific search of the hypothesis space
bounded by the most general possible hypothesis and by the specific bound
hi calculated in step 2. Within this set of hypotheses, it seeks the hypothesis
having minimum description length (measured by the number of literals).
This part of the search is guided by an A*-like heuristic that allows pruning
without running the risk of pruning away the shortest hypothesis.
The details of the PROGOL algorithm are described by Muggleton (1992,
1995).
10.8 SUMMARY AND FURTHER READING
The main points of this chapter include:
The sequential covering algorithm learns a disjunctive set of rules by first
learning a single accurate rule, then removing the positive examples covered
by this rule and iterating the process over the remaining training examples.
It provides an efficient, greedy algorithm for learning rule sets, and an alternative
to top-down decision tree learning algorithms such as ID3, which
can be viewed as simultaneous, rather than sequential covering algorithms.
0 In the context of sequential covering algorithms, a variety of methods have
been explored for learning a single rule. These methods vary in the search
strategy they use for examining the space of possible rule preconditions. One
popular approach, exemplified by the CN2 program, is to conduct a generalto-specific
beam search, generating and testing progressively more specific
rules until a sufficiently accurate rule is found. Alternative approaches search
from specific to general hypotheses, use an example-driven search rather than
generate and test, and employ different statistical measures of rule accuracy
to guide the search.
Sets of first-order rules (i.e., rules containing variables) provide a highly
expressive representation. For example, the programming language PROLOG
represents general programs using collections of first-order Horn clauses.
The problem of learning first-order Horn clauses is therefore often referred
to as the problem of inductive logic programming.
One approach to learning sets of first-order rules is to extend the sequential
covering algorithm of CN2 from propositional to first-order representations.