Machine Learning - DISCo

y first order Horn clauses to learn a set of Horn clauses that approximate
the target function. FOCL employs a sequential covering algorithm, learning
each Horn clause by a general-to-specific search. The domain theory is used
to augment the set of next more specific candidate hypotheses considered
at each step of this search. Candidate hypotheses are then evaluated based
on their performance over the training data. In this way, FOCL combines
the greedy, general-to-specific inductive search strategy of FOIL with the
rule-chaining, analytical reasoning of analytical methods.
0 The question of how to best blend prior knowledge with new observations
remains one of the key open questions in machine learning.
There are many more examples of algorithms that attempt to combine inductive
and analytical learning. For example, methods for learning Bayesian belief
networks discussed in Chapter 6 provide one alternative to the approaches discussed
here. The references at the end of this chapter provide additional examples
and sources for further reading.
EXERCISES
12.1. Consider learning the target concept GoodCreditRisk defined over instances described
by the four attributes HasStudentLoan, HasSavingsAccount, Isstudent,
OwnsCar. Give the initial network created by KBANN for the following domain
theory, including all network connections and weights.
GoodCreditRisk t Employed, LowDebt
Employed t -1sStudent
LowDebt t -HasStudentLoan, HasSavingsAccount
12.2. KBANN converts a set of propositional Horn clauses into an initial neural network.
Consider the class of n-of-m clauses, which are Horn clauses containing m literals
in the preconditions (antecedents), and an associated parameter n where n m.
The preconditions of an n-of-m Horn clause are considered to be satisfied if at least
n of its m preconditions are satisfied. For example, the clause
Student t LiveslnDorm, Young, Studies; n = 2
asserts that one is a Student if at least two of these three preconditions are satisfied.
Give an algorithm similar to that used by KBANN, that accepts a set of
propositional n-of-m clauses and constructs a neural network consistent with the
domain theory.
12.3. Consider extending KBANN to accept a domain theory consisting of first-order
rather than propositional Horn clauses (i.e., Horn clauses containing variables, as in
Chapter 10). Either give an algorithm for constructing a neural network equivalent
to a set of Horn clauses, or discuss the difficulties that prevent this.
12.4. This exercise asks you to derive a gradient descent rule analogous to that used by
TANGENTPROP. Consider the instance space X consisting of the real numbers, and
consider the hypothesis space H consisting of quadratic functions of x. That is,