e + : boss(mary,john). boss(phil,mary).boss(phil,john). e - :
DESCRIPTION
Another example of recursive learning:. E + : boss(mary,john). boss(phil,mary).boss(phil,john). E - : boss(john,mary). boss(mary,phil). boss(john,phil). BK: employee(john, ibm). employee(mary,ibm). employee(phil,ibm). reports_to_imm(john,mary). reports_to_imm(mary,phil). - PowerPoint PPT PresentationTRANSCRIPT
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E+:boss(mary,john). boss(phil,mary).boss(phil,john).
E-:boss(john,mary). boss(mary,phil). boss(john,phil).
BK:employee(john, ibm). employee(mary,ibm). employee(phil,ibm).reports_to_imm(john,mary). reports_to_imm(mary,phil).
h: boss(X,Y):- employee(X,O), employee(Y,O),reports_to(Y, X).
reports_to(X,Y):-reports_to_imm(X,Z), reports_to(Z,Y).reports_to(X,X).
Another example of recursive learning:
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How is learning done: covering algorithm
Initialize the training set T to all k-tuples of constants while the global training set contains + tuples: find a clause that describes part of relationship Q remove the +tuples covered by this clause
Finding a clause:
initialize the clause to Q(V1,…Vk) :- while T contains –tuples find a literal L to add to the right-hand side of the clause
Finding a literal : greedy search
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• ‘Find a clause’ loop describes search – bottom up or top down –
• Need to structure the search space – generality – semantic and syntactic
• since logical generality is not decidable, a stronger property of -subsumption
• then search from general to specific (refinement)
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Refinement
boss(X,Y):-
boss(X,Y):-X=Y
… boss(X,Y):-reports_to(X,Y).
…
boss(X,Y):-empl(X,O).
boss(X,Y):-empl(X,O),empl(Y,O1).
boss(X,Y):-empl(X,O),empl(Y,O).
boss(X,Y):-empl(X,O),empl(Y,O),rep_to(Y,X).
boss(X,Y):-empl(X,O),empl(Y,O),rep_to(X,Y).
Heuristics: link to head
new variables
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How is learning done: covering algorithm
• Inner loop describes search – bottom up and top down - we do the latter
• Need to structure the search space – generality – semantic and syntactic – theta subs.
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Constructive learning
• Do we really learn something new?• Hypotheses are in the same language as
examples• constructive induction• How do we learn multiplication from
examples? We need to invent plus –we have shown [IJCAI93] that true constructivism requires recursion, i.e. in mult(X,s(Y),Z) :- mult(X,Y,T), newp(T,Y,Z)mult(X,0) :- 0.
• Newp – plus - must be recursive.
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Philosophical motivation
• Constructive induction is analogical to “revolution” in the methodology of science
• Kuhn’s Structure of Scientific Revolution: normal science -> crisis -> revolution -> normal science• Normal science = learning a “theory” in a fixed
language• Crisis = failure to cope with anomalies observed,
due to inadequate language• Revolution = introduction of new terms into the
language (cannot be done in AV)
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Example: predicting colour in flowers
• Language: r, y; a is any red flower, b is any yellow flower; col(X,Y) X is of colour Y; ch(X,Y) = result of breeding of X and Y
• Observations (that Czech monk and his peas…)1. col(a,r) % Adam and Eve
2. col(b,y).
3. col(ch(a,a),r). % first generation
4. col(ch(a,b),r).
5. col(ch(b,b),b).
6. col(ch(a,ch(b,b),r).%original and 1st
7. …
8. col(ch(ch(a,b)ch(a,b),y). 1st and 1st
9. ….
10.:-col(ch(a,a),y).
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col(ch(a,X),r).
col(ch(X,Y),a) :- col(X,r), col(Y,r).
col(ch(b,b),y).
col(ch(X,Y), y) :- col(X,y),col(Y,y).
• But in some generations y and r produce r, and in some – y
• We need either infinitely many clauses, or infinitely long clauses
• A revolution is necessary
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A new necessary predicate is invented
• n00 represents purebred flowers with recessive character, n11 – with dominant, and n10 – hybrid with dominant
• In fact, the invented predicates represent the concept of a gene!
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Success story: mutagenicity
• heterogeneous chemical compounds – their structure requires relational representation
• BK: properties of specific atoms and bonds between them (relation!) and generic organic chemistry info (e.g. structure of benzene rings, etc.)
• Regression-unfriendly A learned rule has been published in
Science
conjugated double bond in a five-member ring
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problems
• Expressivity – efficiency• Dimensionality reduction• Therefore, interest in feature
selection