Russell and Norvig, Chapter 21: Knowledge in Learning

21.1 Knowledge in Learning
- find Hypothesis satisfying entailment constraint
  - Hypothesis & Descriptions |= Classifications
- cumulative learning process [Fig21.1, p626]
- explanation-based learning
  - Hypothesis & Descriptions |= Classifications
  - Background |= Hypothesis
- relevance-based learning
  - Hypothesis & Descriptions |= Classifications
  - Background & Descriptions & Classifications |= Hypothesis
- inductive logic programming
  - Background & Hypothesis & Descriptions |= Classifications

21.2 Explanation-Based Learning (EBL)
- Look what Zog (Thag) do! [Far Side cartoon]
- generalize a proof of a query
  - identify necessary conditions
- process [Fig21.2, p631]
  - given example, use BK to construct proof of goal predicate
    - e.g., simplify(1*(0+X),X)
  - construct generalized proof tree in parallel
    - same inferences using variablized goal
  - construct new rule
    - head is variablized goal, given bindings
    - body is leaves of proof tree, given bindings
  - drop conditions always true
    - e.g., ArithmeticUnknown(z) => Simplify(1*(0+z),z)
- implementation in Prolog [Bratko, Fig20.3-4, p541-544]
- improving efficiency
  - learn more general rules
    - which ones?
      - operationality
        - don't include simple proofs in rule body
      - utility problem
        - retain only rules having positive utility
- learning control rules

21.3 Learning Using Relevance Information
- relevance-based learning (RBL)
- determinations
  - constrains predicates used to construct hypotheses
  - e.g., forall(X) nationality(X,usa) => language(X,english)
  - i.e., nationality determines language
- finding determinations [Fig21.3, p635]
  - find smallest subset of attributes with same values and class value
  - can be used to filter attributes for IDT (RBDTL) [bottom, p635]
    - learning curves [Fig21.4, p636]

21.4 Inductive Logic Programming (ILP)
- attribute-based learning algorithms cannot learn relations
- background knowledge allows simpler hypotheses
  - e.g., having 'parent' instead of just 'father' and 'mother'
          to describe 'grandparent' relation
- inverse resolution
  - given correct Hypothesis, resolution can derive Classifications
    - resolve(C1,C2) -> C
  - invert resolution to derive Hypothesis [Fig21.6, p639]
    - invert_resolve(C) -> C1, C2
    - invert_resolve(C,C1) -> C2
    - typically infinite number of resolvents
      - restrict to Horn clauses, eliminate functions, etc.
  - generate new predicates 
    - C1 and C2 contain a new predicate that is resolved away
    - e.g., [Fig21.7, p641]
- top-down learning methods
  - similar to decision-tree learning
  - given examples and BK, start with most general clause
    - e.g., gpa(X,Y).
  - try adding one literal
    - e.g., gpa(X,Y) :- father(X,Y).
            gpa(X,Y) :- parent(X,Z).  % assuming parent in BK
            gpa(X,Y) :- father(X,Z).
  - keep clause describing most positive and fewest negative examples
    - e.g., gpa(X,Y) :- father(X,Z).
  - continue adding literals until clause consistent
    - e.g., gpa(X,Y) :- father(X,Z), parent(Z,Y).
  - remove positive examples covered
  - repeat to find more clauses until all positives covered
  - FOIL [Fig21.8, p643]
    - New-Literals
      - any literal from BK (negated or unnegated) including target
        - arguments must contain a variable used earlier in clause
      - X \== Y or X =< Y, where X and Y appear earlier in clause
        - X and Y can also be constants
      - constrained by type information
    - Choose-Literal
      - heuristic measure based on information gain
      - clauses pruned based on Ockham bias
        - when clause description length exceeds that of covered examples
    - solved many list exercises from Bratko's book