Learning As Search

1. Learning As Search

2. Overview • Inductive learning as search • Current best hypothesis search • Least commitment search

3. Learning as search • An interesting view of learning • Helps understand the learning process, including generalization and specialization • Concepts, such as hypothesis space better come into focus • Will see two more learning algorithms • An instructional tool and elegant, and with some applications too

4. The Setting • Target function is a Logical sentence • In our examples: propositional logic • Task: find a hypothesis or hypotheses for a goal predicate consistent with all examples seen so far • Example: goal predicate would be WillWait(instance), for the restaurant example

5. Hypotheses • Each hypothesis proposes an expression for the goal predicate • Hypotheses: Set of all hypotheses an algorithm entertains. E.g. decision trees • Having seen no examples, any hypothesis could be correct: H1 V H2 V… V Hn

6. Examples • The goal predicate g() may or may not hold for each example • False positive example i for a hypothesis h(): • If g(i) is false, but h(i) is true • False negative example i for a hypothesis h(): • If g(i) is true, but h(i) is false

7. Current-Best-Hypothesis Search • Local search (iterative improvement) • Start with a hypothesis and keep it consistent with examples seen: • If a false positive is seen, then specialize • If a false negative is seen, then generalize • (try to keep the hypothesis consistent with the previous examples)

8. Specialization and Generalization • Specialization (Restriction): Add a conjunction or drop a disjunction • Generalization (Relaxation): Add a disjunction or drop a conjunction • There could be other changes depending on the representation language

9. Discussion • The choice of initial hypothesis and specialization and generalization is nondeterministic (use heuristics) • Problems: • What heuristics to use • Could be inefficient (need to check consistency with all examples), and perhaps backtrack or restart • Handling noise

10. Least-Commitment Search • Or the version space (v.s.) algorithm • Keep all the version space=set of all consistent hypes • As each example is seen, drop inconsistent ones (shrink the v.s.) • Return all the consistent ones • But there is an enormous number of hypes..

11. Represent the Frontier • Solution: don’t maintain explicitly; Keep only the boundary of the version space • There is a partial ordering on the hype space under the relationship of specializes/generalizes • Maintain the most general hypes and the most specific hypes of the version space

12. Version Space Maintenance • S: set of most specific hypes in v.s. (initially False) • G: set of most general hypes in v.s. (initially True) • For each new example and h in S or G: • if false negative for h in S, generalize h • if false positive for h in S, throw h out of S! • Symmetrically for h in G • Generalization or specialization can create multiple hypes (children)

13. Stopping Condition • If no hype left, but examples exist then? • If examples are gone, and one hype left, great! • If multiple hypotheses remain?

14. Discussion • Advantages to Best-Current-Search? • Disadvantages (in general)? • Best-Current-Hypothesis and Version-Space algorithms are examples of incremental or on-line learning algorithms