knowledge in learning copyright, 1996 © dale carnegie & associates, inc. chapter 19 spring 2004
TRANSCRIPT
Knowledge in Learning
Copyright, 1996 © Dale Carnegie & Associates, Inc.
Chapter 19
Spring 2004
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A logical formulation of learning
What’re Goal and Hypotheses Goal predicate Q - WillWait
Learning is to find an equivalent logical expression we can classify examplesEach hypothesis proposes such an expression - a candidate definition of Q r WillWait(r) Pat(r,Some)
Pat(r,Full) Hungry(r)Type(r,French) …
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Hypothesis space is the set of all hypotheses the learning algorithm is designed to entertain.One of the hypotheses is correct:H1 V H2 V…V Hn
Each Hi predicts a certain set of examples - the extension of the goal predicate.Two hypotheses with different extensions are logically inconsistent with each other, otherwise, they are logically equivalent.
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What are ExamplesAn example is an object of some logical description to which the goal concept may or may not apply. Alt(X1)^!Bar(X1)^!Fri/Sat(X1)^…
Ideally, we want to find a hypothesis that agrees with all the examples.The relation between f and h are: ++, --, +- (false negative), -+ (false positive). If the last two occur, example I and h are logically inconsistent.
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Current-best hypothesis search
Maintain a single hypothesisAdjust it as new examples arrive to maintain consistency (Fig 19.1) Generalization for positive examples Specialization for negative examplesAlgorithm (Fig 19.2, page 681) Need to check for consistency with all
existing examples each time taking a new example
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Example of WillWaitFig 18.3
Problems: nondeterministic, no guarantee for simplest and correct h, need backtrack
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Least-commitment searchKeeping one h as its best guess is the problem -> Can we keep as many as possible?Version space (candidate elimination) Algo incremental least-commitment
From intervals to boundary sets G-set and S-set Everything between is guaranteed to be
consistent wit examples.
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Version spaceGeneralization and specialization (Fig 19.4)
False positive for Si, too general, discard it False negative for Si, too specific, generalize it minimally False positive for Gi, too general, specialize it minimally False negative for Gi, too specific, discard it
When to stop One concept left (Si = Gi) The version space collapses Run out of examples
One major problem: can’t handle noise
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Using prior knowledgeFor DT and logical description learning, we assume no prior knowledgeWe do have some prior knowledge, so how can we use it?We need a logical formulation as opposed to the function learning.
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Inductive learning in the logical setting
The objective is to find a hypothesis that explains the classifications of the examples, given their descriptions.Hypothesis ^ Description |= Classifications Descriptions - the conjunction of all the
example descriptions Classifications - the conjunction of all the
example classifications
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A cumulative learning process
Fig 19.6 (p 687)The new approach is to design agents that already know something and are trying to learning some more.Intuitively, this should be faster and better than without using knowledge, assuming what’s known is always correct.How to implement this cumulative learning with increasing knowledge?
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Some examples of using knowledge
One can leap to general conclusions after only one observation. Your such experience?
Traveling to Brazil: Language and name ?
A pharmacologically ignorant but diagnostically sophisticated medical student … ?
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Some general schemes
Explanation-based learning (EBL) Hypothesis^Description |= Classifications Background |= Hypothesis
doesn’t learn anything factually new from instance
Relevance-based learning (RBL) Hypothesis^Descriptions |= Classifications Background^Descrip’s^Class |= Hypothesis
deductive in nature
Knowledge-based inductive learning (KBIL) Background^Hypothesis^Descrip’s |=
Classifications
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Inductive logical programming (ILP)
ILP can formulate hypotheses in general first-order logic Others like DT are more restricted
languages
Prior knowledge is used to reduce the complexity of learning: prior knowledge further reduces the H space prior knowledge helps find the shorter H Again, assuming prior knowledge is correct
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Explanation-based learning
A method to extract general rules from individual observationsThe goal is to solve a similar problem faster next time.Memoization - speed up by saving results and avoiding solving a problem from scratchEBL does it one step further - from observations to rules
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Why EBL?Explaining why something is a good idea is much easier than coming up with the idea.Once something is understood, it can be generalized and reused in other circumstances.
Extracting general rules from examplesEBL constructs two proof trees simultaneously by variablization of the constants in the first treeAn example (Fig 19.7)
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Basic EBLGiven an example, construct a proof tree using the background knowledge In parallel, construct a generalized proof tree for the variabilized goalConstruct a new rule (leaves => the root)Drop any conditions that are true regardless of the variables in the goal
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Efficiency of EBLChoosing a general rule too many rules -> slow inference aim for gain - significant increase in speed as general as possible
Operationality - A subgoal is operational means it is easy to solve Trade-off between Operationality and
Generality
Empirical analysis of efficiency in EBL study
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Learning using relevant information
Prior knowledge: People in a country usually speak the same language
Observation: Given Fernando is Brazilian & speaks Portuguese
We cab logically conclude via resolution
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Functional dependenciesWe have seen a form of relevance: determination - language (Portuguese) is a function of nationality (Brazil)
Determination is really a relationship between the predicatesThe corresponding generalization follows logically from the determinations and descriptions.
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We can generalize from Fernando to all Brazilians, but not to all nations. So, determinations can limit the H space to be considered.Determinations specify a sufficient basis vocabulary from which to construct hypotheses concerning the target predicate.A reduction in the H space size should make it easier to learn the target predicate.
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Learning using relevant information
A determination P Q says if any examples match on P, they must also match on QFind the simplest determination consistent with the observations Search through the space of determinations
from one predicate, two predicates Algorithm - Fig 19.8 (page 696) Time complexity is n choosing p.
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Combining relevance based learning with decision tree learning -> RBDTLIts learning performance improves (Fig 19.9).Other issues noise handling using other prior knowledge from attribute-based to FOL
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Inductive logic programmingIt combines inductive methods with FOL.ILP represents theories as logic programs.ILP offers complete algorithms for inducing general, first-order theories from examples.It can learn successfully in domains where attribute-based algorithms fail completely.An example - a typical family tree (Fig 19.11)
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Inverse resolutionIf Classifications follow from B^H^D, then we can prove this by resolution with refutation (completeness).If we run the proof backwards, we can find a H such that the proof goes through.Generating inverse proofs A family tree example (Fig 19.13)
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Inverse resolution involves search Each inverse resolution step is
nondeterministic For any C and C1, there can be many C2
Discovering new knowledge with IR It’s not easy - a monkey and a typewriter
Discovering new predicates with IR Fig 19.14
The ability to use background knowledge provides significant advantages
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Top-down learning (FOIL)
A generalization of DT induction to the first-order case by the same author of C4.5 Starting with a general rule and specialize it to fit
data Now we use first-order literals instead of attributes,
and H is a set of clauses instead of a decision tree.Example: =>grandfather(x,y) (page 701) positive and negative examples adding literals one at a time to the left-hand side e.g., Father (x,y) => Grandfather(x,y) How to choose literal? (Algorithm on page 702)
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SummaryUsing prior knowledge in cumulative learningPrior knowledge allows for shorter H’s.Prior knowledge plays different logical roles as in entailment constraintsEBL, RBL, KBILILP generate new predicates so that concise new theories can be expressed.