Instance Based Learning

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Instance Based Learning

• Ata Kaban
• The University of Birmingham

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• Today we learn
• K-Nearest Neighbours
• Case-based reasoning
• Lazy and eager learning

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Instance-based learning

• One way of solving tasks of approximating
  discrete or real valued target functions
• Have training examples (xn, f(xn)), n1..N.
• Key idea
• just store the training examples
• when a test example is given then find the
  closest matches

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• 1-Nearest neighbour
• Given a query instance xq,
• first locate the nearest training example xn
• then f(xq) f(xn)
• K-Nearest neighbour
• Given a query instance xq,
• first locate the k nearest training examples
• if discrete values target function then take
  vote among its k nearest nbrs else if real
  valued target fct then take the mean of the f
  values of the k nearest nbrs

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The distance between examples

• We need a measure of distance in order to know
  who are the neighbours
• Assume that we have T attributes for the learning
  problem. Then one example point x has elements xt
  ? ?, t1,T.
• The distance between two points xi xj is often
  defined as the Euclidean distance

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Voronoi Diagram
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Characteristics of Inst-b-Learning

• An instance-based learner is a lazy-learner and
  does all the work when the test example is
  presented. This is opposed to so-called
  eager-learners, which build a parameterised
  compact model of the target.
• It produces local approximation to the target
  function (different with each test instance)

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When to consider Nearest Neighbour algorithms?

• Instances map to points in
• Not more then say 20 attributes per instance
• Lots of training data
• Advantages
• Training is very fast
• Can learn complex target functions
• Dont lose information
• Disadvantages
• ? (will see them shortly)

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Training data
Test instance
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Keep data in normalised form
One way to normalise the data ar(x) to ar(x) is
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Normalised training data
Test instance
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Distances of test instance from training data
Classification 1-NN Yes 3-NN Yes 5-NN No 7-NN
No
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What if the target function is real valued?

• The k-nearest neighbour algorithm would just
  calculate the mean of the k nearest neighbours

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Variant of kNN Distance-Weighted kNN

• We might want to weight nearer neighbors more
  heavily
• Then it makes sense to use all training examples
  instead of just k (Stepards method)

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Difficulties with k-nearest neighbour algorithms

• Have to calculate the distance of the test case
  from all training cases
• There may be irrelevant attributes amongst the
  attributes curse of dimensionality

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Case-based reasoning (CBR)

• CBR is an advanced instance based learning
  applied to more complex instance objects
• Objects may include complex structural
  descriptions of cases adaptation rules

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• CBR cannot use Euclidean distance measures
• Must define distance measures for those complex
  objects instead (e.g. semantic nets)
• CBR tries to model human problem-solving
• uses past experience (cases) to solve new
  problems
• retains solutions to new problems
• CBR is an ongoing area of machine learning
  research with many applications

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Applications of CBR

• Design
• landscape, building, mechanical, conceptual
  design of aircraft sub-systems
• Planning
• repair schedules
• Diagnosis
• medical
• Adversarial reasoning
• legal

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CBR process
New Case
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CBR example Property pricing
Test instance
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How rules are generated

• There is no unique way of doing it. Here is one
  possibility
• Examine cases and look for ones that are almost
  identical
• case 1 and case 2
• R1 If recep-rooms changes from 2 to 1 then
  reduce price by 5,000
• case 3 and case 4
• R2 If Type changes from semi to terraced then
  reduce price by 7,000

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Matching

• Comparing test instance
• matches(5,1) 3
• matches(5,2) 3
• matches(5,3) 2
• matches(5,4) 1

• Estimate price of case 5 is 25,000

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Adapting

• Reverse rule 2
• if type changes from terraced to semi then
  increase price by 7,000
• Apply reversed rule 2
• new estimate of price of property 5 is 32,000

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Learning

• So far we have a new case and an estimated price
• nothing is added yet to the case base
• If later we find house sold for 35,000 then the
  case would be added
• could add a new rule
• if location changes from 8 to 7 increase price by
  3,000

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Problems with CBR

• How should cases be represented?
• How should cases be indexed for fast retrieval?
• How can good adaptation heuristics be developed?
• When should old cases be removed?

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Advantages

• A local approximation is found for each test case
• Knowledge is in a form understandable to human
  beings
• Fast to train

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Summary

• K-Nearest Neighbours
• Case-based reasoning
• Lazy and eager learning

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Lazy and Eager Learning

• Lazy wait for query before generalizing
• k-Nearest Neighbour, Case based reasoning
• Eager generalize before seeing query
• Radial Basis Function Networks, ID3,
• Does it matter?
• Eager learner must create global approximation
• Lazy learner can create many local approximations