CSCE 580 Artificial Intelligence Ch.18: Learning from Observations

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CSCE 580Artificial IntelligenceCh.18 Learning
from Observations

• Fall 2008
• Marco Valtorta
• mgv_at_cse.sc.edu

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Acknowledgment

• The slides are based on the textbook AIMA and
  other sources, including other fine textbooks and
  the accompanying slide sets
• The other textbooks I considered are
• David Poole, Alan Mackworth, and Randy Goebel.
  Computational Intelligence A Logical Approach.
  Oxford, 1998
• A second edition (by Poole and Mackworth) is
  under development. Dr. Poole allowed us to use a
  draft of it in this course
• Ivan Bratko. Prolog Programming for Artificial
  Intelligence, Third Edition. Addison-Wesley,
  2001
• The fourth edition is under development
• George F. Luger. Artificial Intelligence
  Structures and Strategies for Complex Problem
  Solving, Sixth Edition. Addison-Welsey, 2009

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Outline

• Learning agents
• Inductive learning
• Decision tree learning

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Learning

• Learning is essential for unknown environments,
• i.e., when designer lacks omniscience
• Learning is useful as a system construction
  method,
• i.e., expose the agent to reality rather than
  trying to write it down
• Learning modifies the agent's decision mechanisms
  to improve performance

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Learning agents
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Learning element

• Design of a learning element is affected by
• Which components of the performance element are
  to be learned
• What feedback is available to learn these
  components
• What representation is used for the components
• Type of feedback
• Supervised learning correct answers for each
  example
• Unsupervised learning correct answers not given
• Reinforcement learning occasional rewards

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Inductive learning

• Simplest form learn a function from examples
• f is the target function
• An example is a pair (x, f(x))
• Problem find a hypothesis h
• such that h f
• given a training set of examples
• This is a highly simplified model of real
  learning
• Ignores prior knowledge
• Assumes examples are given

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Inductive learning method

• Construct/adjust h to agree with f on training
  set
• (h is consistent if it agrees with f on all
  examples)
• E.g., curve fitting

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Inductive learning method

• Construct/adjust h to agree with f on training
  set
• (h is consistent if it agrees with f on all
  examples)
• E.g., curve fitting

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Inductive learning method

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting

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Inductive learning method

• Construct/adjust h to agree with f on training
  set
• (h is consistent if it agrees with f on all
  examples)
• E.g., curve fitting

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Inductive learning method

• Construct/adjust h to agree with f on training
  set
• (h is consistent if it agrees with f on all
  examples)
• E.g., curve fitting

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Inductive learning method

• Construct/adjust h to agree with f on training
  set
• (h is consistent if it agrees with f on all
  examples)
• E.g., curve fitting
• Ockhams razor prefer the simplest hypothesis
  consistent with data

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Curve Fitting and Occams Razor

• Data collected by Galileo in1608 ball rolling
  down an inclined plane, then continuing in
  free-fall
• Occam's razor ( suggests the simpler model is
  better it has a higher prior probability
• The simpler model may have a greater posterior
  probability (the plausibility of the model)
  Occams razor is not only a good heuristic, but
  it can be shown to follow from more fundmental
  principles
• Jefferys, W.H. and Berger, J.O. 1992. Ockham's
  razor and Bayesian analysis. American Scientist
  8064-72

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Learning decision trees

• Problem decide whether to wait for a table at a
  restaurant, based on the following attributes
• Alternate is there an alternative restaurant
  nearby?
• Bar is there a comfortable bar area to wait in?
• Fri/Sat is today Friday or Saturday?
• Hungry are we hungry?
• Patrons number of people in the restaurant
  (None, Some, Full)
• Price price range (, , )
• Raining is it raining outside?
• Reservation have we made a reservation?
• Type kind of restaurant (French, Italian, Thai,
  Burger)
• WaitEstimate estimated waiting time (0-10,
  10-30, 30-60, gt60)

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Attribute-based representations

• Examples described by attribute values (Boolean,
  discrete, continuous)
• E.g., situations where I will/won't wait for a
  table
• Classification of examples is positive (T) or
  negative (F)
  

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Decision trees

• One possible representation for hypotheses
• E.g., here is the true tree for deciding
  whether to wait

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Expressiveness

• Decision trees can express any function of the
  input attributes
• E.g., for Boolean functions, truth table row ?
  path to leaf
• Trivially, there is a consistent decision tree
  for any training set with one path to leaf for
  each example (unless f nondeterministic in x) but
  it probably won't generalize to new examples
• Prefer to find more compact decision trees

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Hypothesis spaces

• How many distinct decision trees with n Boolean
  attributes?
• number of Boolean functions
• number of distinct truth tables with 2n rows
  22n (for each of the 2n rows of the decision
  table, the function may return 0 or 1)
• E.g., with 6 Boolean attributes, there are
  18,446,744,073,709,551,616 (more than 18
  quintillion) trees

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Hypothesis spaces

• How many distinct decision trees with n Boolean
  attributes?
• number of Boolean functions
• number of distinct truth tables with 2n rows
  22n
• E.g., with 6 Boolean attributes, there are
  18,446,744,073,709,551,616 trees
• How many purely conjunctive hypotheses (e.g.,
  Hungry ? ?Rain)?
• Each attribute can be in (positive), in
  (negative), or out
• ? 3n distinct conjunctive hypotheses
• More expressive hypothesis space
• increases chance that target function can be
  expressed
• increases number of hypotheses consistent with
  training set
• ? may get worse predictions

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Decision tree learning

• Aim find a small tree consistent with the
  training examples
• Idea (recursively) choose "most significant"
  attribute as root of (sub)tree

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Choosing an attribute

• Idea a good attribute splits the examples into
  subsets that are (ideally) "all positive" or "all
  negative"
• Patrons? is a better choice

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Using information theory

• To implement Choose-Attribute in the DTL
  algorithm
• Information Content (Entropy)
• I(P(v1), , P(vn)) Si1 -P(vi) log2 P(vi)
• For a training set containing p positive examples
  and n negative examples

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Information gain

• A chosen attribute A divides the training set E
  into subsets E1, , Ev according to their values
  for A, where A has v distinct values
• Information Gain (IG) or reduction in entropy
  from the attribute test
• Choose the attribute with the largest IG

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Information gain

• For the training set, p n 6, I(6/12, 6/12)
  1 bit
• Consider the attributes Patrons and Type (and
  others too)
• Patrons has the highest IG of all attributes and
  so is chosen by the DTL algorithm as the root

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Example contd.

• Decision tree learned from the 12 examples
• Substantially simpler than true tree---a more
  complex hypothesis isnt justified by small
  amount of data

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Performance measurement

• How do we know that h f ?
• Use theorems of computational/statistical
  learning theory
• Try h on a new test set of examples
• (use same distribution over example space as
  training set)
• Learning curve correct on test set as a
  function of training set size

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Summary (so far)

• Learning needed for unknown environments, lazy
  designers
• Learning agent performance element learning
  element
• For supervised learning, the aim is to find a
  simple hypothesis approximately consistent with
  training examples
• Decision tree learning using information gain
• Learning performance prediction accuracy
  measured on test set

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Outline for Ensemble Learning and Boosting

• Ensemble Learning
• Bagging
• Boosting
• Reading AIMA-2 Sec. 18.4
• This set of slides is based on http//www.cs.uwate
  rloo.ca/ppoupart/teaching/cs486-spring05/slides/L
  ecture21notes.pdf
• In turn, those slides follow AIMA-2

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Ensemble Learning

• Sometimes each learning techniqueyields a
  different hypothesis
• But no perfect hypothesis
• Could we combine several imperfect hypotheses
  into a better hypothesis?

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Ensemble Learning

• Analogies
• Elections combine voters choices to pick a good
  candidate
• Committees combine experts opinions to make
  better decisions
• Intuitions
• Individuals often make mistakes, but the
  majority is less likely to make mistakes.
• Individuals often have partial knowledge, but a
  committee can pool expertise to make better
  decisions

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Ensemble Learning

• Definition method to select and combine an
  ensemble of hypotheses into a (hopefully) better
  hypothesis
• Can enlarge hypothesis space
• Perceptron (a simple kind of neural network)
• linear separator
• Ensemble of perceptrons
• polytope

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Bagging
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Bagging

• Assumptions
• Each hi makes error with probability p
• The hypotheses are independent
• Majority voting of n hypotheses
• k hypotheses make an error
• Majority makes an error
• With n5, p0.1 error( majority ) lt 0.01

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Weighted Majority

• In practice
• Hypotheses rarely independent
• Some hypotheses make fewer errors than others
• Lets take a weighted majority
• Intuition
• Decrease weight of correlated hypotheses
• Increase weight of good hypotheses

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Boosting

• Most popular ensemble technique
• Computes a weighted majority
• Can boost a weak learner
• Operates on a weighted training set

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Weighted Training Set

• Learning with a weighted training set
• Supervised learning -gt minimize training error
• Bias algorithm to learn correctly instances with
  high weights
• Idea when an instance is misclassified by a
  hypotheses, increase its weight so that the next
  hypothesis is more likely to classify it correctly

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Boosting Framework
Read the figure left to right the algorithm
builds a hypothesis on a weighted set of four
examples, one hypothesis per column
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AdaBoost (Adaptive Boosting)
There are N examples. There are M columns
(hypotheses), each of which has weight zm
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What can we boost?

• Weak learner produces hypotheses at least as
  good as random classifier.
• Examples
• Rules of thumb
• Decision stumps (decision trees of one node)
• Perceptrons
• Naïve Bayes models

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Boosting Paradigm

• Advantages
• No need to learn a perfect hypothesis
• Can boost any weak learning algorithm
• Boosting is very simple to program
• Good generalization
• Paradigm shift
• Dont try to learn a perfect hypothesis
• Just learn simple rules of thumbs and boost them

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Boosting Paradigm

• When we already have a bunch of hypotheses,
  boosting provides a principled approach to
  combine them
• Useful for
• Sensor fusion
• Combining experts

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Boosting Applications

• Any supervised learning task
• Spam filtering
• Speech recognition/natural language processing
• Data mining
• Etc.

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Computational Learning Theory
The slides on COLT are from ftp//ftp.cs.bham.ac.u
k/pub/authors/M.Kerber/Teaching/SEM2A4/l4.ps.gz an
d http//www.cs.bham.ac.uk/mmk/teaching/SEM2A4/,
which also has slides on version spaces
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How many examples are needed?
This is the probability that Hebad contains a
consistent hypothesis
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How many examples?
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Complexity and hypothesis language
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Learning Decision Lists

• A decision list consists of a series of tests,
  each of which is a conjunction of literals. If
  the tests succeeds, the decision list specifies
  the value to be returned. Otherwise, the
  processing continues with the next test in the
  list
• Decision lists can represent any Boolean function
  hence are not learnable (in polynomial time)
• A k-DL is a decision list where each test is
  restricted to at most k literals
• K- Dl is learnable! Rivest, 1987