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					 Artificial Intelligence
                -
        an agent approach

   COMP4700 & COMP6424

            Learning


         Eric McCreath
The Australian National University
        Semester 2 2003
                      Outline               2


Introduction (18.1)
A computation approach to induction(18.2)
General learning approaches(19.1)
Decision Trees (18.3)
Inductive Logic Programming (19.5)
                  Introduction                           3



Learning involves moving from a finite set of
observations about an 'object' or 'concept' to a
conclusion that describes the object or concept.
Machine learning is an area in AI that designs and
studies computer programs that undertake learning.
This is done at both empirical and theoretical levels.
                     Example                         4



Could you write a computer program that would
learn the next number in the sequence given below?


   2,4,6,8,10,...


or could you write a computer program that would
learn the set that the following number are from?


   5,7,3,2,19,11,17,...
                    Inference        5



There is three types of inference:
 deduction,
 abduction,
 and induction.
                       Deduction                         6



With deduction premises provide definite reasons
for the conclusion made. This makes any knowledge
gained in the conclusion both certain and justifiable.


       Man(fred).
       Man(X) =>Mortal(X)

       Mortal(fred).
                    Abduction                             7



Abduction is an inference approach where you know
the 'process' and the 'conclusions' and attempt to find
the 'cause'.


       Mortal(fred).
       Man(X) =>Mortal(X)

       Man(fred).
                       Induction                          8



Induction refers to any kind of inference in which
we move from a finite set of observations about an
'object' or 'concept' to a conclusion that is a general
description of the object of the concept.

       Man(fred).
       Mortal(fred).

       Man(X) =>Mortal(X).
                     Induction                          9



Hume noted that an inductive conclusion is not
justifiable, as the conclusion goes beyond the set of
observations. Several attempts have been made to
overcome this problem:
 Inductive argument for induction(Black).
 Science does not rest on induction, rather, it is a
process of disproving conjectures - a completely
deductive process. (Popper)
 Another approach is to view inductive conclusions
as 'probable' rather than 'certain'.
                    Induction                          10



The idea of induction was embraced by the rapidly
expanding field of AI, resulting in the development
of numerous practical learning systems.
Also, researchers in theoretical computer science
became interested in the mathematical foundations
of induction resulting in the field of Computational
Learning Theory.
Computational Approach to Induction                       11



Consider the universe of objects, U. Elements of U
are referred to as instances.
A concept is any subset of U. Let C be a concept.
The an element of C is a positive example of C and
an element of U - C is a negative example.
A concept may be infinite in size. An intensional
description of a concept is a finite 'description' that
characterizes the concept. (eg decision procedure,
decision tree, neural network, grammar, logic
program, computer program, ..)
Computational Approach to Induction                        12



Now let us assume that 'nature' chooses an
underlying reality in the form of a concept, also
referred to as the target concept.
A learner is a computational agent that attempts to
find an intensional description of the target concept.
To assist the learner in its task, nature provides the
learner with data about the target concept. This data
is usually a finite set of labeled instances from U;
the label 1 it the instance is positive (0 if negative).
These are examples of the target concept.
Computational Approach to Induction                      13



The hypothesis space is essentially a sequence of
intensional descriptions:
  h1, h2, h3, ....
The task of the learner is to find a hypothesis hi for
the target concept based on the data presented to it
about the concept.
The conditions under which a learner is said to learn
a target concept is referred to as the criterion of
success.
Computational Approach to Induction   14
Computational Approach to Induction                 15



The golf example.
 outlook : sunny, overcast, rain.
 temperature : integer.
 humidity : integer.
 windy : boolean.
U = outlook x temperature x humidity x windy
The concept would be a subset of U containing all
the example of when someone will play golf.
Examples provided to the learner:
<rain,65,70,true>, 0
<overcast,64,65,true>, 1
<sunny,72,95,false>, 0
<sunny,69,70,false>, 1
  Computational Approach to Induction                            16

The learner must induce a hypothesis from the hypothesis
space.
        h1 = 'It is sunny.'
        h2 = 'It is raining.'
        h3 = 'Humidity less than 90.'
        h4 = 'Humidity less than 90 and it is not raining.'
        h5 = 'The temperature is over 60 and it is not windy.'
In this case our learner may choose h4 as it explains all the
examples.
Generally there will be a number of okay hypotheses so the
learner will need to select between them. Ockham's razor is
often employed. This states that the simplest theory is
often the correct one.
                Types of learning                               17



Different types of learning include:
 Supervised - The learner is provided with an entire labeled
data set. Then the learner must induce a hypothesis which
represents the target concept.
 Unsupervised - Example are provided without class labels.
The learner induces clusters of the data, this partitions the
data.
 Reinforcement - The learner learns actions for a particular
situation. Good outcomes are positively reinforced.
Incremental - The learner updates an old hypothesis as new
data is presented.
              Hypothesis Space                         18



An appropriate selection for the hypothesis space is
critical for the success of a machine learning
approach.
Clearly the target concept must be representable
within the hypothesis space.
The larger the hypothesis space the slower the
search.
Hypothesis spaces must be structured and searched
efficiently for a learning approach to be practical.
              Hypothesis Space                         19



To tame the huge(generally infinite) hypothesis
space a bias may be placed over this space. There is
basically three types of bias':
 language bias,
 search bias, and
 validation bias.
           Problems for Learning        20



A variety of problems arise:
 noise,
 over-fitting,
 insufficient data,
 large amounts of data,
 selecting a hypothesis language, and
 searching the hypothesis space.
         Consistent and Complete                           21



A hypothesis h is said to be consistent with respect to
a set of examples E if its extension does not contain
any negative examples in E.
A hypothesis h is said to be complete with respect to
a set of examples E if its extension contains all the
positive examples of E.
A hypothesis h is said to be correct with respect to E
if it is both consistent and complete with respect to E.
                Generalization                        22



Suppose a hypothesis h is modified from h to h'. If
the extension of h is increased, that is:
                  ext h        ext h '




                            
then this modification is known as a generalization
step.
                Specialization                        23



Suppose a hypothesis h is modified from h to h'. If
the extension of h is decreased, that is:
                  ext h '       ext h




                             
then this modification is known as a specialization
step.
          Current-Best Learning                      24



One approach to learning is to maintain a single
hypothesis h which is both consistent and complete
with respect to the examples seen so far. As new
examples arrive then the hypothesis is either
generalized of specialized such that h remains
correct with respect to all the examples. This
approach is known as current-best learning.
             Current-Best Learning                       25




In some cases there may be no generalization of
specialization. This will cause the algorithm to fail.
           Current-Best Learning                     26


Problems with current-best learning include:
 It will not always lead to the simplest solution.
 In some cases it may lead to no solution.
 It is expensive to consider all the examples for
every modification.
 It is difficult to find a good heuristic for
determining the specialization and generalization
steps.
        Least-Commitment Search                         27



Another approach to learning is to maintain a list of
all possible hypotheses V. Each example e in the
training set E is examined in tern. All hypotheses in
V that are not correct with respect to e are removed
from V. Once this process has finished all the
hypotheses in V will be correct with respect to E.
The set of possible hypotheses V is the version
space. This learning approach is known as a least-
commitment search or version space learning.
      Least-Commitment Learning                   28




The advantage of this approach is that examples
only need to be considered once.
      Least-Commitment Learning                         29



One obvious difficulty with this approach is
generally the hypothesis space is enormous if not
infinite!
One solution to this problem is to have a
generalization/specialization partial ordering on the
hypothesis space. The version space may be
maintained by keeping track of a boundary set. This
requires:
 a most general boundary (the G-set), and
 a most specific boundary (the S-set).
      Least-Commitment Learning                  30



The main disadvantages of the approach are:
 If the examples contain noise or insufficient
attributes then the version space will always
collapse.
 The size of the G-set and the S-set may grow
uncontrollably.

				
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