IT/CS 811 Principles of

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IT/CS 811 Principles of Machine Learning and
Inference
Deductive (explanation-based) learning
Prof. Gheorghe Tecuci
Learning Agents Laboratory Computer Science
Department George Mason University
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Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
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Explanation-based learning problem

Given A training example A positive example of a
concept to be learned. Learning goal A
specification of the desirable features of the
concept to be learned from the training
example. Background knowledge Prior knowledge
that allows proving (explaining) that the
training example is indeed a positive example of
the concept. Determine A concept definition
representing a deductive generalization of the
training example that satisfies the learning goal.
Purpose of learning Improve the problem solving
efficiency of the agent.
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Explanation-based learning problem illustration
Given Training Example - The description of a
particular cup OWNER(OBJ1, EDGAR) COLOR(OBJ1,
RED) IS(OBJ1, LIGHT) PART-OF(CONCAVITY1,
OBJ1) ISA(CONCAVITY1, CONCAVITY)
IS(CONCAVITY1, UPWARD-POINTING)
PART-OF(BOTTOM1, OBJ1) ISA(BOTTOM1, BOTTOM)
IS(BOTTOM1, FLAT) PART-OF(BODY1, OBJ1)
ISA(BODY1, BODY) IS(BODY1, SMALL)
PART-OF(HANDLE1, OBJ1) ISA(HANDLE1, HANDLE)
LENGTH(HANDLE1, 5) Learning goal Find a
sufficient concept definition for CUP, expressed
in terms of the features used in the training
example (LIGHT, HANDLE, FLAT, etc.) Background
Knowledge "x, LIFTABLE(x) STABLE(x)
OPEN-VESSEL(x) CUP(x) "x "y, IS(x, LIGHT)
PART-OF(y, x) ISA(y, HANDLE) LIFTABLE(x) "x
"y, PART-OF(y, x) ISA(y, BOTTOM) IS(y, FLAT)
STABLE(x) "x "y, PART-OF(y,x) ISA(y,
CONCAVITY) IS(y, UPWARD-POINTING)
OPEN-VESSEL(x) Determine A deductive
generalization of the training example that
satisfies the learning goal "x"y1"y2"y3,
PART-OF(y1, x) ISA(y1, CONCAVITY) IS(y1,
UPWARD-POINTING) PART-OF(y2, x)
ISA(y2, BOTTOM) IS(y2, FLAT) IS(x, LIGHT)
PART-OF(y3, x) ISA(y3, HANDLE) gt
CUP(x)
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Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
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Explanation-based learning method

Explain Construct an explanation that proves that
the training example is an example of the concept
to be learned. Generalize Generalize the found
explanation as much as possible so that the proof
still holds, and extract from it a concept
definition that satisfies the learning goal.
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Explain - Prove that the training example is a
cup
The leaves of the proof tree are those features
of the training example that allows one to
recognize it as a cup. By building the proof one
isolates the relevant features of the training
example.
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The semantic network representation of the cup
example. The enclosed features are the relevant
ones.
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Generalize the proof tree as much as possible so
that the proof still holds - replace each rule
instance with its general pattern - find the
most general unification of these patterns.
OPEN-VESSEL (x1) ôôô
OPEN-VESSEL (x2)
STABLE (x1) ôôô STABLE (x3)
LIFTABLE (x1) ôôô LIFTABLE (x4)
Therefore x1x2x3x4x
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The leaves of this generalized proof tree
represent an operational definition of the
concept CUP "x1"y1"y2"y3, PART-OF(y1, x1)
ISA(y1, CONCAVITY) IS(y1,
UPWARD-POINTING) PART-OF(y2, x1)
ISA(y2, BOTTOM) IS(y2, FLAT) IS(x1, LIGHT)
PART-OF(y3, x1) ISA(y3,
HANDLE) gt CUP(x1)
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Discussion
How does this learning method improve the
efficiency of the problem solving process?
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The goal of this learning strategy is to improve
the efficiency in problem solving. The agent is
able to perform some task but in an inefficient
manner. We would like to teach the agent to
perform the task faster. Consider, for
instance, an agent that is able to recognize
cups. The agent receives a description of a cup
that includes many features. The agent will
recognize that this object is a cup by performing
a complex reasoning process, based on its prior
knowledge. This process is illustrated by the
proof tree which demonstrates that object o1 is
indeed a cup The object o1 is light and has a
handle. Therefore it is liftable. An so on
being liftable, stable and an open vessel, it is
a cup. However, the agent can learn from this
process to recognize a cup faster. The next
step in the learning process is to generalize the
proof tree. While the initial tree proves that
the specific object o1 is a cup, the generalized
tree proves that any object x which is light, has
a handle and some other features is a cup.
Therefore, to recognize that an object o2 is a
cup, the agent only needs to look for the
presence of these features discovered as
important. It no longer needs to build a complex
proof tree. Therefore cup recognition is done
much faster. Finally, notice that the agent
needs only one example to learn from. However, it
needs a lot of prior knowledge to prove that this
example is a cup. Providing such prior knowledge
to the agent is a very complex task.
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Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
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The utility problem discussion
Let us assume that we have learned an operational
definition of the concept cup. What happens
with the efficiency of recognizing cups covered
by the learned rule? Why? What happens with the
efficiency of recognizing cups when the input is
not covered by the learned rule? Why? When does
the efficiency increase? How to assure the
increase of the efficiency?
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The utility problem a solution
Cost/benefit formula to estimates the utility of
the learned rule on the efficiency of the
system Utility (AvrSavings ApplicFreq) -
AvrMatchCost where AvrSavings the average
time savings when the rule is applicable ApplicFr
eq the probability that the rule is applicable
when it is tested AvrMatchCost the average
time cost of matching the rule
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The utility problem discussion of the solution
Maintain a statistic on the rule's use during
subsequent problem solving.
Measure rules matching cost during subsequent
problem solving.
Measure the savings requires running the problem
solver with and without the rule on each problem.
Is this practical? Which would be a good
heuristic?
Heuristic One possible solution is to use an
estimate of the rule's average savings based on
the savings that the rule would have produced on
the training example from which it was learned.
Conclusion The system maintains a statistic on
the rule's use during subsequent problem solving,
in order to determine its utility. If the rule
has a negative utility, it is discarded.
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• The utility of the learned rules
• Explanation-based learning has been introduced as
  a method for improving the efficiency of a
  system.
• Let us consider again the explanation-based
  system learning an operational definition of the
  concept CUP. The system has learned a new rule
  for recognizing a certain kind of cup. This rule
  does not contain any new knowledge. It is just a
  compilation of some other rules from the
  knowledge base.
• Adding this new rule in the KB has the following
  effects on system's efficiency
• - increases the efficiency in recognizing cups
  covered by the learned rule
• decreases the efficiency in recognizing cups
  that are not covered by the learned rule.
• Adding the operational definition of cup into the
  KB will increase the global performance of the
  system only if the first effect is more important
  then the second one.
• Both these effects may be combined into a
  cost/benefit formula that indicates the utility
  of the rule with respect to the efficiency of the
  system
• Utility (AvrSavings ApplicFreq) -
  AvrMatchCost
• where
• AvrSavings the average time savings when the
  rule is applicable
• ApplicFreq the probability that the rule is
  applicable when it is tested
• AvrMatchCost the average time cost of matching
  the rule

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Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
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Exercise
Given A training Example The following example
of supports book(book1) material(book1,
rigid) cup(cup1) material(cup1, rigid)
above(cup1, book1) touches(cup1, book1) gt
supports(book1, cup1) Learning goal Find a
sufficient concept definition for supports,
expressed in terms of the features used in the
training example. Background Knowledge "x "y
on-top-of(y, x) material(x, rigid)
supports(x, y) "x "y above(x, y) touches(x,
y) on-top-of(x, y) "x "y "z above(x, y)
above(y, z) above(x, z) Determine A deductive
generalization of the training example that
satisfies the learning goal.
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Discussion
Do we need a training example to learn an
operational definition of the concept? Why?
Answer The learner does not need a training
example. It can simply built proof trees from
top-down, starting with an abstract definition of
the concept and growing the tree until the leaves
are operational features. However, without a
training example the learner will learn many
operational definitions. The training example
focuses the learner on the most typical example.
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Discussion
What is the classification accuracy of deductive
learning?
What is the classification accuracy of an example
classified as positive? Why?
What is the classification accuracy of an example
classified as negative? Why?
How could one improve the classification accuracy?
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Learning from several positive examples
Learn an operational definition from the first
example. Consider this as the first term of a
disjunctive definition. Eliminate all the
examples already covered by this
definition. Learn another operational definition
from an uncovered example. Eliminate all the
examples covered by this new definition and add
it as a new term in the disjunctive definition of
the concept. Continue this process until there
is no training example left.
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Discussion
How to use negative examples?
Develop a theory of why something is a negative
example of some concept and apply the standard
method. Does such an approach make sense when we
already have a theory that explains positive
examples? Why?
Sometimes it is easier to explain that something
is a negative example. Could you provide an
example of such a case?
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Discussion
How could we apply explanation-based learning to
learn inference rules from facts?
How could we apply explanation-based learning to
learn macro-operators from action plans?
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Learning inference rules illustration
Given Training Example An input
fact RICE-AREA(VIETNAM) Learning goal Learn a
general inference rule allowing the direct
derivation of the input fact from facts
explicitly represented in the background
knowledge (e.g., RAINFALL, CLIMATE, SOIL)
Background Knowledge RAINFALL(VIETNAM, HEAVY)
CLIMATE(VIETNAM, SUBTROPICAL) SOIL(VIETNAM,
RED-SOIL) LOCATION(VIETNAM, SE-ASIA) "x,
CLIMATE(x, SUBTROPICAL) TEMPERATURE(x,
WARM) "x, RAINFALL(x, HEAVY) WATER-SUPPLY(x,
HIGH) "x, SOIL(x, RED-SOIL) SOIL(x,
FERTILE-SOIL) "x, WATER-SUPPLY(x, HIGH)
TEMPERATURE(x, WARM) SOIL(x,
FERTILE-SOIL) RICE-AREA(x) This background
knowledge could be used in proving the input
fact. Determine A general inference rule that
allows the direct derivation of the input from
the facts stored in the knowledge base "x,
RAINFALL(x, HEAVY) CLIMATE(x, SUBTROPICAL)
SOIL(x, RED-SOIL) gt RICE-AREA(x)
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Learning macro-operators illustration
Consider the following situation that involves a
robot that could go from one room to another and
could push boxes through the doors
InRoom(Robot, Room1) InRoom(Box, Room2)
Connects(Door1, Room1, Room2)
Connects(Door2, Room2, Room3)
Connects(Door3, Room1, Room4)
Apply explanation-based learning to learn a
general macro-operator from the following example
of problem solving episode to achieve the
goal InRoom(Box, Room1) perform the
actions GoThru(Robot, Door1, Room1,
Room2) PushThru(Robot, Box, Door1, Room2,
Room1) The knowledge of the system consists of
the action models and inference rule from the
next slide.
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Learning macro-operators illustration (cont.)
GoThru(a, d, r1, r2) robot a goes through door
d from room r1 to room r2 Preconditions InRoom
(a, r1) a is in room r1 Connects(d, r1, r2)
door d connects room r1 with room r2
Effects InRoom(a, r2) a is in room
r2 PushThru(a, o, d, r1, r2) a pushes box o
through d from r1 to r2 Preconditions InRoom(a
, r1) a is in room r1 InRoom(o, r1) o is in
room r1 Connects(d, r1, r2) door d connects
room r1 with room r2 Effects InRoom(a, r2)
a is in room r2 InRoom(o, r2) o is in room
r2 Connects(d, r1, r2) gt Connects(d, r2, r1)
if d connects r1 with r2 then it also connects r2
with r1.
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Learning macro-operators illustration (cont.)
GoAndPushThru(a, o, d1, d2, r1, r2, r3) the
robot goes from room r1 into room r2 and pushes
the box into room r3 Preconditions InRoom(a,
r1) a is in room r1 InRoom(o, r2) o
is in room r2 Connects(d1, r1, r2) door
d1 connects room r1 with room r2 Connects(d2,
r2, r3) door d2 connects room r2 with room
r3 Effects InRoom(a, r3) a is in room
r3 InRoom(o, r3) o is in room r3
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Discussion
How does deductive learning compare with
inductive learning?
What comparison criteria to consider?
EIL many, both positive and negative EBL only
one positive example
EIL very little needed (e.g. generalization
hierarchy) EBL complete and correct domain
theory
EIL inductive EBL deductive
EIL improves systems competence EBL improves
systems efficiency
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General features of explanation-based learning
Needs only one example
Requires complete knowledge about the concept
(which makes this learning strategy
impractical).
Improves agent's efficiency in problem solving
Shows the importance of explanations in learning
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Recommended reading
Mitchell T.M., Machine Learning, Chapter 11
Analytical Learning, pp. 307 - 333, McGraw Hill,
1997. Mitchell T.M., Keller R.M., Kedar-Cabelli
S.T., Explanation-Based Generalization A
Unifying View, Machine Learning 1, pp. 47-80,
1986. Also in Readings in Machine Learning,
J.W.Shavlik, T.G.Dietterich (eds), Morgan
Kaufmann, 1990. DeJong G., Mooney R.,
Explanation-Based Learning An Alternative View,
Machine Learning 2, 1986. Also in Readings in
Machine Learning, J.W.Shavlik, T.G.Dietterich
(eds), Morgan Kaufmann, 1990. Tecuci G.
Kodratoff Y., Apprenticeship Learning in
Imperfect Domain Theories, in Kodratoff Y.
Michalski R. (eds), Machine Learning, vol 3,
Morgan Kaufmann, 1990. S. Minton, Quantitative
Results Concerning the Utility of
Explanation-Based Learning, in Artificial
Intelligence, vol. 42, pp. 363-392, 1990. Also in
Shavlik J. and Dietterich T. (eds), Readings in
Machine Learning, Morgan Kaufmann, 1990.