1. Analogical Learning and Problem Solving
1 Aug 2011
Ramakrishna,
Abhijit,
Anup,

2. Duncker's (1945) “Radiation Problem"2

3. Attack-Dispersion story (Cont.)

4. Known Solution

5. Analogy
The analogous solution to the radiation problem is to simultaneously direct multiple low-intensity rays toward the tumor from different directions. In this way the healthy tissue will be left unharmed, but the effects of the multiple low-intensity rays will summate and destroy the tumor 5

7. What is it ? Machine Learning Intuition Supervised Learning
Inductive Learning
Decision Trees, Version Space etc.
Analogical Learning
Unsupervised Learning
Reinforcement Learning
Intuition
If two entities are similar in some respects then they could be similar in other respects as well

8. Steps in Analogical Problem Solving
Identifying Analogy
Find a known/experienced problem that is analogous to the input problem
Mapping
Relevant parts of the experienced problem are selected and mapped on to the input problem to transform the new problem and derive some hypothesis for the solution
Validation
The correctness of the newly constructed solution is validated using theorem or simulation etc.
Learning
If the validation is found to work well, the new knowledge is encoded and saved for future usage.

9. Analogy Representation
Appropriate level of “analogical structures” needs to be represented
Too Detailed or Too Abstract representation will make it had to draw analogy
Example

10. Analogical Structures
A fortress was located in the center of the country.
Many roads radiated out from the fortress.
A general wanted to capture the fortress with his army.
The general wanted to prevent mines on the roads from destroying his army and neighboring villages.
As a result the entire army could not attack the fortress along one road.
However, the entire army was needed to capture the fortress.
So an attack by one small group would not succeed.
The general therefore divided his army into several small groups.
He positioned the small groups at the heads of different roads.
The small groups simultaneously converged on the fortress.
In this way the army captured the fortress.
A tumor was located in the interior of a patient's body. -
A doctor wanted to destroy the tumor with rays.
The doctor wanted to prevent the rays from destroying healthy tissue.
As a result the high-intensity rays could not be applied to the tumor along one path.
However, high-intensity rays were needed to destroy the tumor.
So applying one low-intensity ray would not succeed.
The doctor therefore divided the rays into several low intensity rays.
He positioned the low intensity rays at multiple locations around the patient's body.
The low-intensity rays simultaneously converged on the tumor.
In this way the rays destroyed the tumor.

11. Predicate Analogy Sample Predicates Mapping Inference
locate(fortress, centre(country))
locate(tumour, interior(body))
desire(general, capture(army, fortress))
desire(doctor, destroy(rays, tumour))
Mapping
fortress → tumour
general → doctor
army → rays
Inference
divide(general, small_group(army))
divide(doctor, small_group(rays))
position(small_group(army), different_direction)
position(small_group(rays), different_direction)
simultaneous(converge(small_group(army), fortress))
simultaneous(converge(small_group(rays),tumour))
destroy(army, fortress)
destroy(rays, tumour)

12. Analogical Problem Solving
Needs sophisticated techniques for
Representation of the problem and solution
Matching input problem with existing problem
Concluding inferences
Very hard problem
Let us see one system - EUREKA

13. EUREKA
An analogical problem solving architecture presented by RANDOLPH M. JONES and PAT LANGLEY
Quick look at EUREKA
Existing problem
New problem. Solve by analogy to previous problem
Consists of
Memory Module
Problem Solving Engine A B C E F G H

14. Memory Representation
As Semantic Network
Example network for block movement problem
State100
Trans1
Transforms to a new state which satisfies the goal
Goal17
Ref: Randolph Jones; Problem Solving via Analogical Retrieval and Analogical Search Control

15. Problem Solving Engine
Uses Flexible Means-Ends Algorithm
Two recursive functions are used
TRANSFORM
APPLY
State P
Op1
State C
State X
State Z

16. Transform and Apply Procedures
TRANSFORM(StateX,Conditions): Returns StateZ
If StateX satisfies Conditions
Then Return StateZ as StateX
Else Let Operator be SELEC_OPERAT0R(StateX,Conditions);
If Operator is empty
Then Return StateZ as "Failed State1'
Else Let StateY be APPLY(StateX,Operator);
If StateY is "Failed State"
Then Return StateZ as "Failed State"
Else Return StateZ as
TRANSFORM(StateY,Conditions)
APPLY(StateX,Operator): Returns StateY
Let P be PRECONDITIONS(Operator);
If StateX s a t i s f i e s P
Then Return StateY as EXECUTE(StateX,Operator)
Else Let StateW be TRANSFORM(StateX,P);
If StateW i s "Failed State"
Then Return StateY as "Failed State"
Else Return StateY as APPLY(StateW,Operator)
Ref: Randolph Jones; Problem Solving via Analogical Retrieval and Analogical Search Control

17. Example
Transforming from the initial state (State100) to the final state (State200) which satisfies the given goal (Goal17)
Ref: Randolph Jones; Problem Solving via Analogical Retrieval and Analogical Search Control

18. Identifying Analogy and Problem Solving
Collect some analogical TRANSFORM goals from the existing solution
Use spreading techniques from the current state and goal nodes
Eg: Trans1, Trans10
Select the best matching goals
Degree of match
History data (success/failure)
Make concept analogy
E → A; F → B
Proceed as per the analogical TRANSFORM goal

19. Identifying Analogy and Problem Solving Contd…
Closest Matching TRNSFORMATION Goal
State500
Goal99
On5
On6
On.. E F
……….

20. EUREKA – Initial Stage
EUREKA started without any knowledge in its long-term memory
For eg. First Time
never be able to solve any problems, because there would be no previously solved problems on which to base future decisions
Operators are stored in the form of simple problems

21. Case Based Reasoning (CBR)
Reasoning method that uses specific past experiences rather than a corpus of general knowledge.
Problem solving by analogy
Recognizing its similarity to a specific known problem
Transferring the solution of the known problem to the new one.
Form of intra-domain analogy.

22. CBR terminologies Case : Denotes a problem situation
Past case : A previously experienced situation which has been captured and learned for reuse.
Case based reasoning : A cyclic and integrated process of solving a new problem.

23. Learning in CBR Natural by-product of problem solving.
The experience of a successfully solved is retained inorder to solve future problems
If an attempt to solve problem fails, reason of failure is remembered in order to avoid same mistake in future.

24. CBR Cycle RETRIEVE Retrieve one or more previously experienced cases.
REUSE
Reusing the case in one way or another.
REVISE
Revising the solution based on reusing a previous case.
RETAIN
Retaining the new experience by incorporating it into existing knowledge base.

25. CBR Cycle
Fig . Taken from: Agnar Aamodt, Enric Plaza, “Case-Based Reasoning Foundational Issues, Methodological Variations, and System Approaches”, AI communications, 1994.

26. How “cases” are represented ?
Figure taken from “Agnar Aamodt and Enric Plaza, “Case-Based Reasoning: Foundational Issues, Methodological Variations, and System Approaches”,AI Communications, Vol. 7 Nr. 1, March 1994, pp 39-59”

27. How “cases” are represented ?
In dynamic memory model, cases that share similar properties are organized under a more general structure known as generalized episode – GE.
A generalized episode contains
Norms
denote features common to all cases indexed under a GE.
Indices
are features that discriminate between a GE's cases
may point to a more specific generalized episode, or directly to a case.
An index is composed of
Index name
Index value
Cases

28. How to find a similar problem ?
When a new case description is given and the best matching is searched for, the input case structure is 'pushed down' the network structure, starting at the root node.
When one or more features of the case match one or more features of a GE, the case is further discriminated based on its remaining features.
Eventually, the case with most features in common with the input case is found.

29. How a new case is trained to system ?
During storing of a new case, it is discriminated by indexing it under different indices below its most specific generalized episode.
If, during the storage of a case - two cases (or two GEs) end up under the same index, a new generalized episode is automatically created.

30. Norms: Disease symptoms
An example...
Generalized Episode 1
Norms: Disease symptoms
Indices:
Index:
Values:
Fever symptoms
Dysentry symptoms
Generalized Episode 2
Norms: Fever
Indices:
Generalized Episode 3
Norms: Dysentry
Indices:
Index:
Index:
food poisoning symptoms
Values:
Influenza symptoms
Swine Flu Symptoms
Malaria symptoms
Values:
Cholera Symptoms
Amoebic
symptoms
Cases:
Influenza
Swine Flu
Malaria
Cases:
food poisoning
Cholera
Amoebic dysentry

31. An example... Consider a doctor patient senario.
The case of diseases trained are already stored in the tree fashion.
It has got Generalized Episodes(GE) as the entity.
Suppose a new patient comes with malaria symptoms.
Current case symptoms are compared with the already existing ones. So it is directed to the left subtree. Here norms give the features common to that GE.
Then cases are distinguished according to the symptoms which are specific to those.
Ultimately the current case is directed to the index 3 where it is matched and the solution to the already stored case is applied to the current case.

32. Protos
Case-based problem solving and learning system for heuristic classification tasks.
In Protos, a concept ci is represented extensionally as a collection of examples (called exemplars or cases):
ci = {ei1, ei2, ...}.

33. The classification and learning algorithm
Input: a set of exemplar-based categories C = {c1, c2, ... , cn} and a case (NewCase) to classify.
REPEAT
Classify:
Find an exemplar of ci є C that strongly matches NewCase and classify NewCase as ci.
Explain the classification.
Learn:
If the expert disagrees with the classification or explanation then acquire classification and explanation knowledge and adjust so that NewCase is correctly classified and explained.
UNTIL the expert approves the classification and explanation.

34. Conclusion Analogical problem solving technique
Supervised machine learning
Helps in reducing search space for some kind of problems where analogy can be drawn
Case Based Reasoning
CBR gives a new way to solve problems.
It emphasizes on problem solving as well as learning.
Has got a potential of leading to significant breakthrough in AI.

35. References
Randolph M. Jones, Pat Langley, “Retrieval and Learning in Analogical Problem Solving”, Proceedings of the Seventeenth Conference of the Cognitive Science Society, 1995, pp
RANDOLPH M. JONES, PAT LANGLEY “A CONSTRAINED ARCHITECTURE FOR LEARNING AND PROBLEM SOLVING”, Computational Intelligence, Volume 21, Number 4, 2005
Randolph M. Jones, “Problem Solving via Analogical Retrieval and Analogical Search Control”, Book “Foundations of Knowledge Acquisition: Machine Learning”, 1993
Mary L. Gick and Keith J. Holyoak, "Analogical Problem Solving“, Cognitive Psychology, 1983, pp
Agnar Aamodt and Enric Plaza, “Case-Based Reasoning: Foundational Issues, Methodological Variations, and System Approaches”,AI Communications, Vol. 7 Nr. 1, March 1994, pp
Bareiss, R. (1988): PROTOS; a unified approach to concept representation, classification and learning.Ph.D. Dissertation, University of Texas at Austin, Dep.of Computer Sciences Technical Report AI88-83.