Eduardo Poggi presented on explanation-based learning (EBL). EBL is an analytical learning approach that uses background knowledge to analyze training examples and form generalizations. It involves 3 steps: explaining an example using domain knowledge, analyzing the explanation to identify relevant features, and refining the hypothesis. EBL can learn from a single example by using prior knowledge to reduce the hypothesis space. It differs from inductive learning which does not use background knowledge. Potential issues with EBL include developing overly complex theories from numerous rules and imperfect domain theories.

1. Buenos Aires, junio de 2016
Eduardo Poggi

2. Agenda
 EBL
 Inductive vs Analytical learning
 Perfect Domain Theories
 Examples
 Problems
 Summary

3. ¿EBL?
 Learning general problem-solving techniques by observing and analyzing
human solutions to specific problems.
 EBL attempts to formulate a generalization after observing only a single (few)
example.
 Introduced by Gerald De Jong in 1981.
 Aplicado originalmente en robótica y resolución de problemas.

4. The EBL Hypothesis
 EBL is based on the hypothesis that an intelligent system can learn a
general concept after observing only a single example.
 By understanding why an example is a member of a concept, can
learn the essential properties of the concept.
 EBL uses prior knowledge to analyze or explain each training
example in order to infer what properties are relevant to the target
function and which are irrelevant.

5. Learning by Generalizing Explanations
 Given
 Goal concept (e.g., some predicate calculus statement)
 Training example (facts)
 Domain Theory (inference rules)
 Operationality Criterion
 Given this four inputs, the task is to determine a generalization of the
training example that is sufficient concept definition for the goal concept and
that satisfies the operationality criteria.
 The operationality criterion requires that the final concept definition be
described in terms of the predicates used to describe the training example.

6. Learning algorithms like neural networks,
decision trees, inductive logic programming,
etc. require a good number of examples to
be able to do good predictions.
dataset
Learning
Algorithm hypothesis
Dataset must be sufficiently large
Inductive learning

7. We don’t need a large dataset if besides taking
examples as input, the learning algorithm can take
prior knowledge.
dataset
Learning
Algorithm hypothesis
Dataset does not need to be large
Prior knowledge
Analytical learning

8. Prior knowledge is used to reduce the size of the
hypothesis space.
It analyzes each example to infer which features are
relevant and which ones are irrelevant.
Hypothesis
Space HS
Prior
knowledge Reduced HS
Explanation-based learning

9. Example, learning to play chess
 Suppose we want to learn a concept
like “what is a board position in which
black will lose the queen in x moves?”.
 Chess is a complex game. Each piece
can occupy many positions.
 We would need many examples to
learn this concept.
 But humans can learn these type of
concepts with very few examples.
Why?

10. Example, learning to play chess
 Humans can analyze an example and use prior knowledge
related to legal moves.
 From there it can generalize with only few examples.
 Reasoning like: “Because the white king is attacking both
king and queen; black must avoid check, letting white
capture the queen”

11. Example, learning to play chess
 What is the prior knowledge involved in playing chess?
 It is knowledge about the rules of chess:
 Legal moves for the pieces.
 Players alternate moves in games.
 To win you must capture the opponent’s king.

12.  Inductive Learning
 Input: HS, D
 Output: hypothesis h / h is consistent with D
 Analytical Learning
 Input: HS, D, BK
 Output: hypothesis h / h is consistent with D and BK
 (-h no se infiere de BK)
 With:
 HS: Hypothesis Space
 D: Training Set
 BK: Background knowledge (domain theory)
Inductive and Analytical Learning

13. Standard Approach to EBL
goal
facts
After Learning (go directly from facts to solution):
goal
facts
An Explanation (detailed proof of goal)

14. The EBL Process

15. Example Analytical Learning
 Examples: Dataset where each
instance is a pair of objects
represented by the following
predicates: Color, Volume, Owner,
Material, Density, On. Example:
 On(Obj1,Obj2)
 Type(Obj1,Box)
 Owner(Obj2,Louise)
 Density(Obj1,0.3)
 Color(Obj1,Red)
 Material(Obj1,Cardboard)
 Type(Obj2,Endtable)
 Color(Obj2,Blue)
 Material(Obj2,Wood)
 Volume(Obj1,2)
 Owner(Obj1,Fred)

16. Example, Analytical Learning
 Domain theory
 SafeToStack(x,y)  ¬Fragile(y)
 SafeToStack(x,y)  Lighter(x,y)
 Lighter(x,y)  Weight(x,wx), Weight(y,wy), LessThan(wx,wy)
 Weight(p,w)  Density(p,d), Volume(p,v), Equal(w, times(d,v))
 …
 Fragile(x)  Material(x,Glass)

17. Example, Analytical Learning
 Hypothesis space: set of Horn clause rules.
 The head of each rule has the predicate SafeToStack.
 The body of each rule is based on the instances and the predicates
LessThan, Equal, Greater and plus, minus and times.
 Example: SafeToStack(x,y)  Volume(x,vx) ^ Volume(y,vy) ^
LessThan(vx,vy)

18. Example, Analytical Learning
 Determine
 Hypothesis consistent with both the training examples and the
domain theory
 Notes
 The domain theory refers to predicates not contained in the
examples.
 The domain theory is sufficient to prove the example is true.

19. Perfect Domain Theories
 A domain theory is correct if each statement is true.
 A domain theory is complete if it covers every positive
example of the instance space (ie: a target concept and
instance space).
 A perfect domain theory is correct and complete.

20. Perfect Domain Theories
 Examples of where to find perfect domain theories:
 Rules of chess
 Examples of where not to find perfect domain theories:
 SafetoStack problem
 In general, only learning problems with perfect domain
theories is considered.

21. EBL Algorithm
 We consider an algorithm that has the following
properties:
 It is a sequential covering algorithm considering the data
incrementally
 For each positive example not covered by the current rules it
forms a new rule by:
 Explain how training example satisfies target concept, in terms of
domain theory.
 Analyze the explanation to find a the most general conditions under
which this explanation holds.
 Refine the current hypothesis by adding a new Horn Clause rule to
cover the example.

22. Explanation

23. Explanation
 There might be more than one explanation to the
example. In that case one or all explanations may be
used.
 An explanation is obtained using a backward chaining
search as is done by Prolog. Prolog-EBG stops when it
finds the first proof.

24. Analyze
 Many features appear in an example. Of them, how many
are truly relevant?
 We consider as relevant those features that show in the
explanation.
 Example:
 Relevant feature: Density
 Irrelevant feature: Owner

25. Analyze
 Taking the leaf nodes of the explanation and substituting
variables x and y for Obj1, and Obj2:
 SafeToStack(x,y)  Volume(x,2), Density(x,0.3),
Type(y,Endtable)
 Remove features that are independent of x and y such as
Equal(0.6,times(2,0.3)) and LessThan(0.6,5).
 The rule is now more general and can serve to explain
other instances matching the rule.
 A more general form of generalization (called
“regression”) finds the most general rule explaining the
example.

26. Refine
 The current hypothesis is the set of Horn clauses that we
have constructed up to this point.
 Using sequential covering we keep adding more rules,
thus refining our hypothesis.
 A new instance is negative if it is not covered by any rule.

27. Computing the weakest preimage of explanation

28. Discovering new features
 The PROLOG-EBG system described can formulate new
features that are not in the training examples:
 Example: Volume * Density > 5, derived from the
domain theory.

29. Inductive Bias in Explanation-Based Learning
 What is the inductive bias of explanation based learning?
 The hypothesis h follows deductively from D (database) and B
(Background knowledge)
 Bias: prefer small sets of maximally general Horn Clauses

30. Problems with EBL
 The number of control rules that must be learned is very
large.
 If the control rules are many, much time will be spent
looking for the best rule.
 Utility analysis is used to determine what rules to keep
and what rules to forget.
 Another problem with EBL is that it is sometimes difficult
to create an explanation for the target concept.
 For example, in chess, learning a concept like: “states for
which operator A leads to a solution”
 The search here grows exponentially.

31. Summary
 Different from inductive learning, analytical learning looks
for a hypothesis that fit the background knowledge and
covers the training examples.
 Explanation based learning is one kind of analytical
learning that divides into three steps:
 Explain the target value for the current example
 Analyze the explanation (generalize)
 Refine the hypothesis
 PROLOG-EBG constructs intermediate features after
analyzing examples.
 Explanation based learning can be used to find search
control rules.
 Depend on a perfect domain theory.

32. Componentes del EBL

33. Componentes del EBL
 Resolución del problema:
 Utilizar el dominio y el ejemplo para llegar al objetivo.
 Análisis de la traza:
 Analizamos la solución para obtener una explicación.
 Usamos criterios:
 Criterio de relevancia: aquella información que forme parte en el camino de llegar a la solución.
 Criterio de operatividad: aquellas reglas que se activan directamente.
 Filtrado:
 Filtra la información de la traza para llegar a la explicación.
 Generalización:
 Sustituye las constantes por variables de forma que la expresión siga siendo válida.
 El método más usado es el algoritmo de regresión de objetivos.
 Regresionar una fórmula f a través de una regla r consiste en determinar las condiciones
necesarias y suficientes bajo las cuales puede usarse la regla r para obtener f.
 Construir nueva información:
 La información que construimos puede ser:
 Reglas de dominio que expresaran nuevas definiciones de conceptos en las que la parte derecha de la
regla serán las combinaciones necesarias y suficientes del árbol de explicación generalizado mientras
que la raíz del mismo será la parte izquierda de la regla.
 Reglas de control que se construyen de forma similar.
 Incorporar:
 Las nuevas reglas hay que incorporarlas a la base de conocimiento, pero a veces se obtienen
demasiadas reglas para introducir en nuestro sistema.
 Hay que llegar a una solución de compromiso (velocidad de inferencia o base de afirmaciones
mayor).

34. Ejemplo 1

35. Ejemplo 1

36. Ejemplo 2
 Concepto objetivo: TAZA
 Definición funcional:
 TAZA(x) <- RECIPIENTE_ABIERTO(x) ^ ESTABLE(x) ^ ALZABLE(x)
 Ejemplo de entrenamiento:
 TIENE_PARTE(OBJ1, CONCAVIDAD1)
 COLOR(OBJ1, ROJO)
 CONCAVIDAD(CONCAVIDAD1)
 ORIENTADA_HACIA_ARRIBA(CONCAVIDAD1)
 TIENE_DUEÑO(OBJ1, SAM)
 TIENE_PARTE(OBJ1, FONDO1)
 FONDO(FONDO1)
 PLANO(FONDO1)
 LIGERO(OBJ1)
 TIENE_PARTE(OBJ1, ASA1)
 ASA(ASA1)
 LONGITUD(ASA1, 5)

37. Ejemplo 2
 Teoría del dominio:
 ESTABLE(OBJ) <- TIENE_PARTE(OBJ, F) ^ FONDO(F) ^
PLANO(F)
 RECIPIENTE_ABIERTO(OBJ) <- TIENE_PARTE(OBJ, C) ^
CONCAVIDAD(C) ^ ORIENTADA_HACIA_ARRIBA(C)
 ALZABLE(OBJ) <- TIENE_PARTE(OBJ, A) ^ ASA(A) ^
LIGERO(OBJ)
 Criterio operacional:
 El concepto tiene que definirse en términos de los predicados
usados en el ejemplo.

38. Ejemplo 2
 El proceso de aprendizaje tiene 2 pasos:
 Se usa la teoría del dominio para construir una explicación
(demostración) de que el ejemplo de entrenamiento es un
ejemplo positivo del concepto objetivo. Los nodos terminales del
árbol de explicación tienen que ser operativos
 Transformar los nodos terminales en un conjunto de condiciones
suficientes para que la demostración siga siendo válida
(generalizar la explicación de acuerdo con la teoría del dominio)

39. Ejemplo 2
 Resultado del proceso de aprendizaje:
 TIENE_PARTE(X, Y) ^ CONCAVIDAD(Y) ^
ORIENTADA_HACIA_ARRIBA(Y) ^ TIENE_PARTE(X, Z) ^
FONDO(Z) ^ PLANO(Z) ^ TIENE_PARTE(X, W) ^ ASA(W) ^
LIGERO(X)

40. Problemas de EBL
 Cuando el EBL se aplica a dominios reales surgen un
conjunto de problemas que se deben resolver, estos se
pueden agrupar en dos clases:
 Problemas derivados del nuevo conocimiento incorporado a la
teoría (reformulación de la teoría)
 Problemas derivados de la calidad de la teoría (revisión de la
teoría)

41. Problemas de EBL – Reformulación de la teoría
 La incorporación sistemática de nuevo conocimiento lleva
a la degradación de la teoría debido a dos causas:
 Baja frecuencia de aplicación: es posible que el nuevo
conocimiento se use pocas veces.
 Alto costo de cotejar las reglas: el comprobar si el nuevo
conocimiento es útil es muy costoso.
 Esto produce una reducción de la eficiencia del sistema.
 Como solución se puede reescribir la teoría para reducir
el costo de cotejo de las reglas, evaluar la frecuencia de
uso de las reglas y eliminar las que se usen pocas veces.

42. Problemas de EBL – Revisión de la teoría
 La teoría que se utiliza no permite solucionar
correctamente los problemas y se debe corregir:
 Teorías incompletas: la teoría no es capaz de solucionar todos los
problemas por falta de reglas adecuadas. Se puede completar la
teoría por métodos inductivos
 Teorías incorrectas: la teoría da soluciones incorrectas a algunos
problemas. Se puede intentar determinar que reglas están mal y
eliminarlas o corregirlas inductivamente.
 Teorías inconsistentes: llegan a soluciones contradictorias.
 Teorías intratables: para poder solucionar un problema necesitan
mas recursos que los que se dispone.

43. eduardopoggi@yahoo.com.ar
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http://ar.linkedin.com/in/eduardoapoggi
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