Explanation based learning methods
Explanation Based Learning (EBL) systems, after analysing a single training example, are able to produce a valid generalisation along with a deductive justification of the generalisation in terms of the system knowledge (Mitchell, Keller, Kedar-Cabelli, 1986). The inputs to Explanation Based Learning systems are :
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An example which is a set of facts describing an instance of the goal concept |
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An example which is a set of facts describing an instance of the goal concept |
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Specifies the form in which the generalised concept definition may be expressed |
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A high level description of the concept to be learned |
Given the above, EBL creates a generalisation of the training example which can adequately describe the goal concept and also satisfies the operationality criteria.
The method first constructs an explanation by analysing the training example showing how the example satisfies the definition of the concept. This explanation is then used to formulate the definition of the general concept.
An important feature of EBL methods is that they are able to justify the generalised concept. This is a recognised problem of inductive / similarity-based learning systems.
The EBL methodology is described using the CUP generalisation problem (Mitchell et al 1986) as shown in the table below.
The Training Example
colour(Obj23, Blue) Ù has-part(Obj23, Handle16) Ù has-part(Obj23, Bottom19) Ù
owner(Obj23, Ralph) Ù has-part(Obj23, Concavity12) Ù is(Obj23, Light) Ù
is(Ralph, Male) Ù isa(Handle16,Handle) Ù isa(Bottom19, Bottom) Ù
is(Bottom19, Flat) Ù isa(Concavity12, Concavity) Ù
is(Concavity12, Upward-Pointing)
The Domain Theory
has-part(x,y) Ù isa(y,Concavity) Ù is(y, Upward-Pointing) ® open-vessel(x)
is(x, Light) Ù has-part(x,y) Ù isa(y,Handle) ® liftable(x)
has-part(x,y) Ù isa(y, Bottom) Ù is(y,Flat) ® stable(x)
The Goal Concept
liftable(x) Ù stable(x) Ù open-vessel(x) « cup(x)
Operationality Criterion
The concept definition must be expressed in terms of structural features.
The first stage of the EBL process is to show why the training example is an example of a cup. This is shown in figure 3.11 below which represents a proof. This proof is expressed only in terms of the operationality criterion and irrelevant details relating to the Owner and Colour have been discarded.
Figure 3.11 : The explanation structure of the cup
This proof is now generalised by using a goal regression technique (Mitchell, Keller, Kedar-Cabelli, 1986). In this example replacing the constants with variables gives the required generalisation of the cup.
has-part(x, y) Ù isa(y, Concavity) Ù is(y, Upward-Pointing) Ù
has-part(x, z) Ù isa(z, Bottom) Ù is(z, Flat) Ù has-part(x,w) Ù
isa(w, Handle) Ù is(x, Light)
The EBL procedure is very much domain theory driven with the training example helping to focus the learning. Without the training example the results would be overly general.
Authored by Serengul Smith
E-mail to:
serengul1@mdx.ac.uk
School of Computing Science Middlesex University
Revised: September 1998