Version Spaces
Learning by managing multiple
models
Learning by analyzing
differences


Student must learn a concept. How do you
propose to teach the concept?
Consider the concept of an “Arch”
What make’s an arch an arch


Teacher can provide
examples and counter
examples:
An arch is made up of



Supports
Top
What are an arch’s
properties?
Near-miss improves understanding
NOT an ARCH
But close
Near-miss can
add a link
System learns
“must-support”
Near-miss is a negative example of
the concept
Negative
example can
remove (or
modify) a link
Positive example can help generalize
Arch’s top can
be a brick OR
a wedge

Negative Examples allow us to


Generalize or Specialize?
Positive Examples allow us to

Generalize of Specialize?
Version Spaces: Learn by managing
multiple models
Version spaces

Each time a general model is specialized,
that specialization must be a
generalization of an existing specific
model.


Corollary: Each time a specific model is
generalized, that generalization must be a
specialization of an existing general model
Each time a general model is specialized
that specialization must not be a
specialization of ANOTHER general model
John’s allergies
Number
Restaurant Meal
1
Sam’s
2
Day
Cost
Reaction
Breakfast Friday
Cheap
Yes
Lobdell’s
Lunch
Friday
Expensive No
3
Sam’s
Lunch
Saturday
Cheap
Yes
4
Sarah’s
Breakfast Sunday
Cheap
No
5
Sam’s
Breakfast Sunday
Expensive No
Version Space
[?,?,?,?]
[Sam’s,breakfast,friday,cheap]
General
Specific
[Lobdell, lunch, Friday, expensive]
Negative example:
 What happens to “Most general model”?






Cannot be lobdell’s must be Sam’s
Cannot be lunch, must be breakfast
Cannot be expensive, must be cheap
Both samples say Friday, so that feature must
not matter
What happens to “Most specific model”?