Machine Learning Proceedings 1988. Proceedings of the Fifth International Conference on Machine Learning, June 12–14, 1988, University of Michigan, Ann Arbor

469 Pages·1988·36.08 MB·English

by  John Laird

PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON
MACHINE LEARNING
June 12-14, 1988
University of Michigan, Ann Arbor
Editor/Program Chair: John Laird
Organizing Committee:
John E. Laird (Chairman), University of Michigan
John H. Holland, Steve L. Lytinen, Gary M. Olson, University of Michigan
Jaime G. Carbonell, Tom M. Mitchell, Carnegie Mellon University
Pat Langley, University of California, Irvine
Ryszard S. Michalski, George Mason University
Sponsored by:
The Cognitive Science and Machine Intelligence Laboratory of The University of Michigan
With support from:
American Association of Artificial Intelligence, the ONR Computer Sciences Division and
the ONR Cognitive Science Program
In cooperation with:
Association for Computing Machinery—SIGART
Program Committee:
Saul Amarel, Rutgers University
Gerald DeJong, University of Illinois
Thomas G. Dietterich, Oregon State University
Doug Fisher, Vanderbilt University
John Grefenstette, Naval Research Lab
David Haussler, University of California, Santa Cruz
Dennis Kibler, University of California, Irvine
Yves Kodratoff, Universite de Paris Sud
Pat Langley, University of California, Irvine
Ryszard S. Michalski, George Mason University
Jack Mostow, Rutgers University
Ronald L. Rivest, Massachusetts Institute of Technology
Paul S. Rosenbloom, Information Sciences Institute, University of Southern California
Jeff Schlimmer, Carnegie Mellon University
Jeff Shrager, Xerox Palo Alto Research Center
Derek Sleeman, University of Aberdeen
Robert E. Stepp, University of Illinois
Richard Sutton, GTE Research Labs
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International Conference on Machine Learning (5th: 1988
Ann Arbor, Michigan)
ISBN 0934613-64-8
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PREFACE
This volume contains the written versions of papers accepted for the Fifth
International Conference on Machine Learning. The goal of the conference was to
bring together interested researchers from all areas of machine learning. Over the last
eight years, four workshops on machine learning have been held. These workshops
had an attendance of around 50-150 people, and this small size was an important
factor in their success. Such small workshops were possible only because
participation was restricted to be by invitation only. Last year, 250 researchers
submitted abstracts from which only 150 were chosen to attend.
Based on last year's response, it was decided that the fifth meeting should be an
open conference, so that all interested researchers could attend. The presentations for
the fifth meeting were selected by a review of submitted papers by the program
committee. Of the 150 papers that were submitted, forty-nine papers were accepted.
Twenty of these are long papers that were presented as talks at the conference.
Twenty-nine additional short papers were accepted for presentation as posters.
Thanks are extended to the Office of Naval Research for providing support for all
previous workshops as well as the current conference. The American Association of
Artificial Intelligence also provided support for the organization and planning of the
conference. Special thanks to Suzanne Visel and Joan Britton for help with organizing
the conference.
John Laird
vii
1
Using a Generalization Hierarchy to Learn from Examples
RANDY G. KERBER ([email protected])
Lockheed Artificial Intelligence Center, 2710 Sand Hill Road,
Menlo Park, CA 94025 USA,
Abstract
Cms (OpporTunistic Induction System) is an induction system that learns concepts from positive and negative
examples by searching through the space of possible concept descriptions (the hypothesis space). An agenda
controls search by scheduling tasks for generating concept descriptions via specialization, generalization, internal
disjunction, and constructive induction. To aid the search, OTIS maintains a generalization hierarchy of the
relations, attributes, and values that make up the description language. The hierarchy also classifies each
concept description created and each training example, showing which descriptions are specializations of other
descriptions and which training examples are described by each description. This paper describes the OTIS
induction system, focusing on the generalization hierarchy and its benefits.
1. Introduction
Concept learning from examples is a form of inductive learning in which the learning system is given a
training set of positive and negative examples of a concept and induces a generalized description of the
concept. This process is typically formulated as a search problem where the goal is to find descriptions
that describe every positive example {complete descriptions) but describe none of the negative examples
{consistent descriptions), A complete and consistent concept description is called a solution.
The number of descriptions in a hypothesis space depends on the number and type of objects, relations,
values, and logical operators in the description language. Many induction systems deal only with
objects that can be described by a set of attributes such as shape or color. Objects in an attribute-only
domain can be represented using a feature vector of fixed size. The size of an attribute-only hypothesis
space is Ve, assuming that there are a attributes in the description language and each attribute has v
possible values. Allowing internal disjunctions (disjunctions among the values of a single attribute,
such as color = black-or-white) increases the number of values per attribute from v to 2V. Adding
relations between objects (such as on-top~of or contains) greatly increases the number of descriptions
possible since attributes typically have a limited number of possible values while the value of a relation
is another concept description. The size of a hypothesis space that includes attributes, internal
disjunctions, and relations is approximately 2van+rn(n'l)/n\ (where r = number of relations, n = maximum
number of objects per description). In the case where a = 6, v = 5, r = 3, and n = 3, there are ~1030
possible descriptions! Another factor affecting the size of the search space is whether or not an
induction system can perform constructive induction. Constructive induction is the ability to construct
and use descriptors (relations, attributes, and values) not present in the original description language (as
opposed to selective induction, which is the process of making new descriptions by selecting from
existing descriptors). An example of constructive induction is to create a new relation that is the
transitive closure of an existing relation, such as creating above from on-top-of. Including constructive
induction further fuels the combinatorial explosion by increasing the number of relations, attributes, and
values that can be used to build descriptions.
Considering the immense size of some hypothesis spaces, approaching generalization as a search
problem might seem futile. However, a general-to-specific partial ordering based on the relation
more-specific-than gives the hypothesis space structure that an induction system can use to guide the
search. More-specific-than is defined as follows: description A is more-specific-than description B, if
among the set of all instances describable in the description language, the set of instances described by A
is a proper subset of the set of instances described by B. This definition does not, however, provide a
practical method of computing whether one description is more-specific-than another, since it would
require examining the entire set of possible instance descriptions. Instead, an induction system must
decide by directly comparing the descriptions. This process is called matching.
2 Kerber
The version space approach (Mitchell, 1982) uses the more-specific-than partial ordering to create a
compact representation for the set of all possible solutions (called the version space) by maintaining two
sets, S and G, the maximally specific and maximally general boundaries of the versio nspace. A concept
description is in the version space if it is more-specific-than some member of G and more-general-than
(the inverse of more-specific-than) some member of S. The version space algorithm possesses several
nice feature it can represent all possible solutions, learn concepts incrementally, determine if no
solution is possible, and determine if the version space has converged to a single solution. However,
the version space algorithm requires a lot of matching if 5 and G are large. Each new example is
matched against the members of 5 and G, if the example causes new descriptions to be created matching
is also required to update S and G. For example, if the new instance is a positive example and it causes
descriptions in 5 to be generalized, each new description must be checked to ensure that it is more-
specific-than some member of G and not more-general-than some other member of 5. As the version
space algorithm runs, the size of S and G can grow exponentially (Haussler, 1987)). Also, in general
matching is NP-complete since it is equivalent to determining if one graph is a subgraph of another
(Hoff, Michalski & Stepp, 1983).
2. Approach
OTIS attempts to exploit the structure provided by the general-to-specific partial ordering to a greater
extent than previous induction systems. The goal of the OTIS project i sto build a domain independent
induction system to learn structurally described concepts from examples. The focus is to relax the
requirement to find the set of all solutions and instead to investigate more flexible methods of
performing selective and constructive induction that rely on domain independent heuristics and domain
specific background knowledge. Our initial testbed is based on the "cancer cell" examples (figure 1)
previously used by the INDUCE system (Michalski, 1983; Hoff, Michalski & Stepp, 1983) which
includes the attributes size, shape, weight, color, orientation, nwnber-of-tails, protoplasm-type, it-
segments, and the relation contains. We have augmented the examples by adding the relations below,
above (a synonym for on-top-oj), and next-to (jiext-to means to the near left or near right).
Cancerous cells Normal cells
figure 1. The cancer cell examples
The main components of OTIS are an agenda to control search, tasks to create concept descriptions, and
a generalization hierarchy to store knowledge. The basic search procedure is as follows: the top-rated
task is taken off the agenda and executed, creating new concept descriptions that are added to the
generalization hierarchy; then tasks for modifying these new descriptions are created, rated by an
evaluation function, and added back to the agenda. This process repeats until the agenda is empty or
some other specified termination condition is satisfied. The evaluation function considers factors such
as the classifying accuracy of the description, preference criteria such as simplicity of the description,
and domain specific background knowledge.
Using a Generalization Hierarchy to Learn from Examples 3
The choice of an agenda was motivated by the desire to provide a flexible control structure in which to
organize the execution of a variety of tasks. Presently, OTIS contains tasks for performing
specialization, generalization, constructive induction, and creating internal disjunctions. There are two
specialization tasks: add-slot adds a new slot to a description and descend-hierarchy specializes the value
of an existing slot by descending the hierarchy below the curren tvalue. For example, add-slot would
change the description [contains black-circle-body] to [color white]&[contains black-circle-body] and
descend-hierarchy would change it to [contains large-black-circle-body]. If the hierarchy contained no
specializations of the class black-circle-body, descend-hierarchy would create them first. The
generalization tasks — remove-slot and ascend-hierarchy — are inverses of the specialization tasks.
Creating an internal disjunction of attribute values, such as size=small-or-mediwn, is done by creating
the class small-or-medium, which is a specialization of the class any-size and has the values small and
medium as instances. There are currently two constructive induction tasks: creating the transitive
closure of an existing relation and creating a new attribute by counting the number of objects matching a
certain value of a multi-valued slot, such as the number of black circles an object contains.
Using an agenda permits interleaving the order in which different types o ftasks are executed. Some
induction systems are limited to performing constructive induction before selective induction or
specialization before generalization. An agenda also allows the integration of new tasks in a modular
fashion, easing the process of enhancing the capabilities of the system. These new tasks need not be
tasks for creating new descriptions, but could be tasks for organizing top level strategy, modifying
heuristics, or integrating new training examples into the hierarchy to perform incremental learning.
3. The Generalization Hierarchy
OTIS stores all attributes, relations, values, tasks, training examples, and concept descriptions in a
single generalization hierarchy of classes and instances as shown in figure 2. The classes and instances
are represented as frames, defined by the slots and values they contain. The frames also have slots
containing information about which classes are generalizations or specializations of each other and
which classes each instance is an instance of. The isa* slot contains a list of all generalizations o fa
class, while its inverse, kind*, contains a list of all specializations (isa* is essentially a synonym for
more-specific-than, except that more-specific-than refers to the entire hypothesis space while isa* refers
only to the concept descriptions present in the generalization hierarchy). In addition, the slots isa and
kind — specializations of isa* and kind* — are used to traverse the hierarchy in a general-to-specific or
specific-to-general order. The isa slot contains a list of all maximally-specific generalizations of a class
(MSG), which is the set of all generalizations that are not a generalization of another generalization. Its
inverse, kind, contains all maximally-general specializations (MGS) of a class. By analogy, the
relations isa kind, isa* and kind* are sometimes referred to as the parent, child, ancestor, and
t t
descendent relationships, respectively, of the generalization hierarchy. Finally, the slot instance-of
relates an instance to every class it is an instance of ;instance is its inverse.
When a concept description is created by an agenda task, OTIS updates the hierarchy to include the class
defined by the new description (for most purposes, the terms class and description can be used
interchangably). To avoid redundancy, first the hierarchy is checked to determine if a description
equivalent to the new description (call it Λ0 already exists (this is called locating a description). If N is
indeed new, the sets MSG and MGS described above are computed. To compute MSG, a recursive
function starts at the class object and follows down kind links attempting to match descriptions as it
descends the hierarchy. A description G is in MSG if N matches G (N is more-specific-than G in the
hypothesis space) but matches none of G's children. Similarly, a description S is in MGS if 5 matches
N but none of S"s parents match N. Once MSG and MGS have been determined, the generalizations
and specializations of N are computed. The set of generalizations of N (the isa* slot) consists of the
members of MSG and any generalizations of a member of MSG. The set of specializations of N (the
kind* slot) consists of the members of MGS and any specializations of a member of MGS. Finally, the
instances of N are determined. N inherits every instance that is an instance of some member of MGS. In
addition, any instances of a member of MSG not already inherited from MGS are checked to determine
if they match N, in which case they also become instances.
4 Kerber
anything s l ot (kind) ^attribute. .Ü^JSSSSi ||i..size
domain. (domain object) (domain object)
range (range value (range any-size)
#-yalues . . (#-values single-valued)
relation ||li··
property (domain body)
(domain object)
inverse (range body)
(range object)
task (#-values multi-valued)
aluev
(property asymmetric)
; task-type
value-of (inverse above)
; description
structure-tvpe * iny-size (closure below*)
f sloi
(value-of size]
value
small-or-medium
(structure-type ordered)
score
\(instance small medium)
(ordering-relation successor)
spec-dh:cell/contains-small-body (instance small medium large)
(task-type descend-hierarchy) small
(description cell/contains-small-body) object (successor medium)
(slot contains) ' size
(value small-body shape
(score 9.6)
contains. next-to
color h
Vs ize any-size
cell
weight
classification #-tqÜS
small-or-medium-body
black-body
pplasm-tvpe orientation
I (size small-or-medium)
\ (color black)
it-segments
small-body
Icel l/contains41 -small-body circle body l (size small)
(contains* small-body) (shape circle)
black-circle-body small-body/below* body
cell/contains-small-body (color black) / (size small)
I (contains small-body) (shape circle) / (below body)
cell/contains-small-body/below-black-circle-body / small-body/below-black-circle-body
(contains small-body/below-black-circle-body) / \ (size small)
\ (below black-circle-body)
cell-1 dy- body-1.2
(classification positive-example) (shape circle) (shape boat)
(pplasm-type A) (size large) (size small)
(#-segments 8) (color black) (color white)
(size large) (weight 7-grams) (weight 5-grams)
(shape oval) (contains body-1.4) (#-tails2)
(contains body-1.1 body-1.2 body-1.3) (orientation north)
(contains* body-1.1 body-1.2 body-1.3 body-1.4) (below body-1.3)
Figure 2. The generalization hierarchy
4. Using the Generalization Hierarchy
The hierarchy avoids storing equivalent descriptions (identical except for the order of conjuncts) because
each concept description has a uniquely defined location within the hierarchy. Given a new description,
determining if an equivalent description already exists is done by starting at the class object and
following down kind links as long as the new class matches the description of the class being checked.
This search requires no backtracking, because if a description equivalent to the new one exists there is
guaranteed to be a path of kind links to it from any description that the new description matches.
Using a Generalization Hierarchy to Learn from Examples 5
The generalization hierarchy can also improve the efficiency of computing the sets MSG an dMGS when
adding a new description to the hierarchy. If description N fails to match some description, there is no
need to check if it matches any specializations of that description. For example, if N is not more-
specific-than the class black-circle, then it cannot be more-specific-than the class large-black-circle. UN
did match black-circle, then the process of determining if it also matches large-black-circle is made more
efficient by using information from a slot called the delta slot. The delta slot of a class contains the
difference in the descriptions between a class and every child (kind) ofthat class. For example, the delta
between black-circle and large-black-circle is size-large. If N matches black-circle, it is sufficient to
check if the condition size-large is true for N to determine if it also matches large-black-circle — it is not
necessary to match the entire description, as would be required without the delta information.
4.1 Excluders
Another advantage has been in providing the ability to find and focus attention on classes called
excluders. A class E is defined to be an excluder if for every parent PofE (the isa slot), there is an
instance of P that is not an instance of E (thus E excludes at least one instance from each parent).
Conversely, a non-excluder has a parent with exactly the same set of instances. For example, in figure
1, the class [color grey]&[shape circle] is a non-excluder with respect to the class [color grey], since
every grey cell-body is also a circle. This information is used in two ways: (1) the evaluation function
gives a preference to descriptions that are excluders, reasoning that non-excluders are not making any
progress towards the goal of a consistent description since they describe exactly the same instances as a
more general description, and (2) only excluders are allowed to be specialized with the add-slot
specialization task. New slots are not added to non-excluders because if a description A has a child B
that is a non-excluder, then for any slot s and value v, the descriptions A&[s v] and B&[s v] will describe
the same instances. OTIS prefers to focus on the more general o fthe two descriptions since its goal is
to find discriminant descriptions (sufficient to discriminate between positive and negative examples)
rather than characteristic descriptions (intended to describe the positive examples in full detail).
4.2 Blocked Slots
A similar method of preventing the generation of unnecessary descriptions is called "blocking a slot".
To block a slot with respect to a description means to prevent the slot from being added to any
description which is a specialization (kind*) of that description. A slot is blocked if its values perform
either no discrimination or complete discrimination with respect to the instances of a description being
specialized, reasoning that non-discrimination cannot help you and you can't do better than complete
discrimination. For example, consider trying to use the attribute shape to distinguish between the
cancerous and normal cells in figure 1. Since all cells are oval ,shape performs no discrimination with
respect to the class cell. Thus, the slot shape is blocked from being added to any specializations of cell.
Complete discrimination occurs when the slot ^-segments is applied to cell. The positive examples have
either six or eight or ten segments in the cell wall while the negative examples have five or seven or
nine. Thus, the description [it-segments 6-or-8-or-10] is a complete and consistent solution. There is
nothing to gain from adding the slot ^-segments to any specializations of cell since the result, even if it
were a solution, would be more complicated (contain more conjuncts) than [^-segments 6-or-8-or-10].
4.3 Partial Descriptions
The generalization hierarchy also supports the creation and reuse of partial descriptions, a form of
constructive induction that increases the efficiency of matching and simplifies concept descriptions. A
partial description is a description of a part of an object that can be used to build other descriptions.
Once a description has been created and entered into the hierarchy, its name can be used as a value in
other descriptions for slots for which it is a legal value .Hoff, Michalski & Stepp, (1983) discuss the
desirability of creating and reusing partial descriptions, such as creating a description o fan arch which
can then be used to describe a sequence of arches. In the cancer cell domain the descriptions of cell-
bodies (all specializations of the class body) are partial descriptions. Creating new descriptions from
existing partial descriptions is efficient since no matching is required to determine which instances match
the partial descriptions and which partial descriptions are more-specific-than others — this information
is already stored in the instance, isa*, and kind* slots. For example, consider creating the description
black-circle-body I contains-small-body given the hierarchy in figure 2. The instances of this new class
6 Kerber
are those instances of the class black-circle-body that contain an instance of the class small-body,
Another benefit of using partial descriptions is the opportunity to browse through the hierarchy of partial
descriptions searching for descriptions that include or exclude specific instances.
4.4 Constructive Induction
In addition to creating and reusing partial descriptions, the hierarchy also improves other types of
constructive induction. Consider the case where OTIS tries to generalize a description D by taking the
slot s, creating its transitive closure s', and substituting s' for s in D to create description D'. If D' is
incomplete (does not cover all positive examples), then substituting s' for s in any E that is a
specialization of D would produce a description E' that would also be incomplete (Ε' is a specialization
of D' and any specialization of an incomplete description is incomplete). Therefore, OTIS will not try to
generalize any specializations of D using this method. Also, the descriptor annotations stored in the
knowledge hierarchy below the classes slot and value (see figure 2) are used to decide when to construct
new relations. Current rules include: only compute the transitive closure of relations for which the
domain and range of the relation intersect, and only count the number of matches for a slot that is multi-
valued. In addition, a hierarchy of relations can be constructed to represent which relations are
specializations of other relations, a feature advocated by Hoff, Michalski & Stepp (1983). This could be
maintained in a manner similar to that used for the isa hierarchy, since a uniform representation is used
for all declarative knowledge. However, the ability to dynamically update this hierarchy, as can be done
for the concept descriptions, is not currently supported.
5. Results
OTIS is implemented in Common Lisp on a Symbolics 3640. The following is a list of complete and
consistent solutions found in the cancer cell examples of figure 1. The "A-or-D" refers to the
protoplasm-type of the cell, shown in figure 1 as the circled letter to the lower right of each cell. The "/"
should be read as "which" or "which is". Thus A-or-D-celll contains*-1-tail-body-&-contains-white-
body I below-black-body translates to: "a cell whose protoplasm type is either A or D and which
contains* a body with one tail and also contains a white body which is below a black body". The "*"
indicates a relation that is the transitive closure of another relation that is not transitive.
6-ΟΓ-8-ΟΓ-10-segment-cell A-or-D-cell/contains-circle-body/below*-body
cell/contains-small-body A-or-D-cell/conlains -black-body
cell/contains-five-or-seven-bodies A-or-D-ceU/contains*-black-boat-body
cell/contains*-north-body A-or-D-cell/contains*-5-gram-body
cell/contains* -1 -tail-body A-or-D-cell/contains*-one-grcy-body
cell/contains*-grcy-3-or-4-or-5-gram-body A-or-D-cell/contains * -body/contains -one-small-black-body
cell/contains * -grey-body/below * -body/next-to* -body A-or-D-cell/conlains*-two-or-three-small-black-bodies
œlVœntains*-circle-body/contains-one-small-black-circle-body A-or-D-ceU/contains*-one-3-or-4-or-5-g ram-white -body
cell/contains*-white-ciicle-body/contains-one-body A-or-D-cell/contains * -one-or-two- white-bodies
cell/contains*-circle-body/contains* -one-body A-or-D-cell/contains*-two-or-three-small-bodies
cell/contains*-two-small-black-circle-bodies A-or-D-cell/contains*-six-or-seven-or-eight-bodies
cell/contains* -four-or-five-circle-bodies A-or-D-ceU/contains*-grey-body/below*-body
cell/contains*-grey-body-&-two-or-lhree-small-black-bodies A-or-D-cell/contains*-circle-body/below-body/next-to-body
6. Future Work
Several restrictions limit the generality of OTIS. Currently, the description language restricts
disjunction and existential quantification and allows no negation, universal quantification or implication.
As a result, there are concepts that cannot be learned because they cannot be expressed. Enhancing the
description language would introduce new problems: increasing the size of the search space, requiring
enhancement of the knowledge representation, complicating the matching process, and requiring new
tasks for creating descriptions that contain the new features of the language.
Another restriction is the perfect information assumption, which assumes that all training examples are
classified correctly, the data contain no errors, no data is missing, and all facts are absolute (no fuzzy
data). OTIS could be modified to tolerate uncertainty by relaxing the requirement that solutions classify
100% of the training examples correctly. This would allow finding concept descriptions which, though
not perfect, would perform classification with high accuracy. The disadvantage is that the search might
be adversely affected since fewer descriptions could be pruned.
Using a Generalization Hierarchy to Learn from Examples 7
OTIS currently cannot learn incrementally but was designed with incremental learning in mind. If new
examples become available they can be integrated into the hierarchy the same as new concept
descriptions. However, the classifying accuracy of existing descriptions might change — some
solutions might become non-solutions and some non-excluders might become excluders. The learning
system would have to decide if tasks on the agenda should be reevaluated or if, in extreme cases, it
might be best to completely start over.
Finally, more research is needed in the area of constructive induction. Additional rules for constructing
new descriptors are needed, but of greater importance is being able to recognize situations in which
these constructive induction rules are likely to be useful. A key limitation of current systems that
perform constructive induction is that many of the descriptors "constructed" are either predefined,
constructed prior to examining a single training example, or constructed regardless of which training
examples are encountered. More valuable, are learning systems capable of extending the description
language during run-time by creating new descriptors whose necessity was not pre-anticipated but
whose creation is triggered by the needs of the current situation.
7. Summary
OTIS learns concepts from structurally described examples by searching through a hypothesis space of
concept descriptions. An agenda controls the search by ranking tasks for creating new descriptions via
specialization, generalization, internal disjunction, and constructive induction. OTIS uses a
generalization hierarchy to store information about the training examples, the concept descriptions
created by the agenda tasks, and knowledge about the components of the description language.
Knowledge provided by the generalization hierarchy avoids unnecessary matching, speeds up matching
by using the delta slot, avoids saving canonically-equivalent descriptions, avoids creating unnecessary
descriptions by blocking slots and focusing on excluders, uses partial descriptions to improve efficiency
and create simpler concept descriptions, and dynamically constructs new relations by counting the
number of matches of multi-valued slots and creating transitive closures of existing relations.
Acknowledgements
I would like to thank Ralph B arietta, Eric Raymond, and Robin Hanson, my colleagues in the machine
learning group, for their ideas and help.
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