Learning
Novel
Concepts
in
the
Kinship
Domain
Daniel
M.
Roy
Computer
Science
and
Artificial
Intelligence
Laboratory
Massachusetts
Institute
of
Technology
Abstract
This
paper
addresses
the
role
that
novel
concepts
play
in
learning
good
theories.
To
concretize
the
discussion,
I
use
Hinton’s
kinship
dataset
as
motivation
throughout
the
paper.
The
standpoint
taken
in
this
paper
is
that
the
most
compact
theory
that
describes
a
set
of
examples
is
the
preferred
theory—an
explicit
Occam’s
Razor.
The
kinship
dataset
is
a
good
testbed
for
thinking
about
relational
concept
learning
because
it
contains
interesting
patterns
that
will
undoubtedly
be
part
of
a
compact
theory
describing
the
examples.
To
begin
with,
I
describe
a
very
simple
computational
level
theory
for
inductive
theory
learning
in
firstorder
logic
that
precisely
states
that
the
most
compact
theory
is
preferred.
In
addition,
I
illustrate
the
obvious
result
that
predicate
invention
is
a
necessary
part
of
any
system
striving
for
compact
theories.
I
present
derivations
within
the
Inductive
Logic
Programming
(ILP)
framework
that
show
how
the
intuitive
theories
of
family
trees
can
be
learned.
These
results
suggest
that
encoding
regular
equivalence
directly
into
the
training
sets
of
ILP
systems
can
improve
learning
performance.
To
investigate
theories
resulting
from
optimization,
I
devise
an
algorithm
that
works
with
a
very
strict
language
bias
allowing
all
consistent
rules
to
be
entertained
and
explicitly
optimized
over
for
small
datasets.
The
algorithm,
which
can
be
viewed
as
a
special
case
implementation
of
ILP,
is
capable
of
learning
a
theory
of
kinship
comparable
in
compactness
to
the
intuitive
theories
humans
use
regularly.
However,
this
alternative
approach
falls
short
as
it
is
incapable
of
inventing
the
unary
predicate
sex
to
learn
a
more
compact
theory.
Finally,
I
comment
on
the
philosophical
position
of
extreme
nativism
in
light
of
the
ability
of
these
systems
to
invent
primitive
concepts
not
present
in
the
training
data.
Introduction
eral
because
of
the
semidecidability
of
first
order
logic,
there
has
been
great
success
at
the
algorithmic
level
in
the
field
of
Inductive
Logic
Programming
(ILP).
The
problem
ILP
ad
The
core
of
the
intuitive
theory
of
kinship
in
western
culture
dresses
is:
learn
a
firstorder
logic
theory
that,
together
with
is
the
family
tree,
from
which
any
number
of
queries
about
provided
background
knowledge,
logically
entails
a
set
of
ex
kinship
relationships
can
be
answered.
Could
a
machine,
pre
amples
(NienhuysCheng
and
de
Wolf,
1997).
sented
with
the
kinship
relationships
between
individuals
in
a
family,
learn
the
intuitive
family
tree
representation?
Using
the
ILP
framework,
it
is
possible
to
show
how
inverse
resolution
can
devise
all
three
of
the
basis
set
predicates
that
This
paper
focuses
heavily
on
a
dataset
introduced
in
Hinton
comprise
the
family
tree
representation.
The
most
interesting
(1986).
In
this
dataset,
a
group
of
individuals
are
related
by
result
is
the
discovery
of
sex
which
requires
that
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 Fall '09
 jenisha
 Artificial Intelligence, Data Mining, Equivalence relation, Binary relation, ILP, compact theory, family tree representation

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