From: AAAI-87 Proceedings. Copyright ©1987, AAAI (www.aaai.org). All rights reserved.
ia
mprovement
ensitivity
ggregatioga
A
Keith L. Downing
of Computer
Department
University
Eugene,
*
and Information
Science
of Oregon
Oregon
97403
Abstract
This research involves
fault relationships
This
paper
system
lays the foundation
that improves
for a diagnostic
its performance
ing symptom-fault
associations
lying
and then utilizes
causal model
tionships
“deep”
to impose
model.
further
symptom-fault
constraints.
Parameter
from
a more
abstract
and a first-principle
of knowledge
those relaupon
1. The
2. The
of physical
of structures
the original
where
both
derlying
recognizes
This
in re-
tom
heuristics
and disease
qualitative
to automated
connections
by
to the causal model.
to support
the ag-
to simplify
of that
expert-system
depen-
ad hoc rules and ill-defined
This
version of Campbell’s
paper
symp-
discusses
(1983) sensitivity
methodology
reasoning
can
by an un-
and useful abstractions
hierarchies.
qualitative
diagnostician
supported
avoids the standard
dence upon shallow,
systems.
two approaches
skill
and parameters
an automated
rational
causal model
model.
plifying
(1987)
This
of diagnostic
model.
this process,
acquire
satisfaction
ysis as a knowledge-compilation
Reiter
that in-
and therapy.
of symptom-fault
use of these associations
Through
Key issues include the roles
models
the acquisition
constraint
gregation
by
directly
and abstraction
of the cir-
of reusing
later diagnosis
derivation
applying
diagnosis by
approach,
the intention
of symptom-
model
into two stages:
the
triggered
are compiled
compilation
fining qualitative
partitions
thus employs both an
in this case “experiences”
from first-principles.
approach
causal representation.
The resulting diagnostician
experiential
an under-
the implicit
this new informat ion then simplifies
forming
to simplify
a set of local
aggregation
with
formation
version of sensitiv-
to extract
information
system
by deriv-
structure
A qualitative
ity analysis is introduced
from
culatory
the compilation
from a mechanical
about
a
anal-
for sim-
complex
physical
systems.
diagnosis:
1. Experiential
methods
fault links distilled
facilitate
direct
symptom-
from human expert
in which
knowledge
quick diagnoses
requiring
little
or no in-
depth causal reasoning.
2. First-principle
reasoning
system models
whereby
explict
“deep”
are used to derive the causal path-
eration
of the experiential
of multiple
fault
only by weak probabilistic
nation
capabilities.
include the gen- often
diagnosis
causal explanations
at the price of extensive
and/or
simulation.
However,
system
that retains its derived
a deep-model
symptom-fault
tions can reduce future diagnostic
ficing explanation
resolvable
means - and limited
First-principle
ment , observable
effort
expla-
provides
reasoning
diagnostic
associa-
without
sacri-
abilities.
*This work was supported by FIPSE grant G008440474-02
a Tektronix Graduate Fellowship.
static
as vascular
Property
from
parameters
resistance
deviations
blood
are partitioned
The former
to blood
constitute
of external
by Pesys-
environ-
into “prop-
represent
the rel-
system
such
flow, or heart strength.
“faults”
factors
and result only
not represented
Hence, they are always independent
eters in causal relationships.
Variables,
in
param-
such as cardiac
flow or atrial pressure shift value either in direct
response to property
changes or indirectly
variable
changes.
pendent
system parameters
“symptoms”
and
In this simulation
values of a real circulatory
the actions
the model.
model developed
serves as the physical
diagnosis.
ert ies” and “variables”.
atively
method
hypotheses
cardiovascular
and Campbell(1985)
t em to undergo
ways from faults to symptoms.
Drawbacks
The quantitative
terson
.
In either
through other
case, they represent
whose deviations
the de-
constitute
In the absence of compensatory
responds
source
to a diagnosis
of super-normal
resistance,
pressed cardiac output
Figure
Figure
1: Basic Circulatory
1 (Peterson
and
the basic circulatory
pumps oxygen-rich
arteries
blood
to the body’s
capillary
this cora common
to account
and elevated
arterial
for de-
pressure.
1985) portrays
Briefly,
through
artery,
Topology
Campbell,
topology.
mechanisms,
of a clogged
the left
the systemic
heart
(body)
beds - - the narrow cap-
Variables
Pronerties
A
illaries
flow.
being
the major
So blood
source of resistance
that exited
to blood
the left heart at a pressure
of approximately
100 mm Hg returns to the right heart
via the systemic
veins at a pressure close to 5 nun Hg.
This carbon-dioxide-laden
the pulmonary
re-oxygenated
After
before
filling
with
closed, thereby
and lungs respectively.
venous
blood,
drastically
electrical
flowing
Although
system
the left
remains
toward
single
and only
lated
constant
varies
highly
the veins
factor
more
blood
system),
venous
mapping
behavior,
compliance
of pressure
then
P =
pressure,
conductance,
P, induced
example,
system.
to voltage
indicates
internal
presflow,
with the pressure
strength.
if P increases
that
elec-
G, outputs
by resistance,
and with pump (heart)
RQ
is a
1983) abstracts
A flow source of maximal
Q varies directly
(Pi, - P),
(regu-
and its load into a simple
sure, PO, and internal
diagnostic
like an
compliances
and flow to current, Figure 2 (Campbell,
the left or right heart
itively,
without
whose changes incur inverse changes to
Using the standard
Q, against
vein
volume is the
in circulatory
have dynamic
by the nervous
model.
P = RQ
Figure 2: Heart Pump
uallitative
3
Load
while
R. Intu-
differential,
As a simple
Q decreases,
R must have increased.
Expert Systems
Sk
Due to the presence of feedback,
of blood
tions,
cardiovascular
in many properties.
straints relating
Hence,
the causal model.
many
of which
causal
testing.
tive sensitivities
reasoning
on properties.
model
Calculated
In Figure
these associa-
and take
(i.e.
symptoms)
quantita-
of variables
as the ratio of partial
differ-
is:
= l/(1 + G *R)
2, this represents
that no other properties
faults after
(1983) introduces
(1)
the system-wide
of P to changes in R under the single-fault
vide useful diagnostic
advantage
to identify
of P to R, for instance,
(aP/P)/(m/R)
have changed.
pointers
un-
the diagnostician
to express the dependence
the sensitivity
con-
to single variables
By uncovering
Campbell
interac-
to changes
a great many implicit
are non-local,
of the highly-constrained
minimal
are sensitive
single properties
derlie
can circumvent
of component
variables
tions,
entials,
via both the cyclic flow
and the bi-directionality
sensitivity
assumption
Sensitivities
pro-
from changing
variables
to their most strongly-coupled
proper-
ties, where a “strong”
790
and Hydraulic
Analysis
blood
compliant
Because active-blood
important
of
inversely
all pressure and flow variables in the circulatory
trical
Constraints
over the short
loops
A
compliance.
crucial property
Heart Pressure
Q = G(Po - P)
and
volume
raising its pressure, thus functioning
most
Output
Pressure
the body
the blood
and pulmonary
capacitor.
PO: Maximal
Q: Cardiac
P: Arterial
enough pressure to open the
or sags to accomodate
stretches
Contractility
through
time span of these events, the amount of “active”
with
G: Heart
Resistance
to the left heart.
low-pressure
developing
in the systemic
Circulatory
with both inflow and outflow valves
valves and send blood
the circulatory
gets pumped
to the lungs, where it becomes
returning
right hearts contract
arterial
blood
arteries
R: Total
sensitivity
has an absolute
value
close to (but
diagnostic
never
ity is its sign.
directly
above)
reasoning,
Does
(positive
sensitivity
In short,
1.
However,
the property
sensitivity
a good
resistance
ities exceed
tem constraints
to “mixed”
Brown,
Next,
1985).
These
to define
a qualitative
assumptions
from mixed
then enable
confluences
ter characterize
state.
a large
from
state
behavior
either -I- or -, and all other property’
1986).
capable
jan,
state’s
with
confluence
assignment
these
are set
terms to
tion of qualitative
a comparison
qualitative
Qwx
(5)
(Thyagara-
The
(7)
aP=aR+aQ
V. Modify
a property
(plant
dG
Apply
Sing&-Fault
(8)
a fault):
t
+
Assumption:
aPotO,aR+-0
Call constraint
VII.
ences
7 and
unique
satisfier
8 and
with simultaneous
instantiated
properties.
confluReceive
a
valid interpretation:
(aQ+, aP+>
Calculate
VIII.
to the previous
values.
mixed confhences
to
to G using
Qualitative
Definition
(dP
collec-
Sensitivities
of both variables
2:
= aG)
+
(QLS(P,G)
+
+)
variable values from each interpreta-
tion serves as a fault-table
is the original
- aP)
(6)
assumptions
technique
of the qualitative
set are found subject
of property-derivative
[x]
0.
confluences:
sensitiv-
derivatives
ambiguities
interpretations
pure
4, 6’4 is set to
Using a constraint-satisfaction
all valid
conji?uences.
OT
dQ=dG+dPo-dp
VI.
of the qualitative
the values of all confluence
of dealing
1987),
to derive
The lat-
enthe (-A+)
q uantity space (Forbus, 1985), QUALSA
counters the ambiguities of qualitative arithmetic (Simmons,
IV. Apply parameter
mapping
qualitative
ities of all variables to a selected property
to 0. By restricting
+, -
assumptions:
and
of the system.
to “pure” confluences.
the dynamic
to mixed
whether
Po>P,G>O,Q>O,R>O
a set
assumptions
a one-to-one
Now, to test the system-wide
parameter
all sys-
(De Kleer
a set of parameter
III. Make
sensitiv-
(QUALSA) extracts
information
confluences
of x,
aP=BR*[Q]+[R]*dQ
exploits
might be down, or the
analysis
diagnostic
and transform
the sign
8Q = aG * [PO - P] + [G] * (aP,
pressure is
QUALSA begins by converting
of constraints.
is created
reasoning
“If the arterial
needs while charging
sensitivity
the necessary
represents
(negative
cost.
Qualitative
II. Digerentiate
close to 0 )?
might be up.” Quantitative
informational
computational
most
the variable
inversely
deal of diagnostic
information:
up, then the vascular compliance
only
affect
value),
value) or not at all (sensitivity
only qualitative
arterial
during
the salient aspect of any sensitiv-
setting
of aX
4
defined
applied
Figure
2, QUALSA
equations
variables
= (P,
a
IX.
Repeated
single-fault
calls to the constraint
assumption
II
ifaX=&
-
ifdX#b4anddX#O
0
ifdX=O
aQ+
(2)
890
aQ-
Picat ion
cardiovascular
Table
model
of
as follows:
with properties
=
X.
Calculate
case remain
(G,
Po,
dG+
R)
and
turned
fault
I
I
dP-
1
the
high
nil
nil
nil
1: Faults indexed
II
3R-
nil
dR+
all qualitative
under
faulted
table:
I aP0
or aPo+
unambiguous
satisfier
with each property
aP+
I
to the abstract
I. Initial
X yields
* (QLS(Q, G) + +)
and low yield a complete
+
proceeds
PQ = =>
x
as:
A
When
for &$ = x, where
For each interpretation,
to a4 for any variable
sensitivity
4) =
index
of a4.
nil
aG-
or ZIP,-
by symptoms
sensitivities
, which
over the 6 interpretations
by the 6 calls- to the constraint
in this
Te-
satisfier:
Q)
Q=G*(PO--P)
(3)
Table
2: Qualitative
Sensitivities
Downing
791
5
Ambiguities
The ambiguity
of qualitative
abundance
of interpretations,
conflicting
sensitivities
arithmetic
often spurns an
any two of which will have
QLS(X,
4 ,Il)
and QLS(X,
for at least one variable X and property
tative
sensitivities
dition,
selected
are sometimes
properties
&
indeterminate.
to + or - and run through
mapping
fault
table.
interpretations
erty
setting
ping,
(fault)
backward
QUALSA.
This
for a single prop-
to a many-to-one
no additional
causal reasoning
in-
of indices to faults in the
contribute
but this creates
one or
when individually
creates a one-to-many
Multiple
In ad-
and ~$2 can yield
more of the same interpretations
stantiated
4,12)
Table 4: Aggregated
diagnosis
containing
localized
tolic( “filling”)
a more detailed
ther
similarities
similarities,
heart,
cardiovascular
in their
induced
aggregation.
strength
Let
P and Q. In
model
reveals fur-
sensitivities.
along with their common
make PO and G excellent
plifying
variables
Only
is
shift to the level of PO
such as the left
between
fault
if the fault
heart’s
blood
the two primitive
dias-
volumes
faults.
to diagnosis.
effects upon variables
fact,
R.
for the
that G and PO have
of Table 2 indicate
in the abstracted
H and
and systolic( “emptying”)
will discriminate
the strong
location,
candidates
H represent
These
the left
for a sim-
a general
heart
from
multiple-fault
0 to n faults,
properties)
(+,-,
sumption,
(9)
(i.e.
and 0).
generated.
Normally,
interpretations
set-
the single-property
where
containing
returned
this
to test
of property-derivative
But under
only the confluences
The
covers
of model’
satisfier
only 3n such calls are required,
call involves
con-
a “com-
one that
3n calls to the constraint
call are then intersected
H=G*Po
derivative,
n is the number
the affects of all combinations
tings
that no confluence
table
where
can be efficiently
would require
property.
and define it as:
assumption
than a single property
prehensive”
qualitative
can proceed
only
to H will granularity
and G, where
Under
The sensitivities
Table
map-
ambiguity
indigenous
Now,
space
tains more
identical
Sensitivity
4. Hence, quali-
aseach
a specified
from each such
with the interpretations
other calls to create indices into the comprehensive
from
fault
table.
Under the assumptions:
For example,
G > 0,Po
property
> 0
Equations
derivatives.
dH
steps II-IV
of QUALSA
produce
the pure confluence:
dH=dG+aPo
Substituting
stitution
Equation
in qualitative
10 into Equation
arithmetic
1986) since the coefficient
Equation
(10)
7, a legal sub-
aQ=aH-BP
QUALSA
generate
(11)
(two for each property,
steps V-VIII
simplified
1SETl
=
H and R) of
to confluence Equations
fault and sensitivity
tables:
dP+
i3H+
a90
aQTable
dP0
ap-
nil
nil
nil
aRnil
dR+
nil
tlH-
3: Aggregated
Fault Table
11 to the constraint
{(aP+,
a$-),
Next,
Expert Systems
satisfier cre-
(W+,
aQo),
(aP+,
aQ+)l
aQ+)
(12)
let:
and pass Equation
4 to the constraint
satisfier.
This
returns:
11 and 8
mxr2
=
{(dp-,
After
p-,~Qo),
(dp-,
aQ+), Cap+, aQ+>l
intersecting
ISETS
ag-),
ISETl
=
and ISET
{(a-,
W+,
use each of the three ISETS
for the double fault (aH+
792
+
set:
(=P
aQ+
t
@PO, aQ+), (a-,
(De Kleer and Brown,
of G * PO is the same in both
9 and 3 , yields:
Four applications
and passing Equation
ates interpretation
11 and 8 have only single
Setting:
aQ+),
aQ+>l
aQ+),
(13)
to yield:
W’O,
interpretations
and dR-).
aQ+),
(14)
as an index
INTERNIST-II
By
The
nature
only
local behavioral
ficiently.
of complex
QUALSA
to uncover
between
systems
knowledge
exploits
implicit
properties
them
or similar
structure,
minism
exceeds
I expect
the forand in
“causal”
lationships.
serve only
(Simmons,
QUALSA
with QUALSA
connections
But
as convenient
(no
such as human
QUALSA-derived
the high-level
Also, QUALSA
of empirical
for previously-overlooked
than treating
formation,
diagnosis
generate
Campbell
alterations
to data analysis
associations
can fortify
in-
processes
the drastic
no function
sensitivities
iors of structurally
the behavioral
and their
of locality
in structure)
similar models
from
modelling.
the behav-
and thereby
local
gen-
capture
adjust-
constraints
en-
are well suited
systems.
to supporting
can suggest structural
an understanding
among
In short, sensitivities
capabilities.
more
of minor structural
derivation
of evolving
more organized
(and
for robust
can discriminate
ramifications
hances robustness.
In addition
sensitivity
to the com-
while de Kleer and Brown (1983) have
the importance
systems
rather
as second-class
the inductive
(1983) has detailed
erally,
diagnostic
It can
by provid-
In short,
incurred by minor modifications
Thus,
for models
may inspire a
them.
topology,
illustrated
outputs
data in search of support
causal expectations.
empirical
results.
models used, but
causal relationships.
control
QUALSA
to sup-
a true integra-
is derived both experientially
re-interpretation
ing well-founded
by using
associations
empirically,
and analytically.
thus add top-down
of causal
in complex
Bather,
and experiential
information
structural
abstractions
These
understanding
recognized
changes,
sensi-
to strengthen
aggregations
embody
a
of the modeled
system -
and implemented
in diag-
such as ABEL(Pati1
that unites
experien-
for their mutual
en-
I owe a special thanks to Nils Peterson, whose original version
of qualitative sensitivity analysis inspired a deeper investigation into its implications for diagnostic reasoning, knowledge
compilation and aggregation. Also, I must thank P. Thyagarajan for his constraint satisfier.
His ideas, along with
those of Art Farley, Steve Finer and Nils fueled our initial
discussions of qualitative reasoning and diagnosis. My greatest debt is to my advisor, Sally Douglas, whose relentless criticism and encouragement have guided me through not only
this research but most of my graduate experience.
re-
deep)
of real systems;
Not only are both deep and high-level
nostic
how
especially
symptom-fault
tion of first-principle
tivities
ordinal
matter
physiology.
port or refute those obtained
ments;
needs of a di-
abstractions
observations,
learning
techniques
shift from subjec-
cannot entirely replace the induction
domains
ponent
1986)
this nondeter-
to more objective
deep models
rules from empirical
that
empiri-
venous pressure, and
empirical-knowledge
equipped
diagnostic
of
of
basis
considerably.
agnostician
externally.
from
richment.
in both
to reduce
self-contained
and
1982) but supplied
within, the integration
exhibits
a theory
aggregation
tial and first-principle
to simulation
lattice
QUALSA
(Pople,
structure
meth-
By exploiting
in a quantity
The background
tive
ef-
such as the fact that arterial
greatly
organizing
ambiguity
reasoning.
relationships,
pressure normally
Its qualitative
of quantitative
indigenous
diagnostic
faults
constraints
both local and global,
complexities
ods at the cost of increased
cal ordinal
to diagnose
and variables.
ward causal reasoning
the use of
local behavioral
interactions,
avoids the algebraic
backward
precludes
deriving
et.
al, 1982) and
Campbell, Kenneth, The Physical Basis of the Problem
Environment in Cardiovascular Diagnosis, January,
1983, unpublished.
De Kleer, J. and Brown, J.S., Assumptions and Ambiguities in Mechanistic Mental Models , in: D. Centner
ad AS. Stevens (Eds.)
Mental Models
(Erlbaum,
Hillsdale, NJ, 1983) 155 - 199.
De Kleer, J. and Brown, J.S., Theories of Causal Ordering, Artificialal Inte&gence 29(l), 1986.
Forbus, K.D., Qualitative Reasoning About
Processes, Artificial Intelligence 24, 1984.
Physical
Peterson, Nils S. and Campbell, Kenneth B., Teaching
Cardiovascular Integrations with Computer Laboratories ,The Physiologist
, Vol. 28, No. 3, 1985.
Patil, Ramesh, Peter Szolovits and William Schwartz,
Modeling Knowledge of the Patient in Acid-Base and
Electrolyte
Disorders,
in Artificial
Intelligence
in
Me&&e,
ed. Peter Szolovits, Westview Press, 1982.
Pople, Harry E. Jr., Heuristic Methods for Imposing
Structure on Ill-structured Problems: The Structuring of Medical Diagnosis, in Artifkial
Intelligence
in
Medicine, ed. Peter Szolovits, Westview Press, 1982.
Reiter, Raymond, A Theory of Diagnosis from First
Principles, Univ. of Toronto, Tech Rep. No.187/86, to
appear in Artifkid
Intelligence 1987.
Simmons, Reid, “Commonsense” Arithmetic Reasoning, Proceedings of the Fifth iVationa1 Conference
on
Artificial Intelligence
, 1986.
Thyagarajan, P.,forthcoming master9s thesis, The Univ.
of Oregon, 1987, unpublished.
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Artificial Intelligence
9 30(l), 1986.
Downing
793