Methods and systems for constructing Bayesian belief networks
Methods and systems are described for simplifying a causal influence model that describes influence of parent nodes X i (i=1, . . . , n) on possible states of the child node Y. The child node Y and each one of the parent nodes X i (i=1, . . . , n) are assumed to be either a discrete Boolean node having states true and false, a discrete Ordinal node having a plurality of ordered states; and a Categorical node having a plurality of unordered states. The influence of each parent node X i on the child node Y is assumed to be a promoting influence and an inhibiting influence. User interfaces are described that incorporate these specific node types.
1. An apparatus for making a probabilistic inference based on a belief network including a child node Y and one or more parent nodes X i (i=1, . . . , n) for the child node Y, the apparatus comprising:
a processing system configured to receive as input one or more parameters of a causal influence model that describes influence of the parent nodes X i on possible states of the child node Y, and convert the parameters of the causal influence model into one or more entries of a conditional probability table, using a creation function;
wherein the child node Y and each of the parent nodes X i (i=1, . . . , n) is one of: a discrete Boolean node having states true and false; a discrete Ordinal node having a plurality of ordered states; and a discrete Categorical node having a plurality of unordered states; and
wherein the influence of each of the parent nodes X i on the child node Y is one of a promoting influence and an inhibiting influence;
wherein said each one of the parent nodes X i has a promoting influence on the child node Y when a true state or a higher level state of the parent node increases the probability of the child node being in the true state or the higher level state;
wherein said each one of the parent nodes X i has an inhibiting influence on the child node Y when a false state or a lower level state of the parent node increases the probability of the child node being in the true state or the higher level state;
wherein the child node Y has a number m of states y k (k=1, . . . , m); and wherein each parent node X i (i=1, . . . , n) has a number m i of states x i j (j=1, . . . , m i );
wherein the n parent nodes X i (i=1, . . . , n) has a number l max of possible configurations X l (l=1, . . . , l max ), where
l
max
=
∏
i
=
1
n
m
i
;
and
wherein x l represents the l-th configuration of the parent nodes X i (i=1, . . . , n) in which each parent node X i (i=1, . . . , n) is in a state x i j (j=1, . . . , m i );
wherein the probability distribution for all possible states of the child node Y comprises a set of values P(y k |x l ), where P(y k |x l ) represents the probability that the child node Y is in the state y k , given that the n parents of Y are in the configuration x l ;
wherein the parameters of the causal influence model comprise at least one of: (i) a baseline probability b k (k=1, . . . , m) for each state y k (k=1, . . . , m) of the child node Y, wherein the baseline probability b k represents a probability that the child node Y is in the state y k when none of the parent nodes X i (i=1, . . . , n) exert any influence on the child node Y; and (ii) a causal influence h ijk (i=1 . . . n; j=1 . . . m i ; k=1 . . . m), wherein the causal influence h ijk represents a change in the probability of the state y k (k=1, . . . , m) of the child node Y, when the i-th parent node X i (i=1, . . . , n) is in a state x i j (j=1, . . . , m i );
wherein the creation function includes a parent influence function V lk , and wherein the parent influence function V lk represents an overall influence of the parent nodes X i (i=1, . . . , n) on a probability P(y k |x l ) that the child node Y is in the state y k given that the parent nodes are in the configuration x l , and wherein the creation function includes a scale factor that keeps all probabilities P(y k |x l ) between 0 and one; and
wherein the parent influence function V lk is a function of the causal influences h ijk ; and
wherein V lk is represented mathematically by:
V lk =f ( h 1 jk ,h 2 jk , . . . , h njk ),
where parent node X i takes on a state x i j in the configuration x l ,
where
∑
k
=
1
m
V
lk
=
0
,
and
where the value of the parent influence function V lk is between −1 and 1.
2. The apparatus of claim 1 , wherein the creation function that converts the parameters of the causal influence model is given by:
P
(
y
k
|
x
l
)
=
{
b
k
+
sb
+
(
V
lk
)
V
lk
≥
0
b
k
-
sb
-
(
V
lk
)
V
lk
<
0
,
wherein b + represents the maximum amount that the baseline probabilities b k (k=1, . . . , m) can be increased, and is represented mathematically by:
b
+
=
1
-
∑
k
=
1
V
lk
≥
0
m
b
k
;
wherein b − represents the maximum amount that the baseline probabilities b k (k=1, . . . , m) can be increased, and is represented mathematically by:
b
-
=
∑
k
=
1
V
lk
<
0
m
b
k
;
and
wherein s is the scale factor, and is represented mathematically by:
s
=
min
(
min
k
(
s
k
)
,
1
)
,
where
s
k
=
{
b
k
l
b
-
V
lk
V
lk
≥
0
V
lk
<
0.