JP2008293199A - Bayesian network information processing device and bayesian network information processing program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily set up conditional probability for random variable assigned to a node of Bayesian network information. <P>SOLUTION: A parameter setting part 6 inputs the structure information for the Bayesian network information, in which multiple parent nodes exist to one child node, by input operation to a structure input part 2, and sets up, by the input operation to a setting information input part 3, a prior probability to the node not having the parent node, upper and lower limit values for the conditional probability with respect to the child node having the parent node, and degree of contribution which is the degree of influence of each of the parent nodes to the child node existent to one child node by the input operation to the setting information input part 3. Based on the structure information, the prior probability value, the upper and the lower limit values and the degree of the contribution, a parameter calculation part 12 of a parameter setting part 6 calculates the conditional probability which is the parameter for the child node. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a Bayesian network information processing apparatus and a Bayesian network information processing program that perform information processing related to Bayesian network information.

  Conventionally, Bayesian network information is one type of information that models causal relationships between random variables. Specifically, Bayesian network information assigns random variables to the nodes of the directed graph, expresses the presence or absence of causal relationships between the random variables by arrows between the nodes, and the random variables assigned the strength of the causal relationship to each node It is expressed by the conditional probability of. That is, in the Bayesian network information, the causal relationship between random variables is expressed by structural information on the Bayesian network information and parameters that are probability information (see, for example, Patent Document 1).

  In addition, Bayesian network information not only represents the static causal relationship between random variables, but also the occurrence probability of each value taken by other random variables when the event of a certain node, that is, the value of the random variable is fixed. It is also possible to express dynamic causal relationships such as probabilistic reasoning to find

By using such a technique, Bayesian network information has an advantage that it is easy for a human to intuitively understand the causal relationship between random variables because the causal relationship between random variables is expressed by a directed graph.
JP 2005-107747 A

  When constructing the Bayesian network information described above based on the subjectivity of an expert, it is necessary to effectively extract knowledge about the target area from the expert and determine the structure and parameters of the Bayesian network information. In this regard, it is difficult for an expert to directly ask or set the value of a conditional probability that is a parameter if the expert is not familiar with probability theory. In addition, the larger the scale of the Bayesian network information, the more time is required for this setting.

  Accordingly, an object of the present invention is to provide a Bayesian network information processing apparatus and a Bayesian network information processing program capable of easily setting a conditional probability of a random variable assigned to a node of Bayesian network information. .

  That is, the Bayesian network information processing apparatus according to the present invention includes a plurality of nodes associated with random variables of Bayesian network information taking two values, and Bayesian network information taking two values using the plurality of nodes as parent nodes. Input the structure information consisting of a single child node associated with the random variable of the parent, the prior probability value of the parent node of the input structure information, the upper and lower limit values of the conditional probability of the child node, and the child node of the parent node Relative contribution degree is set, and conditional probabilities of child nodes are calculated based on these.

  According to the present invention, it is possible to easily set a conditional probability of a random variable assigned to a node of Bayesian network information.

  Embodiments of the present invention will be described below with reference to the drawings.

(First embodiment)
First, a first embodiment of the present invention will be described.
FIG. 1 is a block diagram showing an example of a Bayesian network information parameter setting device according to the first embodiment of the present invention.

  As shown in FIG. 1, a Bayesian network information parameter setting device 1 according to a first embodiment of the present invention includes a structure input unit 2, a setting information input unit 3, an output display unit 4, a storage device 5, and a parameter setting unit. 6 is provided.

  The structure input unit 2 and the setting information input unit 3 are, for example, a keyboard and a mouse. Among these, the structure input unit 2 includes a structure information input unit that receives an input of the structure of Bayesian network information that is a parameter setting target. The setting information input unit 3 includes a probability information input unit that receives input of information for setting parameters, a relative ratio input unit, a conditional probability first input unit, and a probability second input unit.

  The output display unit 4 is, for example, a display device that displays information on the structure and parameters of Bayesian network information.

  The storage device 5 is a storage medium such as a hard disk drive or a non-volatile memory, and stores a control program to be executed by the parameter setting unit 6. The storage device 5 also functions as a work memory.

  The parameter setting unit 6 sets parameters of Bayesian network information based on the input information from the structure input unit 2 and the setting information input unit 3.

  The parameter setting unit 6 includes a structure analysis unit 11 and a parameter calculation unit 12. The structure analysis unit 11 is a decomposing unit that analyzes the structure of the input Bayesian network information and performs conversion into a subnetwork as shown in FIG. The parameter calculation unit 12 is calculation means for calculating parameters of Bayesian network information.

  Next, an overview of Bayesian network information will be described. The Bayesian network information associates a random variable with a node, and expresses a causal relationship between the random variables with an arrow between the nodes and a conditional probability given to the node. That is, the Bayesian network information includes “structure information” expressed by a node and an arrow between the nodes, and “parameter” that is a conditional probability given to each node on the Bayesian network information.

FIG. 2 is an example of Bayesian network information, showing the causal relationship between various physical symptoms and influenza.
The Bayesian network information shown in FIG. 2 is Bayesian network information that shows the causal relationship between various physical symptoms such as “headache”, “abdominal pain”, and “fever” and the disease “flu”. Each node in the Bayesian network information is assigned a random variable indicating an event such as the presence or absence of a physical symptom or the presence or absence of influenza. A random variable is a variable that takes different values based on the probability.

  Specifically, four nodes are shown in the Bayesian network information shown in FIG. The first node shows a random variable of headache, the second node has abdominal pain, the third node has fever, and the fourth node has influenza. The value of the random variable of the first to third nodes is either “Yes” or “No”, and the value of the random variable of the fourth node is either “Yes” or “No”. is there. “Yes” or “YES” means that a physical symptom or illness corresponding to a random variable has developed, and “No” or “No” means that a physical symptom or illness corresponding to a random variable has not occurred. Means.

  Further, in this Bayesian network information, the presence or absence of a causal relationship between random variables is expressed by connection of arrows, and the strength of the causal relationship is expressed by a conditional probability given to a node. Here, the notation Pr (A = a) means the probability that the random variable A takes the value a. By performing such modeling, a static relationship between random variables can be expressed. In addition, when the value of a random variable becomes clear for a certain node in the Bayesian network information, probabilistic inference is possible in which the occurrence probability of the value taken by another random variable is inferred.

The first to third nodes shown in FIG. 2 are connected to the fourth node along the arrow. This is because the probability that the random variable of the fourth node takes a certain value is the value that the random variable of the first node takes, the value that the random variable of the second node takes, and the third node Means that it depends on the value taken by the random variable. In such a case, the first to third nodes are called parent nodes of the fourth node, and the fourth node is called a child node of the first to third nodes. Can do.
That is, when there is an arrow from one node to the other node, between the two nodes, the aforementioned one node is called a parent node and the other node is called a child node.

In the Bayesian network information shown in FIG. 2, the probability Pr (headache = present) of developing a headache is 0.1, and the probability Pr (headache = none) of not developing a headache is 0.9.
Further, the probability Pr (abdominal pain = present) of developing abdominal pain is 0.05, and the probability Pr (abdominal pain = no) of not developing abdominal pain is 0.95. The probability Pr of developing fever (fever = present) is 0.03, and the probability Pr of not generating fever (fever = none) is 0.97.

  Further, as shown in FIG. 2, the probability Pr of developing influenza when all symptoms of headache, abdominal pain and fever are observed (influenza = Yes | headache = yes, abdominal pain = yes, fever = yes) is 0.9. The probability Pr (influenza = No | headache = no, abdominal pain = no, fever = no) of not developing influenza when no symptoms of headache, abdominal pain and fever are observed is 0.99.

Next, the notation used in Bayesian network information will be described. In the following description, it is assumed that the node name also serves as a random variable. For example, node A means a node whose random variable is A. The random variable A is assumed to take A = {a ₁ , a ₂ ,..., A _P } as a domain. The value shown in the domain is the value that the random variable takes according to the probability. For example, when the probability variable A represents the truth of a proposition, the number of domain values is 2, and a ₁ = ¬a ₂ holds. a ₁ = ¬a ₂ means that negation of a ₂ is equal to a ₁ .

Further, the relationship between Σ _A Pr (A) and the probability that the random variable A takes each value in the above-described domain is expressed by the following formula (1).
Σ _A Pr (A)
= Pr (A = a ₁ ) + Pr (A = a ₂ ) +... + Pr (A = a _P ) = 1 (1)
In the present embodiment, only a random variable having two values as a domain is handled.

FIG. 3 is a diagram illustrating a first example of a relationship between a parent node and a child node in Bayesian network information.
In the example illustrated in FIG. 3, the node P ₁ , the node P ₂ , the node P ₃ ,..., The node P _n are the parent nodes of the node C.
Node _{P 1, P 2,} ... _{P n} prior probability of _{Pr (P 1), Pr (} P 2), ..., if a Pr _{(P n),} i.e. the node _{P 1, P 2,} ... with the _{P n} When the random variables P ₁ , P ₂ ,... P _n take a certain value, the conditional probability that the random variable C of the node C takes a certain value is Pr (C | P ₁ , P ₂ ,..., P _n ). It becomes.

The purpose of this embodiment is to set these parameters. Since the random variable handled in this embodiment is binary, it is assumed here that the random variable C = {1, 0} and the random variable P _i = {1,0] for convenience, and the occurrence probability of the random variable C = 1. Those that increase are set to P _i = 1, and those that increase are set to P _i = 0. That is, the following formula (2) is established.

Pr (C = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _i = 1,..., P _n = p _n )
> Pr (C = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _i = 0,..., P _n = p _n ) (2)
However, random variables other than P _i are fixed on the right and left sides of Equation (2).

  FIG. 4 is a diagram illustrating a second example of a relationship between a parent node and a child node in Bayesian network information. FIG. 5 is a diagram illustrating an example in which a set of a parent node and a child node in a second example of the relationship between the parent node and the child node in the Bayesian network information is divided.

  In the example illustrated in FIG. 4, the node “1”, the node “2”, and the node “3” are parent nodes of the node “4”. Node “2” is a parent node of node “3”. Nodes “3” and “4” are parent nodes of node “5”. Node “5” is a parent node of node “6”. Node “6” is a parent node of node “7”. Node “7” is a parent node of node “8”. Node “7” is a parent node of node “9”. Nodes “9” and “11” are parent nodes of node “10”.

In order to perform parameter setting for the entire Bayesian network information, parameter setting is performed for a sub-network composed of a plurality of parent nodes and one child node as shown in FIG. 5, and this is repeatedly applied to the entire network. .
For example, when the structure of the Bayesian network information is the structure shown in FIG. 4, the portion surrounded by the dotted line is decomposed into a plurality of independent sub-networks as shown in FIG. You only need to make settings.

Next, the operation of the Bayesian network information parameter setting device configured as shown in FIG. 1 will be described. FIG. 6 is a flowchart showing an example of the processing operation of the Bayesian network information parameter setting device according to the first embodiment of the present invention.
FIG. 7 is a diagram showing an example of Bayesian network information input by the Bayesian network information parameter setting device according to the first embodiment of the present invention.
First, when the Bayesian network information having the structure shown in FIG. 7 is input by the input operation to the structure input unit 2, the parameter setting unit 6 stores this information in the storage device 5 (step S1). In this embodiment, it is assumed that there are a plurality of parent nodes that exist for one child node.
Then, the parameter setting unit 6 sets a prior probability for a node that does not have a parent node by an input operation on the setting information input unit 3.
In the example shown in FIG. 7, nodes P ₁ , P ₂ , and P ₃ exist as nodes that do not have a parent node. Therefore, the parameter setting unit 6 sets the prior probability values Pr (P ₁ ), Pr (P ₂ ), and Pr (P ₃ ) for each node by an input operation on the setting information input unit 3 (step S2). ).

FIG. 8 is a diagram showing, in a tabular form, the probabilities related to the parent node of Bayesian network information input by the Bayesian network information parameter setting device according to the first embodiment of the present invention.
As shown in FIG. 8, in this embodiment, the probability random variables _{P 1} of the node _{P 1} takes the "1" Pr _(P 1 = 1) is 0.8, the random variable _{P 1} of the node _{P 1} is The probability Pr (P ₁ = 0) of taking “0” is 0.2.
Further, as shown in FIG. 8, in the present embodiment, the node _P probability Pr _(P 2 = 1) ₂ of the random variable _{P 2} takes the "1" is 0.3, node _{P 2} of a random variable P _The probability Pr (P ₂ = 0) that ₂ takes “0” is 0.7.
Further, as shown in FIG. 8, in the present embodiment, the node _P probability random variables _{P 3} of ₃ takes the "1" Pr _(P 3 = 1) is 0.5, the random variable P node _{P 3 The} probability Pr (P ₃ = 0) that ₃ takes “0” is 0.5.
If the nodes P ₁ , P ₂ , and P ₃ shown in FIG. 7 further have a parent node, the nodes P ₁ , P ₂ , and P ₃ may be considered as child nodes.

Next, the parameter setting unit 6 sets the upper and lower limit values of the conditional probability Pr (C = 1 | P ₁ , P ₂ ,..., P _n ) relating to the child node having the parent node, that is, The maximum value and the minimum value are set by an input operation to the setting information input unit 3 (step S3).
The upper limit value is the probability when all the conditions are improved, that is, when P ₁ = 1, P ₂ = 1,..., P _n = 1, and the lower limit value works in the direction where all the conditions are bad. In other words, P ₁ = 0, P ₂ = 0,..., P _n = 0.

Here, when the child node is the node C and the parent node is the nodes P ₁ , P ₂ ,..., P _n , the upper limit value C _max of the probability value is expressed by the following equation (3), and the lower limit The value C _min is expressed by the following formula (4).
C _max = Pr (C = 1 | P ₁ = 1, P ₂ = 1,..., P _n = 1) (3)
C _min = Pr (C = 1 | P ₁ = 0, P ₂ = 0,..., P _n = 0) (4)
A combination of the upper limit value C _max and the lower limit value C _min is, for example, “C _max = 1, C _min = 0.05” or “C _max = 0.95, C _min = 0.1”.

  FIG. 9 is a table showing an example of the upper and lower limit values of probabilities related to child nodes of Bayesian network information input to the Bayesian network information parameter setting device according to the first embodiment of the present invention.

As shown in FIG. 9, in the present embodiment, random variables P ₁ of the node P _1, random variables P ₃ of a random variable P ₂ and node P ₃ of the node P ₂ is to take "1" either, node The probability that the random variable C of C takes “1” is the upper limit value C _max = 0.95.
Further, in the present embodiment, the node random variables _{P 1} of _{P 1,} if the random variable _{P 3} of a random variable _{P 2} and node _{P 3} of the node _{P 2} is to take a "0" Both, node C of random variables C Is the lower limit C _min = 0.05.
The upper and lower limit values may be determined for each child node, or the same value may be used for the entire Bayesian network information.

Next, the parameter setting unit 6 sets a contribution degree, which is the degree of influence of each parent node existing on one child node, on the input operation to the setting information input unit 3 (step S4). .
The contribution is the relative ratio of the influence of the parent node on the child nodes. When the contribution degree of the parent node P _{i to} the child node C is R _i , if all the parent nodes have the same contribution degree, the contribution degree of each parent node is expressed by the following formula (5). If the P ₁ has a multiple of the contribution to other nodes, the contribution of each parent node is expressed by the following equation (6).
_{R 1: R 2: ...:} R n = 1: 1: ...: 1 ... formula (5)
_{R 1: R 2: ...:} R n = 2: 1: ...: 1 ... (6)
FIG. 10 is a diagram illustrating an example of a contribution degree of a parent node to a child node of Bayesian network information input by the Bayesian network information parameter setting device according to the first embodiment of the present invention.
As shown in FIG. 10, in this embodiment, the contribution R ₁ of the parent node P _{1 to} the child node C is “6”, and the contribution R ₂ of the parent node P _{2 to} the child node C is “2”. The contribution R ₃ of the parent node P _{3 to} the child node C is “1”.

The parameter calculation unit 12 of the parameter setting unit 6 includes the structure information of the Bayesian network information input in step S1, the prior probability value input in step S2, the upper and lower limit values input in step S3, Based on the contribution level input in the process of step S4, the conditional probability of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node is expressed by the following equation (7). Conditional probabilities Pr (C | P ₁ , P ₂ ,..., P _n ) based on combinations other than the above-described upper limit value and lower limit value are calculated (step S5).

Pr (C = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _n = p _n )
= C _min + Σ _i (p _i × T _i ) (7)
Further, Expression (7) is equal to the following Expression (8).

Pr (C = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _n = p _n )
= C _max −Σ _i {(1−p _i ) × T _i } Equation (8)
Further, T _i in the equations (7) and (8) is expressed by the following equation (9).

T _i = (C _max −C _min ) × R _i / (Σ _i R _i ) (9)
Since the random variable is assumed to be binary here, the following equation (10) is established.

Pr (C = 0 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _n = p _n )
= 1−Pr (C = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _n = p _n ) (10)
FIG. 11 is a table showing an example of conditional probabilities related to child nodes of Bayesian network information input by the Bayesian network information parameter setting device according to the first embodiment of the present invention.

Parameter calculating unit 12 is set prior probability value of the parent node P _1, P _2, P ₃ as described above, the upper and lower limit values are set, if the contribution is set, the parent node P of T _i the _{T 1} about ₁ computed as shown in equation (11) below.
T ₁ = (C _max −C _min ) × R ₁ / (Σ _i R _i )
= (0.95-0.05) x 6/9
= 0.9 x 6/9
= 0.6 Equation (11)

Further, the parameter calculation unit 12 calculates T ₂ related to the parent node P ₂ among T _i as shown in the following formula (12).
T ₂ = (C _max −C _min ) × R ₂ / (Σ _i R _i )
= (0.95-0.05) x 2/9
= 0.9 x 2/9
= 0.2 Formula (12)

Further, the parameter calculation unit 12 calculates T ₃ related to the parent node P ₃ among T _i as shown in the following formula (13).
T ₃ = (C _max −C _min ) × R ₃ / (Σ _i R _i )
= (0.95-0.05) x 1/9
= 0.9 × 1/9
= 0.1 Formula (13)

Then, the parameter calculating unit 12, they calculated _{T 1, T 2, T 3} and Equation (7) based on the node random variables _{P 1} of _{P 1,} node _{P 2} of a random variable _{P 2} are both " take 1 ", the probability Pr _(C = 1 the random variable C of the node C when the random variable _{P 3} of the node _{P 3} takes the" 0 "takes" 1 _{"| P 1 = 1, P 2} = 1, P ₃ = 0) is calculated as shown in equation (14) below.
Pr (C = 1 | P ₁ = 1, P ₂ = 1, P ₃ = 0)
= C _min + Σ _i (P _i × T _i )
= 0.05 + (1 × 0.6 + 1 × 0.2 + 0 × 0.1)
= 0.05 + 0.8
= 0.85 Formula (14)

The parameter calculation unit 12, the calculation result and equation (10) based on the node _P random variables _{P 1 1,} taken together are random variables _{P 2} nodes _{P 2} "1", the node _{P 3} random variable _{P 3} is a random variable C of the node C when taking "0" is "0" probability _Pr taking _{(C = 0 | P 1 =} 1, P 2 = 1, P 3 = 0) the following Calculate as shown in equation (15).
Pr (C = 0 | P ₁ = 1, P ₂ = 1, P ₃ = 0)
= 1-Pr (C = 1 | P ₁ = 1, P ₂ = 1, P ₃ = 0)
= 1-0.85
= 0.15 (15)

Further, the parameter calculation unit 12 calculates Pr (C = 1 | P ₁ = 1, P ₂ = 1, P ₃ = 0) based on T ₁ , T ₂ , T ₃ and Expression (8) below. It can also be calculated as shown in equation (16).
Pr (C = 1 | P ₁ = 1, P ₂ = 1, P ₃ = 0)
= C _max −Σ _i {(1−P _i ) × T _i }
= 0.95- (0x0.6 + 0x0.2 + 1x0.1)
= 0.95-0.1
= 0.85 Formula (16)

Further, the parameter calculation unit 12 takes “1” as the random variable P ₁ of the node P ₁ based on T ₁ , T ₂ , T ₃ and Expression (7) calculated as described above. ₂ of a random variable _{P 2} takes a "0", the node probability Pr (C = 1 the random variable _{P 3} of _{P 3} is a random variable C of the node C when taking "1" takes "1" | _{P 1} = 1, P ₂ = 0, P ₃ = 1) is calculated as shown in the following equation (17).
Pr (C = 1 | P ₁ = 1, P ₂ = 0, P ₃ = 1)
= C _min + Σ _i (P _i × T _i )
= 0.05 + (1 × 0.6 + 0 × 0.2 + 1 × 0.1)
= 0.05 + 0.7
= 0.75 Formula (17)

The parameter calculation unit 12, the calculation result and equation (10) based on the probability variables P ₁ of the node P ₁ takes a "1", the random variable P ₂ of the node P ₂ is "0" taken, the node probability random variables C of the node C when the random variable _{P 3} of _{P 3} takes the "1" take "0" _{Pr (C = 0 | P 1} = 1, P 2 = 0, P 3 = 1) is calculated as shown in equation (18) below.
Pr (C = 0 | P ₁ = 1, P ₂ = 0, P ₃ = 1)
= 1-Pr (C = 1 | P ₁ = 1, P ₂ = 0, P ₃ = 1)
= 1-0.75
= 0.25 Formula (18)

Further, the parameter calculation unit 12 takes “1” as the random variable P ₁ of the node P ₁ based on T ₁ , T ₂ , T ₃ and Expression (7) calculated as described above. the probability variable C of the node C when the random variable _{P 3} of the _second random variable _{P 2} and node _{P 3} are both take "0" takes "1" _{Pr (C = 1 | P 1} = 1, P 2 = 0, P ₃ = 0) is calculated as shown in the following equation (19).
Pr (C = 1 | P ₁ = 1, P ₂ = 0, P ₃ = 0)
= C _min + Σ _i (P _i × T _i )
= 0.05 + (1 × 0.6 + 0 × 0.2 + 0 × 0.1)
= 0.05 + 0.6
= 0.65 ... Formula (19)

The parameter calculation unit 12, the calculation result and equation (10) based on the probability variables _{P 1} of the node _{P 1} takes a "1", the node _{P 2} random variable with _{P 2} and node _{P 3} The probability Pr (C = 0 | P ₁ = 1, P ₂ = 0, P ₃ = 0) that the random variable C of the node C takes “0” when both the random variables P ₃ take “0” is as follows: Calculate as shown in equation (20).
Pr (C = 0 | P ₁ = 1, P ₂ = 0, P ₃ = 0)
= 1-Pr (C = 1 | P ₁ = 1, P ₂ = 0, P ₃ = 0)
= 1-0.65
= 0.35 ... Formula (20)

Further, the parameter calculation unit 12 takes “0” as the random variable P ₁ of the node P ₁ based on T ₁ , T ₂ , T ₃ and Expression (7) calculated as described above. the probability variable C of the node C when the random variable _{P 3} of the _second random variable _{P 2} and node _{P 3} are both take "1" takes "1" _{Pr (C = 1 | P 1} = 0, P 2 = 1, P ₃ = 1) is calculated as shown in the following equation (21).
Pr (C = 1 | P ₁ = 0, P ₂ = 1, P ₃ = 1)
= C _min + Σ _i (P _i × T _i )
= 0.05 + (0 × 0.6 + 1 × 0.2 + 1 × 0.1)
= 0.05 + 0.3
= 0.35 ... Formula (21)

The parameter calculation unit 12, the calculation result and equation (10) based on the probability variables P ₁ of the node P ₁ takes the "0", the random variable P ₂ of the node P ₂ is "0" taken, the node _{P 3} probability random variables C of the node C when the random variable _{P 3} are both take "1" take "0" _{Pr (C = 0 | P 1} = 0, P 2 = 1, P 3 = 1) is calculated as shown in equation (22) below.
Pr (C = 0 | P ₁ = 0, P ₂ = 1, P ₃ = 1)
= 1-Pr (C = 1 | P ₁ = 0, P ₂ = 1, P ₃ = 1)
= 1-0.35
= 0.65 ... Formula (22)

Further, the parameter calculation unit 12 takes “0” as the random variable P ₁ of the node P ₁ based on T ₁ , T ₂ , T ₃ and Expression (7) calculated as described above. ₂ of a random variable _{P 2} takes a "1", the node probability Pr (C = 1 the random variable _{P 3} of _{P 3} is a random variable C of the node C when taking "0" takes "1" | _{P 1} = 0, P ₂ = 1, P ₃ = 0) as shown in the following equation (23).
Pr (C = 1 | P ₁ = 0, P ₂ = 1, P ₃ = 0)
= C _min + Σ _i (P _i × T _i )
= 0.05 + (0 × 0.6 + 1 × 0.2 + 0 × 0.1)
= 0.05 + 0.2
= 0.25 Formula (23)

The parameter calculation unit 12, the calculation result and equation (10) based on the probability variables P ₁ of the node P ₁ takes the "0", the random variable P ₂ of the node P ₂ is "1" taken, the probability _Pr (C = 0 of the random variable _{P 3} of the node _{P 3} has a random variable C of the node C when taking "0" take "0" _{| P 1 = 0, P 2} = 1, P 3 = 0) is calculated as shown in equation (24) below.
Pr (C = 0 | P ₁ = 0, P ₂ = 1, P ₃ = 0)
= 1-Pr (C = 1 | P ₁ = 0, P ₂ = 1, P ₃ = 0)
= 1-0.25
= 0.75 Formula (24)

The parameter calculation unit 12, based on _{T 1} calculated as described above, _{T 2, T 3} and Equation (7), the node random variable _{P 2} random variables _{P 1} and node _{P 2} of _{P 1} There are both taken to "0", the node probability random variables C of the node C when the random variable _{P 3} of _{P 3} takes the "1" takes "1" _{Pr (C = 1 | P 1} = 0, P 2 = 0, P ₃ = 1) is calculated as shown in the following equation (25).
Pr (C = 1 | P ₁ = 0, P ₂ = 0, P ₃ = 1)
= C _min + Σ _i (P _i × T _i )
= 0.05 + (0 × 0.6 + 0 × 0.2 + 1 × 0.1)
= 0.05 + 0.1
= 0.15 Formula (25)

The parameter calculation unit 12 and the calculation result and equation (10) based on the node _{P 1} of the random variables _{P 1} and node _{P 2} of a random variable _{P 2} are both take "0", the node _{P 3} random variable _{P 3} is "1" the probability variable C of the node C in the case of taking the "0" probability _Pr taking _{(C = 0 | P 1 =} 0, P 2 = 0, P 3 = 1) following the Calculate as shown in equation (26).
Pr (C = 0 | P ₁ = 0, P ₂ = 0, P ₃ = 1)
= 1-Pr (C = 1 | P ₁ = 0, P ₂ = 0, P ₃ = 1)
= 1-0.15
= 0.85 Formula (26)

The parameter calculation unit 12, the upper limit value and equation (10) based on the probability variables _{P 1} of the node _{P 1,} any random variable _{P 3} of a random variable _{P 2} and node _{P 3} of the node _{P 2} is The probability Pr (C = 0 | P ₁ = 1, P ₂ = 1, P ₃ = 1) that the random variable C of the node C takes “0” when “1” is taken is shown in the following equation (27). Calculate as
Pr (C = 0 | P ₁ = 1, P ₂ = 1, P ₃ = 1)
= 1-Pr (C = 1 | P ₁ = 0, P ₂ = 0, P ₃ = 1)
= 1-0.95
= 0.05 Formula (27)

The parameter calculation unit 12, the lower limit value and equation (10) based on the probability variables _{P 1} of the node _{P 1,} any random variable _{P 3} of a random variable _{P 2} and node _{P 3} of the node _{P 2} is The probability Pr (C = 0 | P ₁ = 0, P ₂ = 0, P ₃ = 0) that the random variable C of the node C takes “0” when taking “0” is shown in the following equation (28). Calculate as
Pr (C = 0 | P ₁ = 0, P ₂ = 0, P ₃ = 0)
= 1-Pr (C = 1 | P ₁ = 0, P ₂ = 0, P ₃ = 0)
= 1-0.05
= 0.95 Formula (28)

  As described above, in the Bayesian network information parameter setting device according to the first embodiment of the present invention, the prior probability value of the parent node, the upper and lower limit values of the conditional probability of the child node, and the relative of the parent node to the child node And the conditional probability of the child node can be calculated based on these. However, the conditional probability calculated in this way does not consider the correlation between the parent nodes. Therefore, in order to actually perform an appropriate operation, the conditional probability is updated based on the subjectivity of the expert or other information after setting the calculated conditional probability as an initial value.

(Second Embodiment)
Next, a second embodiment of the present invention will be described. In addition, the description similar to what was shown in FIG. 1 among the structures of the Bayesian network information parameter setting apparatus which concerns on each following embodiment is abbreviate | omitted.
In the first embodiment described above, Bayesian network information in which the parent node and the child node of the sub-network of the Bayesian network information are both binary is targeted. On the other hand, in the second embodiment, a parameter setting method in the case where the parent node of the subnetwork is binary but the child node takes three or more values will be described.

  FIG. 12 is a diagram showing an example of Bayesian network information input by the Bayesian network information parameter setting device according to the second embodiment of the present invention.

In the example shown in FIG. 12, nodes P ₁ and P ₂ exist as nodes having no parent node, and node C exists as a child node thereof.

FIG. 13 is a diagram showing, in tabular form, values of prior probabilities of parent nodes P ₁ and P ₂ of Bayesian network information input to the Bayesian network information parameter setting device according to the second embodiment of the present invention. .
FIG. 14 shows the child node C with the values of the random variables of the parent nodes P ₁ and P ₂ of the Bayesian network information input to the Bayesian network information parameter setting device according to the second embodiment of the present invention determined. It is the figure which showed the conditional probability of the random variable in tabular form.

As shown in FIG. 13, random variables _{P 1} of the parent node _{P 1} takes the two values of _P 1 = {1, 0}, random variables _{P 2} of the parent node _{P 2} is that _P 2 = {1, 0} As shown in FIG. 14, the random variable C of the child node C takes the three values C = {2, 1, 0}. Here, the values {1, 0}, {2, 1, 0}, which are the domain of each node, have no quantitative meaning and only a qualitative meaning.
In such a case, the conditional probabilities Pr (C) of the probabilities Pr (P ₁ ), Pr (P ₂ ) of the random variables P ₁ and P ₂ of the parent nodes P ₁ and P _{2 and} the random variable C of the child node C A process for setting | P ₁ , P ₂ ) will be described.

FIG. 15 is a flowchart showing an example of the processing operation of the Bayesian network information parameter setting device according to the second embodiment of the present invention.
FIG. 16 is a diagram illustrating an example of Bayesian network information in which child nodes are expanded by the Bayesian network information parameter setting device according to the second embodiment of the present invention.

First, the structure analysis unit 11 of the parameter setting unit 6 expands child nodes in the structure information in the input Bayesian network information into the same number of nodes as the number of random variables of the child nodes (step S11). That is, in this embodiment, the structure analysis unit 11 functions as a means for expanding Bayesian network information.
Specifically, in the structure analysis unit 11, the input structure information is the information shown in FIG. 12, and the random variable of the child node C in this structure information takes three values as shown in FIG. In this case, as shown in FIG. 16, it is expanded to three nodes C ₂ , C ₁ , C ₀ .

  FIG. 17 is a table showing the relationship between the value of the random variable of the parent node and the value of the random variable of the child node after the expansion of the Bayesian network information by the Bayesian network information parameter setting device according to the second embodiment of the present invention. It is a figure shown by.

The domain of the random variable C of the initial child node C is C = {2, 1, 0} as shown in FIG. 14, whereas the domain of the random variable C ₂ of the expanded node C ₂ is As shown in FIG. 17, C ₂ = {1, 0}, and the domain of the random variable C ₁ of the expanded node C ₁ is C ₁ = {1, 0} as shown in FIG. The domain of the random variable C ₀ of the subsequent node C ₀ is C ₀ = {1, 0} as shown in FIG.
The case where the random variable C _i of the node C _i takes “1” is the case where the random variable C _i of the original node C becomes equal to the case where the random variable C _i of the node C _i takes “0”. Is the case where the random variable C ≠ i of the original node C.

The structure analysis unit 11 of the parameter setting unit 6 divides the structure information of the Bayesian network information developed in this way into sub-networks composed of a plurality of parent nodes and one child node (step S12).
Specifically, when the structure information after the child node is expanded is the information shown in FIG. 16, the structure analysis unit 11 converts the structure information into the parent node P ₁ , the parent node P ₂ , and the child node C. _A first sub-network consisting of ₀ , a second sub-network consisting of a parent node P ₁ , a parent node P ₂ and a child node C ₁ and a third sub-network consisting of a parent node P ₁ , a parent node P ₂ and a child node C ₀ Divide into sub-networks.

Then, the parameter calculation unit 12 of the parameter setting unit 6 selects one of the divided sub-networks, and sets the prior probability value of the parent node for this sub-network as in the first embodiment (step S13), upper and lower limit values are set (step S14), and contributions are set (step S15), and conditional probabilities for child nodes are calculated based on these setting information (step S16).
Specifically, the parameter calculation unit 12 divides the structure information shown in FIG. 16 into three sub-networks, and then calculates a conditional probability corresponding to each area of the table shown in FIG.

  After calculating the conditional probability, the parameter setting unit 6 returns to the process of step S12 when there is an unselected subnetwork that has been divided as described above (NO in step S17), and all the subparts that have been divided are calculated. If the network has been selected (YES in step S17), the process ends.

As the Bayesian network information, the node C can be used while being expanded to three nodes as described above, but these nodes may be combined into one node. That is, when the divided structure information is in the form shown in FIG. 16, this is returned to the form shown in FIG.
In this case, the parameter calculation unit 12 of the parameter setting unit 6 uses the conditional probabilities related to the node C as the following formulas (29) using the conditional probabilities of the nodes C ₂ , C ₁ , and C _{0 obtained} by expanding the node C: ) Calculate as shown.
Pr (C = i | P ₁ = p ₁ , P ₂ = p ₂ )
= Pr (C _i = 1 | P ₁ = p ₁ , P ₂ = p ₂ ) / Σ _i Pr (C _i = 1 | P ₁ = p ₁ , P ₂ = p ₂ ) (29)
Here, the case where the value of the random variable of the child node takes a ternary value is shown as an example, but when the random variable of the child node takes an n value, the child node may be expanded to n nodes.
That is, the random variable C = node C {0,1,2, ···, n- 1} if it is, this node _{C n-1, C n-} 2, ···, the _{C 0} What is necessary is just to expand | deploy to n nodes.

In addition, when there are m parent nodes of the nodes P ₁ , P ₂ ,..., P _m , the parameter calculation unit 12 calculates the conditional probability related to the node C after recombination as follows: 30).
Pr (C = i | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _m = p _m )
= Pr (C _i = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _m = p _m ) / Σ _i Pr (C _i = 1 | P ₁ = p ₁ , P ₂ = p ₂ ,..., P _m = p _m ) (30)
As described above, in the Bayesian network information parameter setting device according to the second embodiment of the present invention, even when the random variable of the child node takes three or more values, the prior probability value of the parent node and the conditional condition of the child node are set. By setting the upper and lower limits of the probability and the relative contribution of the parent node to the child node, the conditional probability of the child node can be calculated based on these.

(Third embodiment)
Next, a third embodiment of the present invention will be described. In this embodiment, a parameter setting method when a random variable of a parent node takes three or more values will be described.
The Bayesian network information input by the Bayesian network information parameter setting device according to the third embodiment of the present invention includes nodes P ₁ and P ₂ as nodes that do not have a parent node as in the second embodiment, and its child nodes Node C exists as follows.

FIG. 18 is a table showing the prior probabilities of the parent nodes P ₁ and P ₂ of the Bayesian network information input to the Bayesian network information parameter setting device according to the third embodiment of the present invention in a tabular format.
FIG. 19 shows the state of the child node C when the values of the random variables of the parent nodes P ₁ and P ₂ of the Bayesian network information input to the Bayesian network information parameter setting device according to the third embodiment of the present invention are determined. It is the figure which showed the conditional probability of the random variable in tabular form.

As shown in FIG. 18, random variables _{P 1} of the parent node _{P 1} takes three values of _P 1 = {2,1,0}, random variables _{P 2} of the parent node _{P 2} is _P 2 = {2,1 , 0}. On the other hand, as shown in FIG. 19, the random variable C of the child node C takes a binary value of C = {1, 0}. Here, the values {1, 0}, {2, 1, 0}, which are the domain of each node, have no quantitative meaning and only a qualitative meaning.

In such a case, the conditional probabilities Pr (C) of the probabilities Pr (P ₁ ), Pr (P ₂ ) of the random variables P ₁ and P ₂ of the parent nodes P ₁ and P _{2 and} the random variable C of the child node C A process for setting | P ₁ , P ₂ ) will be described.
FIG. 20 is a flowchart showing an example of the processing operation of the Bayesian network information parameter setting device according to the third embodiment of the present invention.

First, the structure analysis unit 11 of the parameter setting unit 6 expands the parent node in the structure information in the input Bayesian network information to the same number of nodes as the number of random variables of the parent node (step S21).
FIG. 21 is a diagram showing an example of Bayesian network information in which the parent node is expanded by the Bayesian network information parameter setting device according to the third embodiment of the present invention.

Specifically, the structure analysis unit 11 has the case where the input structure information is the information shown in FIG. 12, and the random variable of the parent node C in the structure information takes a ternary value as shown in FIG. to expands the parent node _{P i} as shown in FIG. 21 _{P i_2, P i_1,} the 3 nodes of the _{P i_0.} Here, the structure analysis unit 11, a parent node _{P 1} Expand _{P 1_2, P 1_1,} the 3 nodes of the _{P 1_0,} to expand the parent node _{P 2 P 2_2, P 2_1,} the 3 nodes of the _{P 2_0.}

FIG. 22 is a diagram showing, in a tabular form, values of prior probabilities of random variables related to each node after the development of the first parent node by the Bayesian network information parameter setting device according to the third embodiment of the present invention. .
FIG. 23 is a diagram showing, in a tabular form, values of prior probabilities of random variables related to each node after the expansion of the second parent node by the Bayesian network information parameter setting device according to the third embodiment of the present invention. .

The domain of the random variables P ₁ and P ₂ of the original parent nodes P ₁ and P ₂ is P ₁ , P ₂ = { ₂ , ₁ , 0}, whereas the expanded nodes P _{1_2 and} P 2 _{1_1, P 1_0, P 2_2,} P 2_1, random variables _{P 1_2} of _{P 2_0, P 1_1, P 1_0} , P 2_2, P 2_1, domain of a random variable _{C 2} of _{P 2_0} is as shown in FIGS. 22 and 23 {1,0}.
The case where the random variable C _i of the node P _{i_j} takes “1” is a case where the random variable P _i = j of the original node P _i becomes j, and the random variable C _i of the node P _{i_j} takes “0”. The case is a case where the random variable P _i ≠ j of the original node P _i .

  Then, the parameter calculation unit 12 of the parameter setting unit 6 treats the Bayesian network information developed in this way as a new subnetwork, and for this subnetwork, the prior probability value of the parent node is the same as in the first embodiment. Setting (step S22), setting of upper and lower limit values (step S23), and setting of contribution (step S24) are performed, and conditional probabilities relating to child nodes are calculated based on these setting information (step S25). .

Moreover, the parameter calculation part 12 should just calculate the conditional probability value of the recombined node according to the following formula | equation (31), when connecting a parent node after parameter setting.
_{Pr (P i = j) =} Pr (P i_j = 1) / Σ j Pr (P i_j = 1) ... Equation (31)
As described above, in the Bayesian network information parameter setting device according to the third embodiment of the present invention, even if the probability variable of the parent node takes three or more values, the prior probability value of the parent node and the conditional condition of the child node are set. By setting the upper and lower limits of the probability and the relative contribution of the parent node to the child node, the conditional probability of the child node can be calculated based on these.

(Fourth embodiment)
Next, a fourth embodiment of the present invention will be described. In this embodiment, a parameter setting method when the random variables of the parent node and the child node both have three or more values will be described.

In this case, the structure analysis unit 11 of the parameter setting unit 6 sets the child nodes in the structure information in the input Bayesian network information to the same number of nodes as the number of random variables of the child nodes as in the second embodiment. expand.
In addition, the structure analysis unit 11 of the parameter setting unit 6 expands the parent node in the structure information in the input Bayesian network information to the same number of nodes as the number of random variables of the parent node as in the third embodiment. To do. Then, the structure information of the Bayesian network information developed in this way is divided into sub-networks composed of a plurality of parent nodes and one child node.

  The parameter calculation unit 12 of the parameter setting unit 6 treats the Bayesian network information expanded and divided in this way as a new subnetwork, and for this subnetwork, the prior probability value of the parent node is the same as in the first embodiment. Settings, upper and lower limit values, and contribution levels are set, and conditional probabilities for child nodes are calculated based on these setting information.

  As described above, in the Bayesian network information parameter setting device according to the fourth embodiment of the present invention, even if the probability variable of the parent node and the probability variable of the child node both take three or more values, the prior probability of the parent node By setting the value, the upper and lower limit values of the conditional probability of the child node, and the relative contribution of the parent node to the child node, the conditional probability of the child node can be calculated based on these.

  The present invention is not limited to the above-described embodiment as it is, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. Various inventions can be formed by appropriately combining a plurality of constituent elements disclosed in the embodiment. For example, some components may be omitted from all the components shown in the embodiment. Furthermore, you may combine suitably the component covering different embodiment.

The block diagram which shows an example of the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention. The figure which shows the causal relationship of various physical symptoms and influenza with an example of Bayesian network information. The figure which shows the 1st example of the relationship between the parent node of a Bayesian network information, and a child node. The figure which shows the 2nd example of the relationship between the parent node of a Bayesian network information, and a child node. The figure which shows the example which divided | segmented the group of the parent node in the 2nd example of the relationship between the parent node of a Bayesian network information, and a child node. The flowchart which shows an example of the processing operation of the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention. The figure which shows an example of the Bayesian network information which the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention inputs. The figure which shows the probability in connection with the parent node of the Bayesian network information which the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention inputs. The figure which showed an example of the upper and lower limit value of the probability regarding the child node of the Bayesian network information input into the Bayesian network information parameter setting device according to the first embodiment of the present invention. The figure which shows an example of the contribution degree of the parent node with respect to the child node of the Bayesian network information which the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention inputs. The figure which shows an example of the conditional probability in connection with the child node of the Bayesian network information which the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention inputs. The figure which shows an example of the Bayesian network information which the Bayesian network information parameter setting apparatus according to the 2nd Embodiment of this invention inputs. The figure which showed the value of the prior probability of the parent node of the Bayesian network information input into the Bayesian network information parameter setting apparatus according to the 2nd Embodiment of this invention in tabular form. The conditional probabilities of child node random variables in a tabular format when the value of the random variable of the parent node of the Bayesian network information input to the Bayesian network information parameter setting device according to the second embodiment of the present invention is determined. The figure shown. The flowchart which shows an example of the processing operation of the Bayesian network information parameter setting apparatus according to the 2nd Embodiment of this invention. The figure which shows an example of the Bayesian network information which expand | deployed the child node by the Bayesian network information parameter setting apparatus according to the 2nd Embodiment of this invention. The figure which shows the relationship between the value of the probability variable of the parent node after the expansion | deployment of the Bayesian network information by the Bayesian network information parameter setting apparatus according to the 1st Embodiment of this invention in the form of a table. The figure which shows the classification of the random variable regarding the parent node of the Bayesian network information which the Bayesian network information parameter setting apparatus according to the 3rd Embodiment of this invention inputs into a table format. The conditional probabilities of the random variables of the child nodes in a tabular format when the value of the random variable of the parent node of the Bayesian network information input to the Bayesian network information parameter setting device according to the third embodiment of the present invention is determined. The figure shown. The flowchart which shows an example of the processing operation of the Bayesian network information parameter setting apparatus according to the 3rd Embodiment of this invention. The figure which shows an example of the Bayesian network information which expand | deployed the parent node by the Bayesian network information parameter setting apparatus according to the 3rd Embodiment of this invention. The figure which shows the value of the prior probability of the random variable regarding each node after the expansion | deployment of the 1st parent node by the Bayesian network information parameter setting apparatus according to the 3rd Embodiment of this invention in a table format. The figure which shows the value of the prior probability of the random variable regarding each node after the expansion | deployment of the 2nd parent node by the Bayesian network information parameter setting apparatus according to the 3rd Embodiment of this invention in a table format.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Bayesian network parameter setting apparatus, 2 ... Structure input part, 3 ... Setting information input part, 4 ... Output display part, 5 ... Memory | storage device, 6 ... Parameter setting part, 11 ... Structural analysis part, 12 ... Parameter calculation part.

Claims (5)

A plurality of nodes associated with a random variable of Bayesian network information taking two values and a single child node associated with a random variable of Bayesian network information taking two values with the plurality of nodes as parent nodes Structure information input means for inputting structure information consisting of:
Probability information input means for inputting occurrence probability information of a value taken by a random variable of a parent node in the structure information;
A relative ratio input means for receiving an input of a relative ratio of the magnitude of the value of the value taken by the parent node random variable to the occurrence probability of the value taken by the child node random variable;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the random variable of the child node is predetermined when the random variable of the parent node takes a predetermined value. A conditional probability first input means for receiving a combination of a conditional probability that is a probability of taking a maximum value and an input of the maximum value;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the combination when the conditional probability is the minimum value of the combination and the conditional input for receiving the input of the minimum value A probability second input means;
Based on the input results by the structure information input means, the relative ratio input means, the conditional probability first input means and the conditional probability second input means, the value taken by the random variable of the parent node and the random variable of the child node A Bayesian network information processing apparatus comprising: calculation means for calculating the conditional probability based on a combination other than the case where the conditional probability is the maximum value or the minimum value among the combinations of values taken by. At least one node is a child node of another node, and the structure information indicating the causal relationship between the random variable of each parent node and the random variable of the child node is input. Structural information input means to
Decomposition means for decomposing the structure information input by the structure information input means into structure information indicating a causal relationship between a random variable of at least one parent node and a random variable of a single child node;
Probability information input means for inputting occurrence probability information of a value taken by a random variable of a parent node in each structure information decomposed by the decomposition means;
A relative ratio input means for receiving an input of a relative ratio of the magnitude of the value of the value taken by the parent node random variable to the occurrence probability of the value taken by the child node random variable;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the random variable of the child node is predetermined when the random variable of the parent node takes a predetermined value. A conditional probability first input means for receiving a combination of a conditional probability that is a probability of taking a maximum value and an input of the maximum value;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the combination when the conditional probability is the minimum value of the combination and the conditional input for receiving the input of the minimum value A probability second input means;
Based on the input results by the structure information input means, the relative ratio input means, the conditional probability first input means and the conditional probability second input means, the value taken by the random variable of the parent node and the random variable of the child node A Bayesian network information processing apparatus comprising: calculation means for calculating the conditional probability based on a combination other than the case where the conditional probability is the maximum value or the minimum value among the combinations of values taken by. A plurality of nodes associated with a random variable of Bayesian network information taking two values and a single child associated with a random variable of a Bayesian network taking two or more values with the plurality of nodes as parent nodes Structure information input means for inputting structure information consisting of nodes;
Expansion means for expanding the child nodes input by the structure information input means into nodes corresponding to the number of values taken by the random variable;
Extraction means for extracting, for each child node, structure information related to a single child node and a parent node having a causal relationship with the child node in the structure information expanded by the expansion means;
Probability information input means for inputting occurrence probability information of a value taken by a random variable of a parent node in the structure information extracted by the extraction means;
A relative ratio input means for receiving an input of a relative ratio of the magnitude of the value of the value taken by the parent node random variable to the occurrence probability of the value taken by the child node random variable;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the random variable of the child node is predetermined when the random variable of the parent node takes a predetermined value. A conditional probability first input means for receiving a combination of a conditional probability that is a probability of taking a maximum value and an input of the maximum value;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the combination when the conditional probability is the minimum value of the combination and the conditional input for receiving the input of the minimum value A probability second input means;
Based on the input results by the structure information input means, the relative ratio input means, the conditional probability first input means and the conditional probability second input means, the value taken by the random variable of the parent node and the random variable of the child node A Bayesian network information processing apparatus comprising: calculation means for calculating the conditional probability based on a combination other than the case where the conditional probability is the maximum value or the minimum value among the combinations of values taken by. A plurality of nodes associated with a random variable of Bayesian network information that takes two or more values and a single node associated with a random variable of Bayesian network information that takes two values with the plurality of nodes as parent nodes Structure information input means for inputting structure information comprising child nodes;
Expansion means for expanding the parent node input by the structure information input means into nodes corresponding to the number of values taken by the random variable;
Probability information input means for inputting occurrence probability information of a value taken by a random variable of a parent node in the structure information expanded by the expansion means;
A relative ratio input means for receiving an input of a relative ratio of the magnitude of the value of the value taken by the parent node random variable to the occurrence probability of the value taken by the child node random variable;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the random variable of the child node is predetermined when the random variable of the parent node takes a predetermined value. A conditional probability first input means for receiving a combination of a conditional probability that is a probability of taking a maximum value and an input of the maximum value;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the combination when the conditional probability is the minimum value of the combination and the conditional input for receiving the input of the minimum value A probability second input means;
Based on the input results by the structure information input means, the relative ratio input means, the conditional probability first input means and the conditional probability second input means, the value taken by the random variable of the parent node and the random variable of the child node A Bayesian network information processing apparatus comprising: calculation means for calculating the conditional probability based on a combination other than the case where the conditional probability is the maximum value or the minimum value among the combinations of values taken by. Computer
A plurality of nodes associated with a random variable of Bayesian network information taking two values and a single child node associated with a random variable of Bayesian network information taking two values with the plurality of nodes as parent nodes Structure information input means for inputting structure information consisting of:
Probability information input means for inputting occurrence probability information of a value taken by a random variable of a parent node in the structure information,
A relative ratio input means for receiving an input of a relative ratio of the magnitude of the influence of the value of the random variable of the parent node on the occurrence probability of the value of the random variable of the child node;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the random variable of the child node is predetermined when the random variable of the parent node takes a predetermined value. A conditional probability first input means for accepting an input of a combination of a conditional probability that is a probability of taking a maximum value and a maximum value;
Of the combination of the value taken by the random variable of the parent node and the value taken by the random variable of the child node, the combination when the conditional probability is the minimum value of the combination and the conditional input for receiving the input of the minimum value A value taken by the random variable of the parent node on the basis of the result input by the probability second input means, and the structure information input means, the relative ratio input means, the conditional probability first input means and the conditional probability second input means And a Bayesian network that functions as a calculation means for calculating the conditional probability by a combination other than the case where the conditional probability is the maximum value or the minimum value among combinations of values taken by the random variables of the child nodes Information processing program.

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