JP5914291B2 - Transition probability calculation device, total value calculation device, transition probability calculation method, total value calculation method - Google Patents

Description

  The present invention relates to a security technique for concealing database data.

  In the database, in order to calculate a statistical value from an individual data group concealed by a probabilistic method, a transition probability that is a rule for concealment is used. As a method for calculating the transition probability, the method shown in Section 5.1 of Non-Patent Document 1 is known. As a method for concealing a numerical attribute that is a continuous value, a method disclosed in Non-Patent Document 2 is known.

Igarashi Univ., Koji Senda, Katsumi Takahashi, “Efficient Privacy Protection Cross Tabulation Applicable to Multi-valued Attributes”, CSS2008, 2008. University of Igarashi, Koji Senda, Katsumi Takahashi, “Randomization method satisfying k-anonymity in numerical attributes”, CSS2011, 2011.

  However, the technique disclosed in Non-Patent Document 1 can be used when the attribute value is discrete, but cannot be used when the attribute value is continuous. An object of this invention is to provide the technique which calculates | requires the transition probability for calculating a statistics value from the individual data group concealed with respect to the database containing a continuous attribute value.

The transition probability calculation device of the present invention includes a subdivision unit, a total value information unit, a subdivision probability calculation unit, and an integration unit, and attribute values for concealing data in a database having a plurality of records including attribute values that take continuous values Find the probability of the transition. First, A _vu is a probability density function in which the attribute value v transitions to the attribute value u, J is a range from a value G _min to a value G _max that is a part of a value range that the attribute value can take, and K is a value range that the attribute value can take A _JK is a transition probability that an attribute value included in the section J transitions to an attribute value included in the section K, M is an integer of 2 or more, m is an integer of 0 to M-1, and j ₀ ,..., J _M-1 is a section obtained by subdividing the section J into M pieces, N _J is the number of records whose attribute value is included in the section J, N _jm is the number of records whose attribute value is included in the section j _m , g ₀ is a value G _min , g _M is a value G _max , and when m is 1 or more and M−1 or less, g _m is an attribute value that delimits the section j _m−1 and the section j _m, and g ₀ <g ₁ <... <g _M. The subdivision section subdivides the section J into M pieces, and obtains subdivided sections j ₀ ,..., J _M−1 . The total value information part obtains the number N _J and the numbers N _j0 ,..., N _jM−1 . The subdivision probability calculation unit calculates the subprobability p _m

Seek like. The integration unit uses the transition probability A _JK

  Seek like.

The total value calculation device of the present invention includes the transition probability calculation device of the present invention, and further includes a section setting unit and a total value update unit. Then, the section setting unit sequentially sets the section J so that all value ranges of the attribute values are set, subdivides the section J in which the subdivision unit is set, obtains a subdivided section, and the total value information section The number of records in which attribute values are included in the subdivided sections in each setting is obtained and used as the aggregated value of the subdivided sections. Next, the section setting unit sequentially sets the section J and the section K so that all combinations of attribute values are set, and subdivides the section J set by the subdivision section into subdivided sections. Then, the subdivision probability calculation unit obtains subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and the integration unit calculates the aggregated values and subdivision probabilities p ₀ ,. , P _M−1 to obtain the transition probability A _JK . Then, the aggregate value update unit uses the transition probabilities A _JK of the sections J and K sequentially set so that combinations of all the range of attribute values are set as each element of the transition probability matrix, and an inverse matrix method Alternatively, the number of records whose attribute values are included in the segment subdivided by the iterative Bayes technique is updated to be the aggregate value of the new subdivided segment. The number of records in the section J is obtained by totaling the number of records in the subdivided sections included in the section J.

  In the transition probability calculation apparatus of the present invention, the range of continuous attribute values is divided into a finite number of sections, and the number of attribute values included in each section is used. Therefore, the transition probability is not a continuous transition probability density function. Can be sought. Moreover, since the total value calculation apparatus of this invention uses the calculated | required transition probability as an element of a transition probability matrix, the individual data group concealed using the technique (inverse matrix method or iterative Bayes method) of nonpatent literature 1 Statistical values can be calculated from

FIG. 3 is a diagram illustrating a functional configuration example of a transition probability calculation apparatus according to the first embodiment. The figure which shows the processing flow of the transition probability calculation apparatus of Example 1. FIG. The function structural example of the total value calculation apparatus of this invention and the figure which shows the functional structural example of the transition probability calculation apparatus of Example 2 are shown. The figure which shows the processing flow of the total value calculation apparatus of this invention. The figure which shows the processing flow of the transition probability calculation apparatus of Example 2. FIG.

  Hereinafter, embodiments of the present invention will be described in detail. In addition, the same number is attached | subjected to the structure part which has the same function, and duplication description is abbreviate | omitted.

  FIG. 1 shows a functional configuration example of the transition probability calculation apparatus according to the first embodiment, and FIG. 2 shows a processing flow of the transition probability calculation apparatus according to the first embodiment. The transition probability calculation apparatus according to the first embodiment obtains a probability that an attribute value changes when concealing data in the database 900 having a plurality of records including attribute values that take continuous values. A record consists of values for several predetermined items. The attribute is each item, and the attribute value is the value of each item. An attribute having discrete attribute values is, for example, “sex” or “age”, and an attribute having a continuous attribute value is, for example, “height” or “weight”.

The transition probability calculation apparatus 100 according to the first embodiment is connected to the database 900 via a network, and includes a subdivision unit 110, a total value information unit 120, a subdivision probability calculation unit 130, an integration unit 140, and a recording unit 190. First, A _vu is a probability density function in which the attribute value v transitions to the attribute value u, J is a range from a value G _min to a value G _max that is a part of a value range that the attribute value can take, and K is a value range that the attribute value can take A _JK is a transition probability that an attribute value included in the section J transitions to an attribute value included in the section K, M is an integer of 2 or more, m is an integer of 0 to M-1, and j ₀ ,..., J _M-1 is a section obtained by subdividing the section J into M pieces, N _J is the number of records whose attribute value is included in the section J, N _jm is the number of records whose attribute value is included in the section j _m , g ₀ is a value G _min , g _M is a value G _max , and when m is 1 or more and M−1 or less, g _m is an attribute value that delimits the section j _m−1 and the section j _m, and g ₀ <g ₁ <... <g _M. The attribute value g _m may belong to either section as long as it belongs to either section j _m-1 or section j _m .

The subdivision section 110 subdivides the section J into M pieces, and obtains subdivided sections j ₀ ,..., J _M−1 (S110). Incidentally, the interval _{j m} is to attribute values may be _{g m} or _{g m + 1} smaller intervals, the attribute value may be a larger _{g m + 1} following section than _{g m.}

The total value information unit 120 calculates the numbers N _J and the numbers N _j0 ,..., N _jM−1 and records them in the recording unit 190 (S120). There are several methods for obtaining the numbers N _J and the numbers N _j0 ,..., N _jM−1 . For example, if a correct aggregate value (N _j0 ,..., N _jM−1 ) of attribute values can be acquired from the database 900, it should be acquired. In this case, the number N _J may be obtained as N _J = N _j0 +... + N _jM−1 . When the total value is unknown, for example, there is a method for obtaining the total value (N _j0 ,..., N _jM−1 ) on the assumption that the attribute value is uniformly distributed. In this case, the maximum value _{V max} of the range of attribute values from the minimum value _{V min,} the total number of records and _{N ALL,} aggregate value information 120, the number _{N J} and the number _N j0, _..., a _{N jM-1,}

You can ask as follows. As another example when the total value is unknown, there is a method of using a secret attribute value distribution as follows. Specifically, the range of attribute values is set from the minimum value V _min to the maximum value V _max , the total number of records is set to N _ALL , and the total value information unit 120 uses a secret attribute value distribution to calculate the number N _j0,. , N _jM−1 and the number N _J may be _calculated as N _J = N _j0 +... + N _jM−1 .

The subdivision probability calculation unit 130 calculates subdivision probability p _m (where m = 0,..., M−1).

And is recorded in the recording unit 190 (S130).

For example, consider the case where the probability density function A _vu is a finite noise function with a Laplace distribution as the basic noise. Here, the value range of the attribute value in the section K is the minimum value H _min to the maximum value H _max , and the attribute value range is the minimum value V _min to the maximum value V _max , and 2σ ² is the dispersion of the Laplace distribution. At this time, the probability density function A _vu is the probability density of the random variable Y obtained by adding the noise X according to the probability density function f _v (x) satisfying the following to the input v. When the basic noise is a probability density function f (x), there is a number α _v depending on a certain v,
V _min −v ≦ x ≦ V _max −v
If
f _v (x) = f (x) / α _v
If not, f _v (x) = 0
Meet.

When A _vu is such a probability density function, it may be calculated as follows.

However,

The integration unit 140 determines the transition probability A _JK

And is recorded in the recording unit 190 (S140).

  According to the transition probability calculation device of the first embodiment, the range of continuous attribute values is divided into a finite number of sections, and the number of attribute values included in each section is used. Therefore, instead of a continuous transition probability density function, Transition probability can be obtained. Therefore, since the obtained transition probability can be used as an element of the transition probability matrix, the statistical value can be calculated from the individual data group concealed using the technique of Non-Patent Document 1.

FIG. 3 shows a functional configuration example of the total value calculation apparatus of the present invention, and FIG. 4 shows a processing flow of the total value calculation apparatus of the present invention. The total value calculation device 200 of the present invention is connected to the database 900 via a network, and includes a transition probability calculation device 100, a section setting unit 250, and a total value update unit 260. The aggregate value calculation apparatus 200 is an apparatus used when a correct aggregate value (N _j0 ,..., N _jM−1 ) is not known.

Hereinafter, the processing will be described while following the processing flow of FIG. The section setting unit 250 selects and sets the section J (G _{min to} G _max ) from the attribute value range (V _{min to} V _max ) (S251). The subdividing unit 110 subdivides the set section J to obtain a subdivided section (j ₀ ,..., J _M−1 ) (S111). The total value information unit 120 obtains the number of records whose attribute values are included in the subdivided section (j ₀ ,..., J _M−1 ) by a predetermined method and sets the total value of the subdivided section. 190 (S121). Specifically, the maximum value _{V max} of the range of attribute values from the minimum value _{V min,} the total number of records and _{N ALL,} aggregate value information 120, the number _N j0, _..., a _{N jM-1,}

You can ask as follows. Or the total value information part 120 should _{just obtain | require} number _Nj0 , ..., _NjM-1 using the distribution of the secret attribute value. Then, the section setting unit 250 confirms whether or not the section J (G _{min to} G _max ) is selected and set for all the attribute value ranges (V _{min to} V _max ) (S252). Returns to step S251.

If step S252 is Yes, the interval setting unit 250, a combination of attribute values of the value range _(V min _{~V max)} interval from the _{J (G} min _{~G max)} and section _{K (H} min _{~H max)} Is selected and set (S253). The subdividing unit 110 subdivides the set section J to obtain a subdivided section (j ₀ ,..., J _M−1 ) (S112). The subdivision probability calculation unit 130 obtains subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and records them in the recording unit 190 (S130). The integration unit 140 obtains the transition probability A _JK using the aggregated values of the subdivided sections and the subdivision probabilities p ₀ ,..., P _M−1 and records them in the recording unit 190 (S140). Steps S130 and S140 may be the same method as in the first embodiment. The section setting unit 250 selects and sets a combination of the section J (G _{min to} G _max ) and the section K (H _{min to} H _max ) for all the attribute value ranges (V _{min to} V _max ). (S254). If No, the process returns to step S253.

When step S54 is Yes, the total value update unit 260 uses the transition probabilities A _JK of the sections J and K that are sequentially set so that combinations of all the range of attribute values are set as elements. A transition probability matrix A is created. And, for example, by updating the number of records whose attribute values are included in the segment subdivided using the transition probability matrix A by the inverse matrix method or the iterative Bayesian method shown in Section 5.2 of Non-Patent Document 1, The total value of the new segmented section is recorded in the recording unit 190 (S260). There is also a method for confirming whether the difference between the total value before the update and the total value after the update is within a predetermined range as an end condition of the iterative processing, such as an iterative Bayes method. In the case of such a method, the total value update unit 260 confirms whether the updated total value satisfies the end condition of the iterative process (S261). In the case of No, the process returns to step S253, and the process proceeds using the total value of the new subdivided section. When Step S261 is Yes and Step S261 is not present, the aggregate value update unit 260 calculates the number of records N _J whose attribute values are included in the section J (G _{min to} G _max ) as N _J = N _j0 +. _jM-1 is obtained and recorded in the recording unit 190 (S262). Note that the processing of steps S251 to S261 shown in this embodiment will be collectively referred to as a subdivided total value calculation step (S200).

  According to the total value calculation device of the present invention, the range of continuous attribute values is divided into a finite number of sections, and the transition probability from section to section is obtained, so a transition probability matrix having the obtained transition probability as an element is obtained. be able to. Therefore, the statistical value can be calculated from the individual data group concealed using the technique of Non-Patent Document 1.

FIG. 3 shows the transition probability calculation apparatus 300 of this embodiment, and FIG. 5 shows the processing flow. In the present embodiment, the transition probability is obtained using the aggregate value of the segment with high accuracy obtained by the method of the second embodiment. As shown in FIG. 3, the configuration is the same as that of the total value calculation device 200. However, as shown in FIG. 5, after performing the subdivided total value calculation step (S200) shown in the second embodiment, the integration unit 140 calculates the total value of the subdivided sections obtained by the total value update unit 260. The difference is that the transition probabilities A _JK are obtained. In the subdivided aggregate value calculation step (S200), since the sections J and K are sequentially set so that combinations of all the range of attribute values are set, the aggregate values of the subdivided sections are obtained, so the transition probability Transition probabilities can be obtained for all elements of the matrix.

Specifically, after executing the subdivided total value calculation step (S200), the section setting unit 250 selects the section J (G _{min to} G _max ) and the section from the attribute value range (V _{min to} V _max ). A combination of K (H _{min to} H _max ) is selected and set (S253). The subdividing unit 110 subdivides the set section J to obtain a subdivided section (j ₀ ,..., J _M−1 ) (S112). The subdivision probability calculation unit 130 obtains subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and records them in the recording unit 190 (S130). The integration unit 140 obtains the transition probability A _JK using the aggregated values of the subdivided sections and the subdivision probabilities p ₀ ,..., P _M−1 and records them in the recording unit 190 (S140). Steps S130 and S140 may be the same method as in the first embodiment. The section setting unit 250 selects and sets a combination of the section J (G _{min to} G _max ) and the section K (H _{min to} H _max ) for all the attribute value ranges (V _{min to} V _max ). (S254). If No, the process returns to step S253. If step S54 is Yes, the process ends.

  According to the transition probability calculation device 300 of the third embodiment, since the aggregate value of the segment with high accuracy is used, the transition probability with high accuracy can be obtained. Furthermore, since the section J and the section K can be set sequentially so that combinations of all the range of attribute values are set, all elements (transition probabilities) of the transition probability matrix used for reconstruction can be obtained.

Incidentally, the point of the present invention which is common in Examples 1 to 3 is that it divides the interval J into smaller sections j _m in order to increase the accuracy. A transition probability matrix is created from the transition probabilities when the aggregated value is obtained by “reconstruction” from the secret data. That is, the probability of probabilistically changing to v and u is calculated for the set of attribute value v and attribute value u. When restructuring a cross tabulation for a plurality of attributes, the amount of calculation for the reconstruction is a product of the size of the attribute value range for the attribute, which is very large. If the section J is a fine section, the number of sections and the size of the range will be large, so the section J cannot be made very fine. However, when calculating the transition probability matrix of each attribute, it is only necessary to pay attention to that attribute. From the point of view, calculation is possible. The present invention focuses on this point.

[Program, recording medium]
The various processes described above are not only executed in time series according to the description, but may also be executed in parallel or individually as required by the processing capability of the apparatus that executes the processes. Needless to say, other modifications are possible without departing from the spirit of the present invention.

  Further, when the above-described configuration is realized by a computer, processing contents of functions that each device should have are described by a program. The processing functions are realized on the computer by executing the program on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. As the computer-readable recording medium, for example, any recording medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory may be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads a program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).

  In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

100, 300 Transition probability calculation device 110 Subdivision unit 120 Total value information unit 130 Subdivision probability calculation unit 140 Integration unit 190 Recording unit 200 Total value calculation device 250 Section setting unit 260 Total value update unit 900 Database

Claims (10)

A transition probability calculation device for obtaining a probability of transition of the attribute value when concealing data in a database having a plurality of records including attribute values taking continuous values,
A _vu is a probability density function in which the attribute value v transitions to the attribute value u, J is a range from a value G _min to a value G _max that is a part of a value range that the attribute value can take, and K is a value range that the attribute value can take A _JK is a transition probability that an attribute value included in the section J transitions to an attribute value included in the section K, M is an integer of 2 or more, m is an integer of 0 to M−1, j ₀ ,. , J _M−1 is a section obtained by subdividing section J into M pieces, N _J is the number of records whose attribute value is included in section J, N _jm is the number of records whose attribute value is included in section j _m , and g ₀ Is a value G _min , g _M is a value G _max , and when m is 1 or more and M−1 or less, g _m is an attribute value that delimits the section j _m−1 and the section j _m, and g ₀ <g ₁ <.・ ・ <G _M
Subdividing the section J into M pieces, and subdividing sections for obtaining the subdivided sections j ₀ ,..., J _M−1 ;
A total value information part for _{obtaining the} number N _J and the numbers N _j0 ,..., N _jM−1 ;
The subdivision probability _{p m}

Subdivided probability calculation unit to be obtained as follows,
Transition probability A _JK

And the integration department
A transition probability calculation device comprising: The transition probability calculation device according to claim 1,
The attribute value range of the section K is from the minimum value H _min to the maximum value H _max , the attribute value range is from the minimum value V _min to the maximum value V _max , and the probability density function A _vu is a finite noise function based on Laplace distribution. 2σ ² is the dispersion of the Laplace distribution,
The subdivision probability calculation unit, said subdivision probability p _m,

However,

The transition probability calculation device characterized by obtaining like this. The transition probability calculation device according to claim 1 or 2,
The total value information part is
The number _N j0 from the database, ... _to obtain the _{N jM-1,} the number _{N J N J = N j0 +} ... + N jM-1
The transition probability calculation device characterized by obtaining like this. The transition probability calculation device according to claim 1 or 2,
The range of the attribute value is a minimum value V _min to a maximum value V _max , and the total number of records is N _ALL ,
The total value information part is
The number N _J and the number N _j0 ,..., N _jM−1 are

The transition probability calculation device characterized by obtaining like this. The transition probability calculation device according to claim 1 or 2,
The range of the attribute value is a minimum value V _min to a maximum value V _max , and the total number of records is N _ALL ,
The total value information part is
Said number _N j0 using the distribution of confidential attribute value, _..., the determined _{N jM-1,} the number _{N J N J = N j0 +} ... + N jM-1
The transition probability calculation device characterized by obtaining like this. A total value calculation device comprising the transition probability calculation device according to claim 4 or 5,
further,
A section setting unit for setting the section J and the section K;
From the already calculated total value and transition probability, there is also a total value update unit that calculates a new total value,
The section setting unit sequentially sets the section J so that all the ranges of the attribute values are set, and subdivides the section J in which the subdivision section is set to obtain a subdivided section, and the aggregate value The information part calculates the number of records whose attribute values are included in the subdivided section in each setting and sets it as the aggregate value of the subdivided section,
The section setting unit sequentially sets the section J and the section K so that all combinations of the attribute values are set, and subdivides the section J set by the subdivision section into subdivided sections. The subdivision probability calculation unit calculates subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and the integration unit calculates the aggregated values of the subdivided sections and the subdivision probabilities p. ₀ ,..., P _M−1 are used to determine the transition probability A _JK ,
The aggregate value updating unit uses the transition probabilities A _JK of the sections J and K that are sequentially set so that combinations of all the range of the attribute values are set as each element of the transition probability matrix, and an inverse matrix method Alternatively, an aggregate value calculation apparatus characterized by updating the number of records whose attribute values are included in a segment subdivided by an iterative Bayes technique, and obtaining a new aggregate segment value. The transition probability calculation device according to claim 4 or 5,
further,
A section setting unit for setting the section J and the section K;
From the already calculated total value and transition probability, there is also a total value update unit that calculates a new total value,
The section setting unit sequentially sets the section J so that all the ranges of the attribute values are set, and subdivides the section J in which the subdivision section is set to obtain a subdivided section, and the aggregate value The information part calculates the number of records whose attribute values are included in the subdivided section in each setting and sets it as the aggregate value of the subdivided section,
The section setting unit sequentially sets the section J and the section K so that all combinations of the attribute values are set, and subdivides the section J set by the subdivision section into subdivided sections. The subdivision probability calculation unit calculates subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and the integration unit calculates the aggregated values of the subdivided sections and the subdivision probabilities p. ₀ ,..., P _M−1 are used to determine the transition probability A _JK ,
The aggregate value updating unit uses the transition probabilities A _JK of the sections J and K that are sequentially set so that combinations of all the range of the attribute values are set as each element of the transition probability matrix, and an inverse matrix method Or, update the number of records whose attribute values are included in the segment refined by the iterative Bayesian method, and set it as the aggregate value of the new segment,
The said integration part calculates _| requires transition probability _AJK using the total value of the segment which the said total value update part calculated _| required. The transition probability calculation apparatus characterized by the above-mentioned. A transition probability calculation method using a transition probability calculation device including a subdivision unit, a summary value information unit, a subdivision probability calculation unit, and an integration unit ,
A _vu is a probability density function in which the attribute value v transitions to the attribute value u, J is a range from a value G _min to a value G _max that is a part of a value range that the attribute value can take, and K is a value range that the attribute value can take A _JK is a transition probability that an attribute value included in the section J transitions to an attribute value included in the section K, M is an integer of 2 or more, m is an integer of 0 to M−1, j ₀ ,. , J _M−1 is a section obtained by subdividing section J into M pieces, N _J is the number of records whose attribute value is included in section J, N _jm is the number of records whose attribute value is included in section jm, and g ₀ is The values G _min and g _M are values G _max , and when m is 1 or more and M−1 or less, g _m is an attribute value that separates the section j _m−1 and the section j _m, and g ₀ <g ₁ <.・ <G _M
The subdivision section subdivides the section J into M pieces and obtains subdivided sections j ₀ ,..., J _M−1 ;
The aggregate value information section, said number _{N J} and the number _N j0, _..., and the aggregate value information determining the _{N jM-1,}
The sub-probability calculation unit calculates sub-probabilities p _m

Subdivided probability calculation step obtained as follows:
The integration unit _calculates the transition probability A _JK

The integration steps you want
A transition probability calculation method comprising: 6. A transition probability calculating apparatus according to claim 4; a section setting unit for setting the section J and the section K; and a total value updating unit for determining a new total value from the already calculated total value and the transition probability. A total value calculation method using the total value calculation device,
The section setting unit sequentially sets the section J so that all the ranges of the attribute values are set, and subdivides the section J in which the subdivision section is set to obtain a subdivided section, and the aggregate value The information part calculates the number of records whose attribute values are included in the subdivided section in each setting and sets it as the aggregate value of the subdivided section,
The section setting unit sequentially sets the section J and the section K so that all combinations of the attribute values are set, and subdivides the section J set by the subdivision section into subdivided sections. The subdivision probability calculation unit calculates subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and the integration unit calculates the aggregated values of the subdivided sections and the subdivision probabilities p. ₀ ,..., P _M−1 are used to determine the transition probability A _JK ,
The aggregate value updating unit uses the transition probabilities A _JK of the sections J and K that are sequentially set so that combinations of all the range of the attribute values are set as each element of the transition probability matrix, and an inverse matrix method Alternatively, the number of records whose attribute values are included in the segment subdivided by the iterative Bayesian method is updated to the aggregate value of the new subdivided segment, and the number of records in the subdivided segment included in the segment J is added to the segment J An aggregate value calculation method characterized by obtaining the number of records. 6. A transition probability calculating apparatus according to claim 4; a section setting unit for setting the section J and the section K; and a total value updating unit for determining a new total value from the already calculated total value and the transition probability. A transition probability calculation method using the transition probability calculation device,
The section setting unit sequentially sets the section J so that all the ranges of the attribute values are set, and subdivides the section J in which the subdivision section is set to obtain a subdivided section, and the aggregate value The information part calculates the number of records whose attribute values are included in the subdivided section in each setting and sets it as the aggregate value of the subdivided section,
The section setting unit sequentially sets the section J and the section K so that all combinations of the attribute values are set, and subdivides the section J set by the subdivision section into subdivided sections. The subdivision probability calculation unit calculates subdivision probabilities p ₀ ,..., P _M−1 for the set sections J and K, and the integration unit calculates the aggregated values of the subdivided sections and the subdivision probabilities p. ₀ ,..., P _M−1 are used to determine the transition probability A _JK ,
The aggregate value updating unit uses the transition probabilities A _JK of the sections J and K that are sequentially set so that combinations of all the range of the attribute values are set as each element of the transition probability matrix, and an inverse matrix method Or, update the number of records whose attribute value is included in the segment refined by the iterative Bayesian method to the aggregate value of the new segment,
The said integration part calculates _| requires transition probability _AJK using the total value of the subdivided area which the said total value update part updated. The transition probability calculation method characterized by the above-mentioned.

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