Abstract:
There is provided with a method, including: optimizing a first objective function defined by using an explanatory variable belonging an attribute in each sample, a target variable in each sample, and a first conversion parameter to find a value of the first conversion parameter; generating by using the first conversion parameter corresponding to the attribute a conversion function for converting an explanatory variable belonging to the attribute to an intermediate variable with certain range; optimizing a second objective function defined by using a plurality of the intermediate variables corresponding to the plurality of variables in each sample, the target variable in each sample, and a second conversion parameter to find a value of the second conversion parameter; and generating by using the second conversion parameter a probabilistic model for calculating from a plurality of intermediate variables a probability that a predetermined event occurs or does not occur.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is based upon and claims the benefit of priority from the prior Japanese Patent Applications No. 2005-234813 filed on Aug. 12, 2005, the entire contents of which are incorporated herein by reference.  
       BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention relates to a probabilistic model generation method, a probabilistic model generation apparatus, and a program.  
         [0004]     2. Related Art  
         [0005]     As for the credit risk model, it has become the mainstream to adopt a binary logit model supplied with financial indexes as inputs, from the viewpoint of precision and easiness of interpretation. A technique of calculating a bankruptcy probability of an enterprise by using a logit model is described in JP-A 2000-259729(KOKAI). It is necessary to set upper and lower limit values of financial indexes suitably in order to reduce the sense of incompatibility when an analyst actually utilizes the logit model.  
         [0006]     It is effective in preventing the estimated bankruptcy probability from being changed greatly by outlier values to set upper and lower limit values for financial indexes. In determining upper and lower limit values for respective financial indexes, however, expert knowledge concerning financial statements and actual operation are requested.  
       SUMMARY OF THE INVENTION  
       [0007]     According to an aspect of the present invention, there is provided with a probabilistic model generation method for generating a probabilistic model calculating a probability that a predetermined event occurs or does not occur, by using learning data as a set of samples each of which includes a plurality of explanatory variables belonging to respectively different attributes and a target variable representing whether the predetermined event occurs or not, comprising: optimizing a first objective function defined by using the explanatory variable belonging the attribute in each sample, the target variable in each sample, and a first conversion parameter to find a value of the first conversion parameter as for each of the attributes; generating by using the first conversion parameter corresponding to the attribute a conversion function for converting an explanatory variable belonging to the attribute to an intermediate variable with certain range of value as for each of the attributes; optimizing a second objective function defined by using a plurality of intermediate variables corresponding to the plurality of explanatory variables in each sample, the target variable in each sample, and a second conversion parameter to find a value of the second conversion parameter; and generating by using the second conversion parameter a probabilistic model for calculating from a plurality of intermediate variables a probability that the predetermined event occurs or does not occur.  
         [0008]     According to an aspect of the present invention, there is provided with a probabilistic model generation method for generating a probabilistic model calculating a probability that a predetermined event occurs or does not occur, by using learning data as a set of samples each of which includes a plurality of explanatory variables belonging respectively different attributes and a target variable representing whether the predetermined event occurs or not, comprising: optimizing an objective function defined by using the plurality of variables in each sample, the target variable in each sample, a first conversion parameter provided for each of the attributes, and a second conversion parameter to find values of the first conversion parameters and a value of the second conversion parameter; generating by using the first conversion parameter corresponding to the attribute a conversion function for converting an explanatory variable belonging to the attribute to an intermediate variable with certain range of value, as for each of the attributes; and generating by using the second conversion parameter a probabilistic model for calculating from a plurality of intermediate variables a probability that the predetermined event occurs or does not occur.  
         [0009]     According to an aspect of the present invention, there is provided with a probabilistic model generation apparatus, comprising: a database configured to store learning data as a set of samples each of which includes a plurality of explanatory variables belonging to respectively different attributes and a target variable representing whether the predetermined event occurs or not; a conversion function generator configured to optimize a first objective function defined by using the explanatory variable belonging the attribute in each sample, the target variable in each sample, and a first conversion parameter to find a value of the first conversion parameter as for each of the attributes and configured to generate by using the first conversion parameter corresponding to the attribute a conversion function for converting an explanatory variable belonging to the attribute to an intermediate variable with certain range of value as for each of the attributes; a model generator configured to optimize a second objective function defined by using a plurality of intermediate variables corresponding to the plurality of explanatory variables in each sample, the target variable in each sample, and a second conversion parameter to find a value of the second conversion parameter and configured to generate by using the second conversion parameter a probabilistic model for calculating from a plurality of intermediate variables a probability that the predetermined event occurs or does not occur.  
         [0010]     According to an aspect of the present invention, there is provided with a program which is executed by a computer, comprising instructions for: accessing a database configured to store learning data as a set of samples each of which includes a plurality of explanatory variables belonging to respectively different attributes and a target variable representing whether the predetermined event occurs or not; optimizing a first objective function defined by using the explanatory variable belonging the attribute in each sample, the target variable in each sample, and a first conversion parameter to find a value of the first conversion parameter as for each of the attributes; generating by using the first conversion parameter corresponding to the attribute a conversion function for converting an explanatory variable belonging to the attribute to an intermediate variable with certain range of value as for each of the attributes; optimizing a second objective function defined by using a plurality of intermediate variables corresponding to the plurality of variables in each sample, the target variable in each sample, and a second conversion parameter to find a value of the second conversion parameter; and generating by using the second conversion parameter a probabilistic model for calculating from a plurality of intermediate variables a probability that the predetermined event occurs or does not occur. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]      FIG. 1  is a block diagram showing schematically a probabilistic model generation apparatus according to a first embodiment;  
         [0012]      FIG. 2  is a diagram showing an example of financial index values;  
         [0013]      FIG. 3  is a diagram showing an example of bankruptcy information of enterprises;  
         [0014]      FIG. 4  is a diagram showing an example of a graph of a logistic function;  
         [0015]      FIG. 5  is a diagram showing financial index values before and after conversion;  
         [0016]      FIG. 6  is a diagram showing a table which represents bankruptcy probabilities of enterprises;  
         [0017]      FIG. 7  is a block diagram showing schematically a probabilistic model generation apparatus according to a second embodiment;  
         [0018]      FIG. 8  is a diagram showing an example of a network structure;  
         [0019]      FIG. 9  is a diagram showing a graph example of a broken line function used to convert financial index values;  
         [0020]      FIG. 10  is a diagram showing an example of explanatory variables;  
         [0021]      FIG. 11  is a diagram showing data used to generate a model to estimate a loss accident occurrence probability half a year hence;  
         [0022]      FIG. 12  is a diagram showing a data example of a operation branch A;  
         [0023]      FIG. 13  is a diagram showing a data example of all operation branches;  
         [0024]      FIG. 14  is a diagram showing an example of explanatory variables; and  
         [0025]      FIG. 15  is a diagram showing an example determining by an expert upper and lower limit values of a financial index value. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
     First Embodiment  
       [0026]      FIG. 1  is a block diagram showing schematically a probabilistic model generation apparatus according to a first embodiment of the present invention.  
         [0027]     The probabilistic model generation apparatus includes a financial database DB 1 , a bankruptcy information database DB 2 , a financial data reader A 1 , a financial data storage A 2 , a bankruptcy information reader A 3 , a bankruptcy information storage A 4 , a financial index value upper and lower limit setter A 5  (hereinafter simply, referred to as upper and lower limit setter), a post-conversion index value storage A 6 , a bankruptcy probability calculator A 7 , and a bankruptcy probability storage A 8 . The upper and lower limit setter A 5 , for example, corresponds to a conversion function generator. The bankruptcy probability calculator A 7 , for example, corresponds to a model generator.  
         [0028]     Processing conducted in each of units shown in  FIG. 1  may be conducted in one computer device or may be conducted in a plurality of computer devices distributively. Furthermore, the processing conducted in each of units may be implemented by causing a CPU to execute a previously created program, using hardware, or using a combination of them.  
         [0029]     The financial data reader A 1  reads financial index values of enterprises in certain fiscal year from the financial database DB 1 .  
         [0030]      FIG. 2  shows an example of financial data stored in the financial database DB 1 . Five financial indexes (attributes)  1  to  5  (gross profit ratio on sales, owned capital ratio, ordinary income, accounts receivable collection period, and sales increase ratio) are shown in  FIG. 2 . Each of values of the financial indexes  1  to  5  in one enterprise corresponds to an explanatory variable.  
         [0031]     Specified financial index values (such as, for example, owned capital ratio, sales increase ratio, and ordinary income increase rate) of a specified enterprise group (for example, enterprises of the building industry) are read out from data having a form shown in  FIG. 2 , and stored in the financial data storage A 2 . The financial data storage A 2  may be a memory such as a DRAM (Dynamic Random Access Memory). If the data amount is large, the financial data storage A 2  may be a hard disk.  
         [0032]     The bankruptcy information reader A 3  reads bankruptcy information of enterprises from the bankruptcy information database DB 2 , and stores it in the bankruptcy information storage A 4 . The bankruptcy information contains information as to whether bankruptcy has occurred a year or less after a predetermined reference day (such as account day of the enterprise). The bankruptcy information storage A 4  may be a memory such as a DRAM. If the data amount is large, the bankruptcy information storage A 4  may be a hard disk.  
         [0033]      FIG. 3  shows an example of bankruptcy information of enterprises stored in the bankruptcy information database DB 2 .  
         [0034]     “1” in the bankruptcy information represents that the enterprise has gone bankrupt a year or less after, whereas “0” in the bankruptcy information represents that the enterprise has not gone bankrupt a year or less after. Bankruptcy information corresponds to, for example, a target variable, and “bankruptcy” corresponds to, for example, a predetermined event. A set of explanatory variables and a target variable corresponds to, for example, a sample. In the present embodiment, the bankruptcy information database DB 2  and the financial database DB 1  are provided separately. Data in these databases DB 1  and DB 2  may be stored in one database, and the present invention incorporates this case.  
         [0035]     The upper and lower limit setter A 5  receives financial index values from the financial data storage A 2  and bankruptcy information from the bankruptcy information storage A 4 , and converts financial index values as described hereafter.  
         [0036]     A value obtained by converting an ith financial index value X ij  of a jth enterprise is denoted by Y ij . Y corresponds to, for example, an intermediate variable. When converting a financial index value by using the logit conversion, the conversion is represented by (Expression 1), where α and β are parameters in the conversion.  
               Y   ij     =     1     1   +     exp   ⁡     (         α   i     ⁢     X   ij       +     β   i       )                   (     Expression   ⁢           ⁢   1     )             
 
         [0037]     Since the logistic function gradually approaches 0 or 1, this conversion is equivalent to setting upper and lower limit values of the financial index value. An example of a graph of the logistic function is shown in  FIG. 4 . As for the conversion parameters α and β, learning is conducted to maximize the logarithmic likelihood:  
                     1   ⁢     (       α   i     ,     β   i       )       =     log   ⁢       ∏     j   =   1     N     ⁢           ⁢         Y   ij     c   j       ⁡     (     1   -     Y   ij       )         (     1   -     c   j       )                       =       ∑     j   =   1     N     ⁢     (         c   j     ⁢   log   ⁢           ⁢     Y   ij       +       (     1   -     c   j       )     ⁢     log   ⁡     (     1   -     Y   ij       )           )                     (     Expression   ⁢           ⁢   2     )             
 
 In the case of the logistic function, optimization of the logarithmic likelihood is the so-called convex problem. Therefore, the optimization of the logarithmic likelihood can be conducted by using a well-known technique such as the Newton method or the steepest descent method. 
 
         [0038]     In (Expression 2), N represents the number of enterprises stored in the financial data storage A 2 , and c j  is a random variable. If the jth enterprise will go bankrupt within one year, the random variable c j  assumes 1. If the jth enterprise will not go bankrupt within one year, the random variable c j  assumes 0.  
         [0039]     The upper and lower limit setter A 5  stores the financial index value Y after conversion in the post-conversion index value storage A 6 . The post-conversion index value storage A 6  may be a memory such as a DRAM. If the data amount is large, the post-conversion index value storage A 6  may be a hard disk. An example of conversion of financial index values 1 (gross profit ratios on sales) in  FIG. 2  conducted by using the (Expression 1) is shown in  FIG. 5 . Financial index values of enterprises before the conversion are converted into a range of 0 to 1.  
         [0040]     The bankruptcy probability calculator A 7  receives the financial index value Y after conversion from the post-conversion index value storage A 6 , and calculates a bankruptcy probability of an enterprise by using a logit model (a binary logit model based on linear combination of financial indexes after the conversion) represented by (Expression 3).  
               P   j     =     1     1   +     exp   ⁡     (         ∑     i   =   1     M     ⁢       γ   i     ⁢     Y   ij         +   δ     )                   (     Expression   ⁢           ⁢   3     )             
 
         [0041]     Here, P j  is a bankruptcy probability of the jth enterprise, and M is a total number of financial indexes used to calculate the bankruptcy probability. As for conversion parameters γ and ε, learning is conducted to maximize the logarithmic likelihood  
                     1   ⁢     (     γ   ,   δ     )       =     log   ⁢       ∏     j   =   1     N     ⁢     P   j       c   j     ⁡     (     1   -     c   j       )                         =       ∑     j   =   1     N     ⁢     (         c   j     ⁢   log   ⁢           ⁢     P   j       +       (     1   -     c   j       )     ⁢     log   ⁡     (     1   -     P   j       )           )                     (     Expression   ⁢           ⁢   4     )             
 
 by using the Newton method or the like. Thus, in the present embodiment, after the parameters of the financial index value conversion are learned, parameters of a logit model are learned. 
 
         [0042]     The bankruptcy probability calculator A 7  stores the calculated bankruptcy probability P in the bankruptcy probability storage A 8 . The bankruptcy probability storage A 8  may be a memory such as a DRAM. If the data amount is large, the bankruptcy probability storage A 8  may be a hard disk.  FIG. 6  shows bankruptcy probabilities of the enterprises calculated using the (Expression 1) and (Expression 3) on the basis of the data shown in  FIG. 2  and  FIG. 3 .  
         [0043]     It is thus possible to calculate a probability that an enterprise to be evaluated will go bankrupt within a year on the basis of financial index values of the enterprise by using the (Expression 1) with the parameters α and β determined and the (Expression 3) with the parameters γ and δ determined.  
         [0044]     In more detail, financial index values of a certain enterprise are input from an input unit which is not illustrated. Input financial indexes may be the same as those used when determining the parameters α and β. The upper and lower limit setter A 5  receives the financial index values input from the input unit into X in the (Expression 1), converts the financial index values, and then stores the financial index values after conversion in the post-conversion index value storage A 6 . The bankruptcy probability calculator A 7  reads out the financial index values after conversion from the post-conversion index value storage A 6 , inputs the financial index values read out into Y in the (Expression 3), and calculates a probability that the enterprise will go bankrupt within one year. The bankruptcy probability calculator A 7  stores the calculated bankruptcy probability in the bankruptcy probability storage A 8 .  
         [0045]     Heretofore, the (Expression 1) has been used as the logit conversion Expression of the financial index values. Alternatively, a conversion Expression obtained by adding a quadratic term and a logarithmic term to the (Expression 1) may be used. As an example, (Expression 5) is obtained by adding a quadratic term to the (Expression 1).  
               Y   ij     =     1     1   +     exp   ⁡     (         α   i     ⁢     X   ij       +       α   i     ⁢     X   ij   2       +     β   i       )                   (     Expression   ⁢           ⁢   5     )             
 
         [0046]     A financial index which is not linear in relation between its financial index value and bankruptcy probability can also be modeled by thus adding the quadratic term and the logarithmic term.  
         [0047]     Conventionally, the upper and lower limit value of a financial index values are determined by an expert having expert knowledge concerning financial statements and actual operation as shown in  FIG. 15 . In this example, financial index values of at least 100 are converted to 100 and financial index values of −100 or less are converted to −100. “100” and “−100” in these original financial index values correspond to the upper limit and the lower limit, respectively. Conventionally, expert knowledge is needed to set the upper and lower limit values, and the upper and lower limit values cannot be determined simply.  
         [0048]     On the other hand, in the present embodiment, parameters of the logistic function for converting a financial index value are learned, and parameters of a probabilistic model for calculating the bankruptcy probability of an enterprise from the financial index value after conversion are learned. It can be said that learning of parameters of the logistic function is substantially equivalent to setting the upper and lower limit values. In the present embodiment, the upper and lower limit values can be thus set automatically and a probabilistic model having high precision can be generated simply.  
       Second Embodiment  
       [0049]     In the first embodiment, parameters of the financial index value conversion and the parameters of the logit model are learned separately. According to a feature of the second embodiment, however, parameters of the financial index value conversion and the parameters of the logit model are learned at a time. Hereafter, the present embodiment will be described in detail.  
         [0050]      FIG. 7  is a block diagram showing schematically a probabilistic model generation apparatus according to the second embodiment of the present invention.  
         [0051]     The probabilistic model generation apparatus includes a financial database DB 11 , a bankruptcy information database DB 12 , a financial data reader B 1 , a financial data storage B 2 , a bankruptcy information reader B 3 , a bankruptcy information storage B 4 , a financial index value upper and lower limit setter &amp; bankruptcy probability calculator B 5  (hereinafter simply referred to as upper and lower limit setter &amp; bankruptcy probability calculator), a post-conversion index value storage B 6 , and a bankruptcy probability storage B 7 .  
         [0052]     The financial data reader B 1  reads financial data of enterprises in certain fiscal year from the financial database DB 11 . The financial data reader B 1  reads specified financial index values (such as, for example, owned capital ratio, sales increase ratio, and ordinary income increase rate) of a specified enterprise group (for example, enterprises of the building industry) from data having a form shown in  FIG. 2 , and stores the specified financial index values in the financial data storage B 2 . The financial data storage B 2  may be a memory such as a DRAM. If the data amount is large, the financial data storage B 2  may be a hard disk.  
         [0053]     The bankruptcy information reader B 3  reads bankruptcy information of enterprises (whether the enterprises went bankrupt one year or less after) as shown in  FIG. 3  from the bankruptcy information database DB 12 , and stores it in the bankruptcy information storage B 4 . The bankruptcy information storage B 4  may be a memory such as a DRAM. If the data amount is large, the bankruptcy information storage B 4  may be a hard disk.  
         [0054]     The upper and lower limit setter &amp; bankruptcy probability calculator B 5  receives financial index values from the financial data storage B 2  and bankruptcy information from the bankruptcy information storage B 4 , converts financial index values, and calculates the bankruptcy probability as described in detail hereafter.  
         [0055]     A value obtained by converting an ith financial index value X ij  of a jth enterprise is denoted by Y ij . When converting a financial index value by using the logit conversion, the conversion is represented by (Expression 6), where α and β are parameters in the conversion.  
               Y   ij     =     1     1   +     exp   ⁡     (         α   i     ⁢     X   ij       +     β   i       )                   (     Expression   ⁢           ⁢   6     )             
 
         [0056]     Since the logistic function gradually approaches 0 or 1, this conversion is equivalent to setting upper and lower limit values of the financial index value. A bankruptcy probability of an enterprise is calculated by using a logit model represented by (Expression 7). P j  is a bankruptcy probability of the jth enterprise, and M is a total number of financial indexes used to calculate the bankruptcy probability.  
               P   j     =     1     1   +     exp   ⁡     (         ∑     i   =   1     M     ⁢       γ   i     ⁢     Y   ij         +   δ     )                   (     Expression   ⁢           ⁢   7     )             
 
         [0057]     As for conversion parameters α, β, γ and δ in the (Expression 6) and (Expression 7), learning is conducted to maximize the logarithmic likelihood  
                     1   ⁢     (     α   ,   β   ,   γ   ,   δ     )       =     log   ⁢       ∏     j   =   1     N     ⁢     P   j     (     1   -     c   j       )                       =       ∑     j   =   1     N     ⁢     (         c   j     ⁢   log   ⁢           ⁢     P   j       +       (     1   -     c   j       )     ⁢     log   ⁡     (     1   -     P   j       )           )                     (     Expression   ⁢           ⁢   8     )             
 
 by using the Newton method or the like. Or the parameters may be learned so as to maximize the logarithmic likelihood by utilizing a network having a structure shown in  FIG. 8  (which can be said to be a special neural network in that an intermediate node is not connected to all input nodes). In (Expression 8), N represents the number of enterprises stored in the financial data storage B 2  and c j  is a random variable. If the jth enterprise goes bankrupt within one year, the random variable c j  assumes 1. If the jth enterprise does not go bankrupt within one year, the random variable c j  assumes 0. 
 
         [0058]     The financial index value Y after conversion is stored in the post-conversion index value storage B 6 . The post-conversion index value storage B 6  may be a memory such as a DRAM. If the data amount is large, the post-conversion index value storage B 6  may be a hard disk.  
         [0059]     On the other hand, the calculated bankruptcy probability P is stored in the bankruptcy probability storage B 7 . The bankruptcy probability storage B 7  may be a memory such as a DRAM. If the data amount is large, the bankruptcy probability storage B 7  may be a hard disk.  
         [0060]     As heretofore described, it is possible to calculate a probability that an enterprise to be evaluated will go bankrupt within a year on the basis of financial index values of the enterprise by using the (Expression 6) with the parameters α and β determined and the (Expression 7) with the parameters γ and δ determined.  
         [0061]     In more detail, financial index values of a certain enterprise are input from an input unit which is not illustrated. Input financial indexes may be the same as those used when determining the parameters α, β, γ and δ. The upper and lower limit setter &amp; bankruptcy probability calculator B 5  receives the financial index values input from the input unit into X in the (Expression 6), converts the financial index values, and then stores the financial index values after conversion in the post-conversion index value storage B 6 . The upper and lower limit setter &amp; bankruptcy probability calculator B 5  reads out the financial index values after conversion from the post-conversion index value storage B 6 , inputs the financial index values read out into Y in the (Expression 7), and calculates a probability that the enterprise will go bankrupt within one year. The upper and lower limit setter &amp; bankruptcy probability calculator B 5  stores the calculated bankruptcy probability in the bankruptcy probability storage B 7 .  
         [0062]     According to the present embodiment, the parameters of the financial index value conversion and the parameters of the logit model are learned at a time, as heretofore described. As a result, the total time required for parameter calculation can be shortened.  
       Third Embodiment  
       [0063]     In the present embodiment, a broken line function is adopted as the function for converting the financial index values. Hereafter, the present embodiment will be described with reference to  FIG. 1 .  
         [0064]     The financial data reader A 1  reads specified financial index values (such as, for example, owned capital ratio, sales increase ratio, and ordinary income increase rate) of a specified enterprise group (for example, enterprises of the building industry) from the financial database DB 1  which stores financial data of enterprises in certain fiscal year, and stores the read financial index values in the financial data storage A 2 .  
         [0065]     The bankruptcy information reader A 3  reads bankruptcy information of enterprises (whether the enterprises went bankrupt one year or less after) from the bankruptcy information database DB 2 , and stores it in the bankruptcy information storage A 4 .  
         [0066]     The upper and lower limit setter A 5  receives financial index values from the financial data storage A 2  and bankruptcy information from the bankruptcy information storage A 4 , and converts the financial index values. Here, a value obtained by converting an ith financial index value X ij  of a jth enterprise is denoted by Y ij . In the present embodiment, the financial index values are converted by using a broken line function. For example, the following method is used.  
         [0067]     It is now supposed that {b 1 , . . . , b K+1 } are section boundary points of the financial index X i  (where b 1  and b K+1  are minimum and maximum values of the financial index X i , respectively), and {q 1 , . . . , q K } are bankruptcy probabilities corresponding to respective sections. In other words, q k =(The number of bankrupt enterprises corresponding to a section k)/(the number of all enterprises corresponding to the section k) (Expression 9) 
 
 Furthermore, {m 1 , . . . , m K } are middle points in respective sections (in other words, m t =(b t +b t+1 )/2, t=1, . . . , K). A value Y ij  obtained by conversion of the financial index value X ij  is defined by the following (Expression 10).  
             {             q   1     ,             b   1     ≦     X   ij     ≦     m   1                                       q     t   +   1       -     q   t           m     t   +   1       -     m   t         ⁢     (     x   -     m   t       )       +     q   t       ,               m   t     ≦     X   ij     ≦     m     t   +   1         ,                                       1   ≦   t   ≦     K   -   1                               q   K     ,             m   K     ≦     X   ij     ≦     b     K   +   1                                   (     Expression   ⁢           ⁢   10     )             
 
         [0068]     This conversion corresponds to conversion using a broken line function.  FIG. 9  shows a graph example of a broken line function. This example corresponds to setting the upper and lower limit values respectively to 20 and 100 in the financial index before conversion.  
         [0069]     Here, section boundary points {b 2 , . . . , b K } are found so as to maximize logarithmic likelihood l(b 2 , . . . , b K ) defined by the following (Expression 11) by using the financial index values and the bankruptcy information as learning data. For example, values of respective elements are found so as to maximize the logarithmic likelihood with respect to each of {b 2 , b 3 }, {b 2 , b 3 , b 4 }, {b 2 , b 3 , b 4 , b 5 },  
                     1   ⁢     (       b   2     ,   …   ⁢           ,     b   K       )       =     log   ⁢       ∏     j   =   1     N     ⁢       Y   ij     ⁢       (     1   -     Y   ij       )           (     1   -     c   j       )             cj                       =       ∑     j   =   1     N     ⁢     (         c   j     ⁢   log   ⁢           ⁢     Y   ij       +       (     1   -     c   j       )     ⁢     log   ⁡     (     1   -     Y   ij       )           )                     (     Expression   ⁢           ⁢   11     )             
 
         [0070]     Here, N represents the number of enterprises stored in the financial data storage A 2 , and c j  is a random variable. If the jth enterprise goes bankrupt within one year, the random variable c j  assumes 1. If the jth enterprise does not go bankrupt within one year, the random variable c j  assumes 0.  
         [0071]     As for a method for determining the number K of sections, there is, for example, a method of utilizing the financial index value and the bankruptcy information in a different fiscal year as test data and adopting the number K of sections which maximizes the logarithmic likelihood  
                       1   ′     ⁢     (       b   2     ,   …   ⁢           ,     b   K       )       =     log   ⁢       ∏     j   =   1       N   ′       ⁢           Y   ij   ′       c   j   ′       ⁡     (     1   -     Y   ij   ′       )         (     1   -     c   j   ′       )                       =       ∑     j   =   1       N   ′       ⁢     (         c   j   ′     ⁢   log   ⁢           ⁢     Y   ij   ′       +       (     1   -     c   j   ′       )     ⁢     log   ⁡     (     1   -     Y   ij   ′       )           )                     (     Expression   ⁢           ⁢   12     )             
 
 for the test data. For example, with respect to each of {b 2 , b 3 }, {b 2 , b 3 , b 4 }, {b 2 , b 3 , b 4 , b 5 }, . . . found using the (Expression 11), logarithmic likelihood of test data is calculated using the (Expression 12), and the number of sections which maximizes the logarithmic likelihood of test data is selected out of them. Here, N′ represents the number of enterprises in the different fiscal year utilized for the calculation, and c′ j  is a random variable. If the jth enterprise goes bankrupt within one year, the random variable c′ j  assumes 1. If the jth enterprise does not go bankrupt within one year, the random variable c′ j ; assumes 0. 
 
         [0072]     The upper and lower limit setter A 5  stores the financial index value Y after conversion in the post-conversion index value storage A 6 .  
         [0073]     The bankruptcy probability calculator A 7  receives the financial index value Y after conversion from the post-conversion index value storage A 6 , and calculates a bankruptcy probability of an enterprise by using a logit model represented by (Expression 13).  
               P   j     =     1     1   +     exp   ⁡     (         ∑     i   =   1     M     ⁢       γ   i     ⁢     Y   ij         +   δ     )                   (     Expression   ⁢           ⁢   13     )             
 
         [0074]     Here, P j  is a bankruptcy probability of the jth enterprise, and M is a total number of financial indexes used to calculate the bankruptcy probability. As for conversion parameters γ and δ, learning is conducted to maximize the following logarithmic likelihood.  
                     1   ⁢     (     γ   ,   δ     )       =     log   ⁢       ∏     j   =   1     N     ⁢         P   j     c   j       ⁡     (     1   -     P   j       )         (     1   -     c   j       )                       =       ∑     j   =   1     N     ⁢     (         c   j     ⁢   log   ⁢           ⁢     P   j       +       (     1   -     c   j       )     ⁢     log   ⁡     (     1   -     P   j       )           )                     (     Expression   ⁢           ⁢   14     )             
 
         [0075]     The bankruptcy probability calculator A 7  stores the calculated bankruptcy probability P in the bankruptcy probability storage A 8 .  
         [0076]     According to the present embodiment, parameters of the broken line function for converting the financial index value are learned and parameters of a probabilistic model for calculating the bankruptcy probability of the enterprise from the financial index value after conversion are learned, as heretofore described. It can be said that the learning of the parameters of the broken line function is equivalent to setting the upper and lower limit values. In the present embodiment, the upper and lower limit values can be thus set automatically and a probabilistic model having high precision can be generated simply.  
       Fourth Embodiment  
       [0077]     In the present embodiment, it is attempted to evaluate the probability of occurrence of a loss accident in office work conducted at an operation branch of a bank.  
         [0078]     First, office work is divided into unit office work (such as new passbook issue and remittance). Change of office work in banks to online has been promoted, and consequently it is possible to easily count times of occurrence of various kinds of business such as new passbook issue and remittance. If standard time is previously set for each business to represent necessary time, therefore, a business amount in each business can be calculated from a product of the standard time and the number of times. As appreciated from the calculation method, the business amount is represented by a time period. Here, the business amount is handled on the second time scale. With respect to certain business, the business amount thus calculated is divided into unit businesses having equal lengths beforehand and the length of the unit business is made sufficiently short. In the present embodiment, the length of the unit business is set equal to 3,600 seconds. At this time, occurrence of loss accidents twice in one unit business is rare and consequently it is supposed that such a case is disregarded. Therefore, the number of loss accident times in the unit business becomes 0 or 1. Supposing that the business amount of certain business in a bank per month is 100 hours, 100 unit businesses exist. In certain business, each of individual unit businesses is identified by j. If an accident has occurred within the unit business, then c j =1. If an accident has not occurred within the unit business, then c j =0. Explanatory variables are supposed to be indexes shown in  FIG. 10 . The explanatory variables is represented as vector x j =(x 1j , . . . , x 16j ).  
         [0079]     With respect to certain business executed in the same operation branch, all indexes of vector x j  in each unit business are supposed to be equal. Furthermore, as for the vector x j , index values obtained half a year before are used. In other words, as shown in  FIG. 11 , a model is constructed to estimate the loss accident occurrence probability half a year hence on the basis of the vector z j  (here, for convenience, z j  is used instead of x j ) and data of c j  half a year after a year of the z j .  
         [0080]     For example, if the number of unit businesses in an operation branch A is 100 and two loss accidents have occurred, then data shown in  FIG. 12  are obtained with respect to the operation branch A (all of Za are the same vectors).  
         [0081]     In the same way, data are generated with respect to other operation branches as well, and data concerning all operation branches are put together as shown in  FIG. 13 . By using the data, a model having high precision is generated simply in the same way as the first to third embodiments.  
       Fifth Embodiment  
       [0082]     As for a mistake in hospital care, an instance in which a mistake is found before execution of care or an instance in which the patient has not been affected despite a mistake is called incident. On the other hand, an instance in which the patient is affected by a mistake, an instance in which the patient becomes dead or disabled, or an instance in which heavy treatment or remedy becomes needed is called accident. In the present embodiment, a model for calculating an accident occurrence probability is constructed for each nursing person.  
         [0083]     Whether a nursing person causes an accident during a predetermined half year is represented by a variable c. In other words, if a nursing person j causes an accident, c j =1. If a nursing person j does not cause an accident, c j =0. Since the nursing person j scarcely causes accidents twice during a half year, c assumes 0 or 1 in the present embodiment as well. Furthermore, indexes shown in  FIG. 14  are measured during the same half year.  
         [0084]     These values are represented as vector x j =(x 1j , . . . , x 16j ). The vector x j =(x 1j , . . . , x 16j ) corresponds to the explanatory variables. Here, a model is generated for data of {(x j , c j )|j=1, . . . , N} in the same way as the first to third embodiments. N represents the number of nursing persons.  
         [0085]     In the present embodiment, the vector x j  and c j  are data measured during the same time period. For estimating the probability of c j =1, therefore, it is necessary to estimate a future vector x j  and substitute this value into the model. The following use is also conceivable. If the probability of c j =1 is high even though c j =0, it is judged that a risk is not actualized although the risk is present, then a countermeasure is taken.