Probabilistic model generation method, apparatus, and program

• US 20070038558A1
• Filed: 08/01/2006
• Published: 02/15/2007
• Est. Priority Date: 08/12/2005
• Status: Active Grant

• Current Assignee: Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Original Assignee: Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Inventors: Nakatsugawa, Minoru, Nishikawa, Takeichiro
• Granted Patent: US 7,899,767 B2
• Time in Patent Office: Days
• US Class Current: 705/38
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G06Q 40/03 Credit; Loans; Processing thereof

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.

Claims

1. 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.

2. The method according to claim 1, wherein

the first objective function or the second object function are a logarithmic likelihood function, and

the optimizing the first objective function or the second object function includes maximizing the logarithmic likelihood function.

3. The method according to claim 1, wherein the generating the conversion function includes generating a logistic function as the conversion function.

4. The method according to claim 3, wherein the logistic function has an nth-order term of an explanatory variable (where n is an integer of at least 2), or a logarithmic term of an explanatory variable.

5. The method according to claim 1, wherein

the generating the conversion function includes generating a broken line function as the conversion function,

when an explanatory variable to be input into the broken line function is a first threshold or more, the broken line function outputs a first definite value as an intermediate variable, and

when an explanatory variable to be input into the broken line function is a second threshold or less, the broken line function outputs a second definite value as an intermediate variable.

6. The method according to claim 1, wherein

the generating the probabilistic model includes generating a binary logit model which has a linear combination of a plurality of intermediate variables, as the probabilistic model.

7. 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.

8. The method according to claim 7, wherein

the object function are a logarithmic likelihood function, and

the optimizing the objective function includes maximizing the logarithmic likelihood function.

9. The method according to claim 7, wherein the generating the conversion function includes generating a logistic function as the conversion function.

10. The method according to claim 9, wherein the logistic function has an nth-order term of an explanatory variable (where n is an integer of at least 2), or a logarithmic term of an explanatory variable.

11. The method according to claim 7, wherein

the generating the conversion function includes generating a broken line function as the conversion function,

when an explanatory variable to be input into the broken line function is a first threshold or more, the broken line function outputs a first definite value as an intermediate variable, and

when an explanatory variable to be input into the broken line function is a second threshold or less, the broken line function outputs a second definite value as an intermediate variable.

12. The method according to claim 7, wherein

the generating the probabilistic model includes generating a binary logit model which has a linear combination of a plurality of intermediate variables, as the probabilistic model.

13. 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.

14. The apparatus according to claim 13, wherein

the first objective function or the second object function are a logarithmic likelihood function, and

the conversion function generator or the model generator optimizes the first objective function or the second object function by maximizing the logarithmic likelihood function.

15. The apparatus according to claim 13, wherein the conversion function generator generates a logistic function as the conversion function.

16. The apparatus according to claim 15, wherein the logistic function has an nth-order term of an explanatory variable (where n is an integer of at least 2), or a logarithmic term of an explanatory variable.

17. The apparatus according to claim 13, wherein

the conversion function generator generates a broken line function as the conversion function,

when an explanatory variable to be input into the broken line function is a first threshold or more, the broken line function outputs a first definite value as an intermediate variable, and

when an explanatory variable to be input into the broken line function is a second threshold or less, the broken line function outputs a second definite value as an intermediate variable.

18. The apparatus according to claim 13, wherein

the model generator generates a binary logit model which has a linear combination of a plurality of intermediate variables, as the probabilistic model.

19. 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.