Stable data-driven discovery of a symbolic expression

Patent metadata

Field	Value
Publication number	US-2019197079-A1
Application number	US-201715850200-A
Country	US
Kind code	A1
Filing date	Dec 21, 2017
Priority date	Dec 21, 2017
Publication date	Jun 27, 2019
Grant date	—

Abstract

A method includes receiving, by a controller, a set of data. The set of data includes data of at least one explanatory variable and data of at least one response variable. The method also includes receiving, by the controller, an input that identifies a relevant explanatory variable. The method also includes generating, by the controller, an output data that corresponds to a symbolic expression that represents a relationship between the at least one explanatory variable and the at least one response variable. The symbolic expression is responsive to the identified relevant explanatory variable, and the symbolic expression includes a mathematically stable expression.

First claim

What is claimed is:

1 . A computer-implemented method comprising:
receiving, by a controller, a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable; receiving, by the controller, an input that identifies a relevant explanatory variable; and generating, by the controller, an output data that corresponds to a symbolic expression that represents a relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified relevant explanatory variable, and the symbolic expression comprises a mathematically stable expression.

2 . The computer-implemented method of claim 1 , further comprising determining a set of grammatical rules that define a valid expression syntax for the symbolic expression, wherein the symbolic expression follows the set of grammatical rules.

3 . The computer-implemented method of claim 1 , wherein the symbolic expression being responsive to the identified relevant explanatory variable corresponds to a symbolic expression whose derivative with respect to the identified relevant explanatory variable is a non-zero expression.

4 . The computer-implemented method of claim 3 , further comprising determining the derivative of the symbolic expression with respect to the identified relevant explanatory variable, wherein the determining the derivative comprises expressing sub-expressions of the symbolic expression within an expression tree and determining partial derivatives of the sub-expressions with respect to the identified relevant explanatory variable.

5 . The computer-implemented method of claim 4 , wherein the generating the output data that corresponds to the symbolic expression comprises determining reciprocals or eigenvalues of the partial derivatives, and the determined reciprocals or the eigenvalues are bounded expressions.

6 . The computer-implemented method of claim 1 , wherein the symbolic expression corresponds to an expression of minimal complexity.

7 . The computer-implemented method of claim 1 , wherein output that is based on the symbolic expression does not deviate from the inputted data beyond a threshold.

8 . A computer system comprising:
a memory; and a processor system communicatively coupled to the memory; the processor system configured to perform a method comprising:
receiving a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable;
receiving an input that identifies a relevant explanatory variable; and
generating an output data that corresponds to a symbolic expression that represents a relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified relevant explanatory variable, and the symbolic expression comprises a mathematically stable expression.

9 . The computer system of claim 8 , wherein the method further comprises determining a set of grammatical rules that define a valid expression syntax for the symbolic expression, wherein the symbolic expression follows the set of grammatical rules.

10 . The computer system of claim 8 , wherein the symbolic expression being responsive to the identified relevant explanatory variable corresponds to a symbolic expression whose derivative with respect to the identified relevant explanatory variable is a non-zero expression.

11 . The computer system of claim 10 , wherein the method further comprises determining the derivative of the symbolic expression with respect to the identified relevant explanatory variable, wherein the determining the derivative comprises expressing sub-expressions of the symbolic expression within an expression tree and determining partial derivatives of the sub-expressions with respect to the identified relevant explanatory variable.

12 . The computer system of claim 11 , wherein the generating the output data that corresponds to the symbolic expression comprises determining reciprocals or eigenvalues of the partial derivatives, and the determined reciprocals or the eigenvalues are bounded expressions.

13 . The computer system of claim 8 , wherein the symbolic expression corresponds to an expression of minimal complexity.

14 . The computer system of claim 8 , wherein output that is based on the symbolic expression does not deviate from the inputted data beyond a threshold.

15 . A computer program product comprising a computer-readable storage medium having program instructions embodied therewith, the program instructions readable by a processor system to cause the processor system to:
receive a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable; receive an input that identifies a relevant explanatory variable; and generate an output data that corresponds to a symbolic expression that represents a relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified relevant explanatory variable, and the symbolic expression comprises a mathematically stable expression.

16 . The computer program product of claim 15 , wherein the processor system is further caused to determine a set of grammatical rules that define a valid expression syntax for the symbolic expression, wherein the symbolic expression follows the set of grammatical rules.

17 . The computer program product of claim 15 , wherein the symbolic expression being responsive to the identified relevant explanatory variable corresponds to a symbolic expression whose derivative with respect to the identified relevant explanatory variable is a non-zero expression.

18 . The computer program product of claim 17 , wherein the processor system is further caused to determine the derivative of the symbolic expression with respect to the identified relevant explanatory variable, wherein the determining the derivative comprises expressing sub-expressions of the symbolic expression within an expression tree and determining partial derivatives of the sub-expressions with respect to the identified relevant explanatory variable.

19 . The computer program product of claim 18 , wherein the generating the output data that corresponds to the symbolic expression comprises determining reciprocals or eigenvalues of the partial derivatives, and the determined reciprocals or the eigenvalues are bounded expressions.

20 . The computer program product of claim 15 , wherein the symbolic expression corresponds to an expression of minimal complexity.

21 . A computer-implemented method comprising:
receiving, by a symbolic expression discovery engine, a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable; receiving, by the symbolic expression discovery engine, an input that identifies a relevant explanatory variable; learning, by the symbolic expression discovery engine, a relationship between the at least one explanatory variable and the at least one response variable; and generating, by the symbolic expression discovery engine, an output data that corresponds to a symbolic expression that represents the relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression

Assignees

• IBM

Inventors

• Horesh Lior
• Horesh Raya
• Nannicini Giacomo

Classifications

• G06N20/00

  Machine learning · CPC title

• G06F17/10 Primary

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• G06F30/00

  Computer-aided design [CAD] · CPC title

• G06N99/005

  Physics · mapped topic