Symbolic regression embedding dimensionality analysis

• US 10,599,766 B2
• Filed: 12/15/2017
• Issued: 03/24/2020
• Est. Priority Date: 12/15/2017
• Status: Active Grant

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Gunawan, Oki, Horesh, Lior, Nannicini, Giacomo, Zhou, Wang
• Primary Examiner(s): McFadden, Susan I
• Application Number:
  US15/843,118
• Publication Number:
  US 20190188256A1
• Time in Patent Office: 830 Days
• Field of Search: 704 9
• CPC Class Codes: G06F 16/3344 using natural language analysis
• CPC Class Codes: G06F 40/211 Syntactic parsing, e.g. based on context-free grammar [CFG] or unification grammars
• CPC Class Codes: G06F 40/253 Grammatical analysis; Style critique

Abstract

A dimensionality analysis method, system, and computer program product, include defining a grammar that describes an admissible relationship between quantities in a data set, discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar, conducting a search that determines which valid expression in the data set satisfy the grammar, and selecting the expression that fits the dataset and minimizes a measure of a complexity of the expression.

Claims

1. A computer-implemented dimensionality analysis method, the method comprising:

defining a free-form grammar that describes an admissible relationship between quantities in a data set;

discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar;

conducting a search that determines which valid expressions in the data set satisfies the grammar and that determines a measure of a complexity of the expression; and

selecting the valid expressions that fits the dataset and minimizes the measure of the complexity of the expression.

2. The computer-implemented dimensionality analysis method of claim 1, wherein the plurality of valid expressions are determined, and the valid expressions comprise a set of symbols representing viable operators, variables, and coefficients, along with grammatical rules that define a syntax of the valid expressions.

3. The computer-implemented dimensionality analysis method of claim 2, wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

4. The computer-implemented dimensionality analysis method of claim 3, wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

5. The computer-implemented dimensionality analysis method of claim 1, wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

6. The computer-implemented dimensionality analysis method of claim 5, wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationship between quantities.

7. The computer-implemented method of claim 1, embodied in a cloud-computing environment.

8. A computer program product, the computer program product comprising a non-transitory computer-readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to perform:

defining a free-form grammar that describes an admissible relationship between quantities in a data set;

discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar;

conducting a search that determines which valid expressions in the data set satisfies the grammar and that determines a measure of a complexity of the expression; and

selecting the valid expressions that fits the dataset and minimizes the measure of the complexity of the expression.

9. The computer program product of claim 8, wherein the valid expressions comprise a set of symbols representing viable operators, variables, and coefficients, along with grammatical rules that define a syntax of the valid expressions.

10. The computer program product of claim 9, wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

11. The computer program product of claim 10, wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationship between quantities.

12. The computer program product of claim 8, wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between an admissible relationship are allowed, depending on the corresponding attributes.

13. The computer program product of claim 12, wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

14. A dimensionality analysis system, said system comprising:

a processor; and

a memory, the memory storing instructions to cause the processor to;

defining a free-form grammar that describes an admissible relationship between quantities in a data set;

discovering symbolic expressions that intrinsically account for a dimensionality analysis based on the grammar;

conducting a search that determines which valid expressions in the data set satisfies the grammar and that determines a measure of a complexity of the expression; and

selecting the valid expressions that fits the dataset and minimizes the measure of the complexity of the expression.

15. The system of claim 14, wherein the valid expressions comprise a set of symbols representing viable operators, variables, and coefficients, along with grammatical rules that define a syntax of the valid expressions.

16. The system of claim 15, wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between admissible relationships are allowed, depending on the corresponding attributes.

17. The system of claim 16, wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

18. The system of claim 14, wherein the symbolic expressions include a set of attributes associated with each variable that specifies a dimensional property, and a grammar, that specifies which operations between admissible relationship are allowed, depending on the corresponding attributes.

19. The system of claim 18, wherein the set of attributes and the grammar are generalized to properties that do not relate to dimensional properties, but encode an abstract relationships between quantities.

20. The system of claim 14, embodied in a cloud-computing environment.