SYSTEM, METHOD AND COMPUTER-ACCESSIBLE MEDIUM FOR NORMALIZING DATABASED THROUGH MIXING

• US 20100312745A1
• Filed: 12/12/2008
• Published: 12/09/2010
• Est. Priority Date: 12/12/2007
• Status: Active Grant

• Current Assignee: New York University
• Original Assignee: New York University
• Inventors: Tabak, Esteban G.
• Granted Patent: US 8,577,828 B2
• Time in Patent Office: Days
• US Class Current: 706/52
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

An exemplary methodology, procedure, system, method and computer-accessible medium can be provided to assign a joint-probability distribution to a set of continuous variables, given a sample of independent joint observations. The exemplary embodiments can transform at least a portion of particular data into transformed data, repeat the transformation until a marginal distribution of at least the portion of the particular data has been transformed to be at least sufficiently near or to reach a predetermined distribution, and estimate at least one likelihood of at least one predetermined result associated with the particular data as a function of the transformed data, whereas the repeated transformation ascends a likelihood function and/or is performed by unitary transformations.

Claims

1. A computer-accessible medium having instructions thereon wherein, when a processing arrangement executes the instructions, the processing arrangement is configured to execute procedures comprising:

(a) transforming at least a portion of particular data into transformed data;

(b) repeating the transformation until a marginal distribution of at least the portion of the particular data has been transformed to be at least sufficiently near or to reach a predetermined distribution; and

(c) estimating at least one likelihood of at least one predetermined result associated with the particular data as a function of the transformed data, wherein the repeated transformation at least one of (i) ascends a likelihood function, or (ii) is performed by unitary transformations.

2. The computer-accessible medium according to claim 1, wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional near-identity transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.

3. The computer-accessible medium according to claim 1, wherein the likelihood function is a log likelihood function.

4. The computer-accessible medium according to claim 1, wherein the unitary transformations are uniformly distributed.

5. The computer-accessible medium according to claim 1, wherein the transformation is performed by at least one-dimensional non-linear transformations.

6. The computer-accessible medium according to claim 1, wherein the transformation is performed by a near identity transformation.

7. The computer-accessible medium according to claim 1, wherein the transformation is preferably a low-dimensional transformation compared to a number variables in the data.

8. The computer-accessible medium according to claim 1, wherein the processing arrangement is further configured to receive the particular data in at least a one-dimensional format.

9. The computer-accessible medium according to claim 1, wherein the predetermined distribution is a Gaussian distribution.

10. The computer-accessible medium according to claim 9, wherein the Gaussian distribution is an isotropic Gaussian distribution.

11. The computer-accessible medium according to claim 1, wherein the transformed data satisfies a predetermined Gaussianity evaluation.

12. The computer-accessible medium according to claim 1, wherein the at least the portion of the particular data is transformed using a near-identity transformation procedure.

13. The computer-accessible medium according to claim 1, wherein the at least the portion of the particular data is transformed using a random orthogonal transformation which rotates the particular data.

14. The computer-accessible medium according to claim 1, wherein the particular data has a form of an n×

m matrix, whereas m is associated with independent observations of n variables.

15. A computer method for providing information from data, comprising the steps of:

(a) transforming at least a portion of particular data into transformed data;

(b) repeating the transformation until a marginal distribution of at least the portion of the particular data has been transformed to be at least sufficiently near or to reach a predetermined distribution; and

(c) estimating at least one likelihood of at least one predetermined result associated with the particular data as a function of the transformed data, wherein the repeated transformation at least one of (i) ascends a likelihood function, or (ii) is performed by unitary transformations.

16. The computer method according to claim 15, wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional near-identity transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.

17. The computer method according to claim 15, wherein the likelihood function is a log likelihood function.

18. The computer method according to claim 15, wherein the unitary transformations are uniformly distributed.

19. The computer method according to claim 15, wherein the transformation is performed by at least one-dimensional non-linear transformations.

20. The computer method according to claim 15, wherein the transformation is performed by a near identity transformation.

21. The computer method according to claim 15, wherein the transformation is preferably a low-dimensional transformation compared to a number variables in the data.

22. The computer method according to claim 15, wherein the particular data is received in at least a one-dimensional format.

23. The computer method according to claim 15, wherein the predetermined distribution is a Gaussian distribution.

24. The computer method according to claim 23, wherein the Gaussian distribution is an isotropic Gaussian distribution.

25. The computer method according to claim 15, wherein the transformed data satisfies a predetermined Gaussianity evaluation.

26. The computer method according to claim 15, wherein the at least the portion of the particular data is transformed using a near-identity transformation procedure.

27. The computer method according to claim 15, wherein the at least the portion of the particular data is transformed using a random orthogonal transformation which rotates the particular data.

28. The computer method according to claim 15, wherein the particular data has a form of an n×

m matrix, whereas m is associated with independent observations of n variables.

29. A system for providing information from data, comprising:

a computer arrangement which, upon an execution of a software program embodied on a computer-readable medium, is configured to perform procedures comprising;

(a) transform at least a portion of particular data into transformed data;

(b) repeat the transformation until a marginal distribution of at least the portion of the particular data has been transformed to be at least sufficiently near or to reach a predetermined distribution; and

(c) estimate at least one likelihood of at least one predetermined result associated with the particular data as a function of the transformed data, wherein the repeated transformation at least one of (i) ascends a likelihood function, or (ii) is performed by unitary transformations.

30. The system according to claim 29, wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional near-identity transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.