System, method and computer-accessible medium for normalizing databased through mixing
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.
1. A non-transitory 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 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 gradient of 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 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 non-linear transformation.
7. 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.
8. The computer-accessible medium according to claim 1 , wherein the predetermined distribution is a Gaussian distribution.
9. The computer-accessible medium according to claim 8 , wherein the Gaussian distribution is an isotropic Gaussian distribution.
10. The computer-accessible medium according to claim 1 , wherein the transformed data satisfies a predetermined Gaussianity evaluation.
11. The computer-accessible medium according to claim 1 , wherein the at least the portion of the particular data is transformed using a non-linear transformation procedure.
12. 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.
13. 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.
14. A 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 a predetermined distribution; and
(c) using a computer hardware arrangement, 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 gradient of a likelihood function, or (ii) is performed by unitary transformations.
15. The method according to claim 14 , wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.
16. The method according to claim 14 , wherein the likelihood function is a log likelihood function.
17. The method according to claim 14 , wherein the unitary transformations are uniformly distributed.
18. The method according to claim 14 , wherein the transformation is performed by at least one-dimensional non-linear transformations.
19. The method according to claim 14 , wherein the transformation is performed by a non-linear transformation.
20. The method according to claim 14 , wherein the particular data is received in at least a one-dimensional format.
21. The method according to claim 14 , wherein the predetermined distribution is a Gaussian distribution.
22. The method according to claim 21 , wherein the Gaussian distribution is an isotropic Gaussian distribution.
23. The method according to claim 14 , wherein the transformed data satisfies a predetermined Gaussianity evaluation.
24. The method according to claim 14 , wherein the at least the portion of the particular data is transformed using a non-linear transformation procedure.
25. The method according to claim 14 , wherein the at least the portion of the particular data is transformed using a random orthogonal transformation which rotates the particular data.
26. The method according to claim 14 , wherein the particular data has a form of an n×m matrix, whereas m is associated with independent observations of n variables.
27. 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 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 gradient of a likelihood function, or (ii) is performed by unitary transformations.
28. The system according to claim 27 , wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.
29. A non-transitory 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 towards 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 gradient of a likelihood function, or (ii) is performed by unitary transformations.
30. The computer-accessible medium 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 transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.
31. The computer-accessible medium according to claim 29 , wherein the transformed data satisfies a predetermined Gaussianity evaluation.
32. The computer-accessible medium according to claim 29 , wherein the particular data has a form of an n×m matrix, whereas m is associated with independent observations of n variables.
33. A 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 towards a predetermined distribution; and
(c) using a computer hardware arrangement, 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 gradient of a likelihood function, or (ii) is performed by unitary transformations.
34. The method according to claim 33 , wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.
35. The method according to claim 33 , wherein the transformed data satisfies a predetermined Gaussianity evaluation.
36. The method according to claim 33 , wherein the particular data has a form of an n×m matrix, whereas m is associated with independent observations of n variables.
37. 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 towards 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 gradient of a likelihood function, or (ii) is performed by unitary transformations.
38. The system according to claim 37 , wherein the repeated transformation further comprises a combination of a change of coordinates, which are linear and unitary, and low-dimensional transformations that move at least one or more marginals of a probability distribution underlying the transformed data toward corresponding marginals of the predetermined distribution.
39. The system according to claim 37 , wherein the transformed data satisfies a predetermined Gaussianity evaluation.
40. The system according to claim 37 , wherein the particular data has a form of an n×m matrix, whereas m is associated with independent observations of n variables.