Errors-in-variables data processing including essential weighting of mapped path-oriented deviations with normal component discrimination

• US 20080294371A1
• Filed: 05/23/2007
• Published: 11/27/2008
• Est. Priority Date: 05/23/2007
• Status: Active Grant

• Current Assignee: Larry S. Chandler
• Original Assignee: Larry S. Chandler
• Inventors: Chandler, Larry S.
• Granted Patent: US 7,930,146 B2
• Time in Patent Office: Days
• US Class Current: 702/179
• 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

Representations of data inversions are generated by alternate forms of maximum likelihood estimating which are rendered in correspondence with dependent coordinate mappings of path-oriented displacements. The dependent coordinate mappings are alternately considered to represent either path coincident deviations, path-oriented data-point projections. Normal displacements are rendered in normalized coordinates as a shortest distance between respective data samples and successive fitting function approximations. Deficiencies in representing likelihood as related to nonlinearities and heterogeneous precision are compensated by essential weighting of respectively mapped path-oriented displacements.

Claims

1. A method for accessing processing and representing information whereby a data representation is generated in correspondence with at least one common regression of a plurality variable pairs,

said data representation being generated in correspondence with a multidimensional ensemble of observation samples,

said processing system comprising means for alternately representing any system related variable as the dependent variable,

each of said variable pairs comprising a considered dependent variable being paired with a considered independent variable,

said plurality of variable pairs comprising paired combinations of at least three system variables,

sample measurements of said variable pairs being represented in correspondence with each considered observation of said ensemble,

said variable pairs being represented in correspondence with respective system related variables so as to render said sample measurements as assumed to be characterized by respective non-skewed uncertainty distributions,

said sample measurements corresponding to said paired combinations being included in rendering respective two dimensional reduction deviations,

said reduction deviations being rendered to describe two dimensional path-oriented displacements,

said two dimensional path-oriented displacements being constrained by rendition to the two degrees of freedom that correspond to respective said variable pairs, and

said reduction deviations being rendered in compatible format to be included in representing at least one common multivariate sum;

said multivariate sum being distinguished for the generating of said at least one data representation;

said method comprising;

activating means for said accessing processing and representing information, accessing provided data,

representing information whereby at least one form of data processing is effectuated in correspondence with a parametric approximative form, and

effectuating said at least one form of data processing,

said effectuating including;

implementing at least one form of calculus of variation to

optimize representation for fitting parameters in correspondence with a sum of addends,

said addends being established as represented by the square of said reduction deviations being rendered in said compatible form,

said means for accessing processing and representing information comprising;

a control system, and

said control system being configured for providing said activating, said effectuating, and said representing information.

2. A method for accessing processing and representing information as in claim 1 wherein said processing includes generating a plurality of essential weight factors in correspondence with said plurality of reduction deviations,

said essential weight factors being rendered to accommodate respective skew ratios,

said essential weight factors comprising products of the square of said skew ratios multiplied by respective pre-estimated tailored weight factors and divided by respective pre-estimated dependent component deviation variability, and

said skew ratios comprising ratios of pre-estimated representations for dependent component deviations respectively divided by pre-estimated representations for respective said reduction deviations;

said data representation being generated by;

rendering representations for said reduction deviations and said weight factors as a function of a plurality of fitting parameters and provided data, and

combining said representations by manipulations to render an inversion of said provided data;

said data representation being rendered in correspondence with an evaluation of said fitting parameters.

3. A data processing system as in claim 2 wherein said data representation is rendered in correspondence with a constrained minimizing of said distinguished sum,

said constrained minimizing being rendered in correspondence with undetermined fitting parameters,

said distinguished sum comprising the weighted sum of squares of said reduction deviations,

said reduction deviations being represented as functions of said fitting parameters,

said minimizing being constrained by weight factors being held constant during said minimizing, and

said weight factors being evaluated in correspondence with successive estimates for at least one fitting parameter;

said effectuating including evaluating respective variable pair coordinates corresponding to the intersections of lines normal to said fitting function with said fitting function,

said lines being rendered normal in a coordinate system with respective coordinates normalized on corresponding coordinate observation sample uncertainty.

said lines passing through a respective observation sample data points,

coordinates of said intersections being implemented to establish additional constraints for searching for said successive estimates along the locus of successive estimations corresponding to said constrained minimizing.

4. A method for accessing processing and representing information whereby a data representation is generated in correspondence with a plurality of reduction deviations,

said processing including generating a plurality of weight factors in correspondence with said plurality of reduction deviations,

said weight factors being rendered to accommodate respective skew ratios, and

said skew ratios comprising ratios of pre-estimated representations for dependent component deviations respectively divided by pre-estimated representations for respective said reduction deviations;

said data representation being generated by;

rendering representations for said reduction deviations and said weight factors as a function of a plurality of fitting parameters and provided data, and

combining said representations by manipulations to render an inversion of said provided data,

said data representation being rendered in correspondence with an evaluation of said fitting parameters;

said method comprising;

activating means for said accessing processing and representing information, accessing provided data,

representing information whereby at least one form of data processing is effectuated in correspondence with a parametric approximative form, and

effectuating said at least one form of data processing,

said effectuating including;

implementing at least one form of calculus of variation to optimize representation for fitting parameters in correspondence with a sum of addends,

said data representation comprising representation of established said fitting parameters,

said addends being established as represented by the square of said reduction deviations being rendered to include said weight factors;

said means for accessing processing and representing information comprising;

a control system, and

said control system being configured for providing said activating, said effectuating, and said representing information.

5. A method for accessing processing and representing information as in claim 4 whereby a data representation is generated by rendering at least one common regression of a plurality variable pairs,

said data representation being generated in correspondence with a multidimensional ensemble of observation samples,

said processing system comprising means for alternately representing any system related variable as the dependent variable,

each of said variable pairs comprising a considered dependent variable being paired with a considered independent variable,

said plurality of variable pairs comprising paired combinations of at least three system variables,

sample measurements of said variable pairs being represented in correspondence with each considered observation of said ensemble,

said variable pairs being represented in correspondence with respective system related variables so as to render said sample measurements as characterized by respective non-skewed uncertainty distributions,

said paired combinations being represented in correspondence with respective two-dimensional reduction deviations,

said two dimensional reduction deviations being constrained by rendition to the two degrees of freedom that correspond to respective said variable pairs,

said two-dimensional reduction deviations being rendered in compatible format to be included in representing at least one common multivariate sum,

said multivariate sum being distinguished for the generating of said at least one data representation.

6. A method for accessing processing and representing information as in claim 4 wherein said weight factors are essential weight factors comprising products of the square of said skew ratios multiplied by respective pre-estimated tailored weight factors and divided by respective pre-estimated dependent component deviation variability.

7. A method for accessing processing and representing information as in claim 6 wherein said respective pre-estimated dependent component deviation variability is rendered as sampling variability, said sampling variability being associated with respective said dependent component observation sampling,

said reduction deviations being rendered as assumed path coincident deviations, and

said tailored weight factors being rendered in correspondence with said path coincident deviations.

8. A method for accessing processing and representing information as in claim 6 wherein said respective pre-estimated dependent component deviation variability is rendered in correspondence with pre-estimated variabilities of evaluations for the dependent variable being determined as a function of independent variable observation samples;

said reduction deviations being rendered as path oriented data-point projections; and

said tailored weight factors being rendered in correspondence with said path oriented data-point projections.

9. A method for accessing processing and representing information as in claim 4 wherein said processing includes:

generating a plurality of lines and respective fitting function intersections,

said fitting function being evaluated in correspondence with pre-estimated fitting parameters,

said lines being rendered normal to said fitting function in a coordinate system with respective coordinates normalized on corresponding coordinate observation sample uncertainty,

said lines passing through respective observation sample data points, and

said intersections being evaluated in correspondence with said data, said fitting function, said pre-estimated fitting parameters, and at least one pair of variables;

Said at least one pair of variables comprising a considered dependent variable and a considered independent variable.

10. A data processing system comprising:

a control system, means for accessing, processing, and representing information;

said control system being configured for providing said accessing, processing, and representing information, and

said control system being configured for generating at least one data representation in correspondence with a plurality of lines and respective fitting function intersections,

said fitting function being evaluated in correspondence with pre-estimated fitting parameters,

said lines being rendered normal to said fitting function in a coordinate system with respective coordinates normalized on corresponding coordinate observation sample uncertainty,

said lines passing through respective observation sample data points, and

said intersections being evaluated in correspondence with said data, said fitting function, said pre-estimated fitting parameters, and at least one pair of variables;

Said at least one pair of variables comprising a considered dependent variable and a considered independent variable, and

said control system being configured for generating a plurality of reduction deviations in correspondence with said at least one pair of variables;

said data representation being generated by;

rendering representations for said reduction deviations as functions of provided data and at least two fitting parameters,

rendering an inversion of said provided data in correspondence with said representations for said reduction deviations,

said reduction deviations being represented in correspondence with a plurality of undetermined said fitting parameters, and

said data representation being rendered in correspondence with an evaluation of said undetermined fitting parameters.

11. A data processing system as in claim 10 wherein said control system is configured for generating a plurality of weight factors in correspondence with said plurality of reduction deviations;

said weight factors being rendered to accommodate respective skew ratios, and

said skew ratios comprising ratios of pre-estimated representations for dependent component deviations respectively divided by pre-estimated representations for respective said reduction deviations;

said data representation being generated by;

rendering representations for said weight factors as functions of provided data and at least one pre-estimated fitting parameter, and

rendering an inversion of said provided data in correspondence with said representations for said reduction deviations and pre-estimated representations for said weight factors.

12. A data processing system as in claim 11 wherein said data representation is rendered in correspondence with a constrained minimizing of a distinguished sum,

said constrained minimizing being rendered in correspondence with undetermined fitting parameters,

said distinguished sum comprising the weighted sum of squares of said reduction deviations,

said minimizing being constrained by weight factors being held constant during said minimizing, and

said weight factors being evaluated in correspondence with successively pre-determined estimates for said fitting parameters.

13. A data processing system as in claim 11 wherein said weight factors are essential weight factors comprising products of the square of said skew ratios multiplied by respective pre-estimated tailored weight factors and divided by respective pre-estimated dependent component deviation variability.

14. A data processing system as in claim 13 wherein said respective pre-estimated dependent component deviation variability is rendered as sampling variability, said sampling variability being associated with respective said dependent component observation sampling;

said reduction deviations being rendered as assumed path coincident deviations; and

said tailored weight factors being rendered in correspondence with said path coincident deviations.

15. A data processing system as in claim 13 wherein said respective pre-estimated dependent component deviation variability is rendered in correspondence with pre-estimated variabilities of evaluations for the dependent variable being determined as a function of independent variable observation samples;

said reduction deviations being rendered as path oriented data-point projections; and

said tailored weight factors being rendered in correspondence with said path oriented data-point projections.

16. A data processing system as in claim 11 comprising means for alternately representing any system related variable as the dependent variable, said system related variable being represented in a form so as to render respective sample measurements as characterized by respective non-skewed uncertainty distributions.

17. A data processing system as in claim 11 wherein said weight factors are cursory weight factors comprising products of the square of said skew ratios multiplied by respective pre-estimated spurious weight factors and divided by respective pre-estimated dependent component deviation variability.

18. A data processing system as in claim 11 whereby said data representation is is generated by rendering at least one common regression of a plurality variable pairs,

said data representation being generated in correspondence with a multidimensional ensemble of observation samples,

said processing system comprising means for alternately representing any system related variable as the dependent variable,

each of said variable pairs comprising a considered dependent variable being paired with a considered independent variable,

said plurality of variable pairs comprising paired combinations of at least three system variables,

sample measurements of said variable pairs being represented in correspondence with each considered observation of said ensemble,

said variable pairs being represented in correspondence with respective system related variables so as to render said sample measurements as characterized by respective non-skewed uncertainty distributions,

said sample measurements corresponding to said paired combinations being included in rendering respective two dimensional reduction deviations,

said reduction deviations being rendered to describe two dimensional path-oriented displacements,

said two dimensional path-oriented displacements being constrained by rendition to the two degrees of freedom that correspond to respective said variable pairs, and

said reduction deviations being rendered in compatible format to be included in representing at least one common multivariate sum;

said multivariate sum being included in generating said at least one data representation.

19. A data processing system as in claim 11 wherein at least one fitting parameter which corresponds to a considered offset and related bias is replaced by a mean value,

said mean value being rendered in correspondence with the available data and at least one form of weighting, said mean value being rendered as a function of respective pre-estimates for the remaining fitting parameters.

20. A data processing system as in claim 11 wherein alternate processing techniques are combined to render a single inversion,

said alternate processing techniques being implemented to include at least two alternate forms for the rendering of a reduction deviations,

said alternate forms being appropriately weighted for compatibility, a being included in representing a common sum of squared deviations.