Method and system for predicting multi-variable outcomes

• US 20040083452A1
• Filed: 03/27/2003
• Published: 04/29/2004
• Est. Priority Date: 03/29/2002
• Status: Active Grant

• Current Assignee: Agilent Technologies, Inc.
• Original Assignee: Agilent Technologies, Inc.
• Inventors: Illouz, Mika, Minor, James M.
• Granted Patent: US 7,191,106 B2
• Time in Patent Office: Days
• US Class Current: 717/109
• CPC Class Codes: G16B 40/00 ICT specially adapted for biostatistics; ICT specially adapted for bioinformatics-related machine learning or data mining, e.g. knowledge discovery or pattern finding
• CPC Class Codes: G16B 50/00 ICT programming tools or database systems specially adapted for bioinformatics
• CPC Class Codes: G16B 50/20 Heterogeneous data integration
• CPC Class Codes: G16H 50/50 for simulation or modelling of medical disorders
• CPC Class Codes: Y02A 90/10 Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

Systems methods and recordable media for predicting multi-variable outcomes based on multivariable inputs. Additionally, the models described can be used to predict the multi-variable inputs themselves, based on the multi-variable inputs, providing a smoothing function, acting as a noise filter. Both multi-variable inputs and multi-variable outputs may be simultaneously predicted, based upon the multi-variable inputs. The models find a critical subset of data points, or “tent poles” to optimally model all outcome variables simultaneously to leverage communalities among outcomes.

Claims

1. A method of generating a predictor model for predicting multivariable outcomes based upon multivariable inputs with consideration of nuisance variables, said method comprising the steps of:

a) defining an initial model as Model Zero and inputting Model Zero as column one of a similarity matrix T;

b) performing an optimization procedure to solve for matrix values of an a matrix which is a transformation of outcome profiles associated with input profiles;

c) calculating a residual matrix E based on the difference between the actual outcome values and the predicted outcome values determined through a product of matrix T and matrix α

;

d) selecting a row of the a residual matrix e which contains an error value most closely matching a pre-defined error criterion;

e) identifying a row from a matrix of the multivariable inputs which corresponds to the selected row from the residual matrix ε

;

f) calculating similarity values between the identified row and each of the rows in the matrix of the multivariable inputs, including the identified row with itself,

g) populating the next column of similarity matrix T with the calculated similarity values if it is determined that the identified row is not collinear or nearly collinear with any previously identified row the similarity values for which were used to populate a previous column of similarity matrix T; and

h) repeating steps b) through g) until a predefined stopping criterion has been reached.

2. The method of claim 1, wherein the step of performing an optimization procedure comprises performing a least squares regression procedure.

3. A method comprising forwarding a result obtained from the method of claim 1, to a remote location.

4. A method comprising transmitting data representing a result obtained from the method of claim 1 to a remote location.

5. A method comprising receiving a result obtained from a method of claim 1 from a remote location.

6. The method of claim 1, wherein the predefined stopping criterion comprises a determination that all error criteria of the residual matrix are within bounds of a predefined error threshold having been predefined as acceptable for an intended application of the model.

7. The method of claim 1, wherein the predefined stopping criterion comprises determining that all remaining rows of the matrix of multivariable inputs which have not been used to calculate similarity values to populate a column of matrix T are collinear or nearly collinear with at least one of the rows of the matrix of multivariable inputs which have been used to calculate similarity values to populate a column of matrix T.

8. The method of claim 1, further comprising trimming the number of columns in the T matrix to an optimized minimum number to optimize prospective predictions.

9. The method of claim 1, wherein the pre-defined error criterion comprises maximum absolute ensemble error.

10. The method of claim 1, wherein the pre-defined error criterion is selected from the group consisting of:

mean absolute ensemble error, median absolute ensemble error, mode absolute ensemble error, weighted average absolute ensemble error, and robust average absolute ensemble error.

11. The method of claim 1, further comprising estimating validation error of the model derived using the leave-one-out (LOO) cross validation technique.

12. The method of claim 11, wherein the leave-one-out (LOO) cross validation technique efficiently predicts the variance in the validation error according to the formula:

13. A method of predicting multivariable outcomes (row vectors, called Y-profiles) in an outcome-variable matrix Y using matched profiles of multivariable inputs (row vectors, called X-profiles) in an input-data matrix X, said method comprising:

adding n row vectors of X-profiles and Y-profiles, respectively, to the input and outcome profiles used to determine the predictor model of claim 1,

adding n rows of values to Model Zero;

calculating similarity values for each of the n rows of X-profiles with each of the identified rows used to calculate similarity values used in populating columns of matrix T, and adding the calculated similarity values in corresponding positions in an additional n rows in similarity matrix T; and

multiplying the n rows of the similarity matrix T by the α

matrix to arrive at predictions of the Y-profiles, within an acceptable predefined range of error.

14. A method of self-predicting multi-variable profiles, comprising the steps of:

generating the predictor model according to claim 1 through use of X-variable profiles as both the multivariable inputs and the multivariable outcomes;

wherein the identified rows populating the similarity matrix T are essential profiles of the prediction model, and wherein the predicted multivariable outcomes smooth the X-variable profiles input function, reduce noise due to the nuisance variables, and restrict candidate profiles in the X-variable profiles to enhance causal leverage between profiles.

15. A method of imputation of missing values in multi-variable X-profile inputs, comprising the steps of:

a) modifying the multi-variable X-profile inputs by replacing the missing values with initial starting values;

b) self-predicting multi-variable X-profile outputs of the modified multi-variable inputs according to the method of claim 14;

c) replacing the modifications to the missing variables with the predicted variables obtained by self-predicting multi-variable X-profile outputs in step b); and

repeating steps b) and c) until differences between the current replacement modifications and the previous iteration of replacement modifications are less than a predefined threshold value of correction difference.

16. A method of simultaneously predicting both multi-variable X-input profiles and multi variable Y-output profiles based on the multi-variable X-input profiles, said method comprising the steps of:

generating the predictor model according to claim 1 through use of the X-variable profiles as the multivariable inputs and both the X-variable profiles and Y-variable profiles as the multivariable outputs.

17. The method of claim 16, wherein the X-variable profiles and Y-variable profiles are stacked vertically to form a combined matrix of the multivariable outputs.

18. The method of claim 16, wherein the X-variable profiles and Y-variable profiles are concatenated horizontally to form a combined matrix of the multivariable outputs.

19. The method of claim 16, wherein the identified rows used to calculate similarity values used in populating columns of matrix T are strategic X-profile rows, and wherein said method further comprises clustering the strategic X-profile rows in a combined matrix defining both the X-variable profiles and Y-variable profiles.

20. A method of simultaneously predicting both multi-variable X-input profiles and multi variable Y-output profiles based on the multi-variable X-input profiles and the multi-variable Y-output files, said method comprising the of:

generating the predictor model according to claim 1 through use of an X/Y matrix, resulting from the catenation of the X-variable profiles and Y-variable profiles, as the multivariable inputs and using the X/Y matrix as the multivariable outputs.

21. The method of claim 20, wherein said step of identifying a row is restricted to only the X-profile portion of the X/Y input matrix, resulting in enhanced causal leverage between the X- and Y-profiles.

22. The method of claim 1, further comprising assigning score functions to the multi-variable outcomes for use in any multivariate distribution process.

23. The method of claim 1, further comprising testing the ellipticity of the identified rows of X-profiles as a function of the X-space, using the Marquardt-Levenberg algorithm, and ranking the X-variable in the identified rows of X-profiles according to said testing.

24. The method of claim 1, further comprising determining a decay constant for each of the identified rows of X-profiles used to calculate similarity values to populate the T matrix.

25. The method of claim 24, wherein the step of determining a decay constant for each of the identified rows comprises the steps of:

determining the working dimension of the domain for each data location of the multi-variable data;

computing a domain simplex of data adjacent to each said data location; and

setting each decay constant as the inverse of a largest of dissimilarity values calculated between each data location and the domain simplex of the data adjacent to that data location.

26. The method of claim 25, further comprising adding data points to each domain simplex to form a domain complex.

27. A method of generating a predictor model for predicting multivariable outcomes (a matrix of rows of Y-profiles) based upon multivariable inputs (a matrix of rows of X-profiles) with consideration of nuisance variables, said method comprising the steps of:

analyzing each X-profile row of multivariable inputs as an object;

calculating similarity among the objects;

selecting tent poles determined to be critical profiles in supporting a prediction function for predicting the Y-profiles;

optimizing the number of tent poles to minimize the error between the X-profiles and the Y-profiles.

28. A system for predicting multivariable outcomes based upon multivariable inputs with consideration of nuisance variables, said system comprising:

a) defining an initial model as Model Zero and inputting Model Zero as column one of a similarity matrix T;

means for performing an optimization procedure to solve for matrix values of an α

matrix which is a transformation of outcome profiles associated with input profiles;

means for calculating a residual matrix ε

based on the difference between the actual outcome values and the predicted outcome values determined through a product of a similarity matrix T and matrix α

,

means for selecting a row of the residual matrix ε

which contains an error value most closely matching a pre-defined error criterion;

means for identifying a row from a matrix of the multivariable inputs which corresponds to the selected row from the residual matrix ε

;

means for calculating similarity values between the identified row and each of the rows in the matrix of the multivariable inputs, including the identified row with itself;

means for populating next columns of similarity matrix T with the calculated similarity values if it is determined that the identified row is not collinear or nearly collinear with any previously identified row the similarity values for which were used to populate a previous column of similarity matrix T; and

means for determining when to stop populating columns of similarity matrix T.

29. The system of claim 28, further comprising means for trimming the number of columns in the T matrix to an optimized minimum number to optimize prospective predictions.

30. The system of claim 28, further comprising means for estimating validation error of the model derived using the leave-one-out (LOO) cross validation technique.

31. The system of claim 30, wherein the leave-one-out (LOO) cross validation technique efficiently predicts the variance in the validation error according to the formula:

32. A system for generating a predictor model for predicting multivariable outcomes (a matrix of rows of Y-profiles) based upon multivariable inputs (a matrix of rows of X-profiles) with consideration of nuisance variables, said system comprising:

means for analyzing each X-profile row of multivariable inputs as an object;

means for calculating similarity among the objects;

means for selecting tent poles determined to be critical profiles in supporting a prediction function for predicting the Y-profiles; and

means for optimizing the number of tent poles to minimize the error between the X-profiles and the Y-profiles.

33. A computer-readable medium carrying one or more sequences of instructions from a user of a computer system for predicting multivariable outcomes based upon multivariable inputs with consideration of nuisance variables, wherein the execution of the one or more sequences of instructions by one or more processors cause the one or more processors to perform the steps of:

a) defining an initial model as Model Zero and inputting Model Zero as column one of a similarity matrix T;

b) performing an optimization procedure to solve for matrix values of an α

matrix which is a transformation of outcome profiles associated with input profiles;

c) calculating a residual matrix ε

based on the difference between the actual outcome values and the predicted outcome values determined through a product of matrix T and matrix α

,

d) selecting a row of the a residual matrix ε

which contains an error value most closely matching a pre-defined error criterion;

e) identifying a row from a matrix of the multivariable inputs which corresponds to the selected row from the residual matrix ε

;

f) calculating similarity values between the identified row and each of the rows in the matrix of the multivariable inputs, including the identified row with itself;

g) populating the next column of similarity matrix T with the calculated similarity values if it is determined that the identified row is not collinear or nearly collinear with any previously identified row the similarity values for which were used to populate a previous column of similarity matrix T; and

h) repeating steps b) through g) until a predefined stopping criterion has been reached.

34. The computer readable medium of claim 33, wherein the following further step is performed:

trimming the number of columns in the T matrix to an optimized minimum number to optimize prospective predictions.

35. The computer readable medium of claim 33, wherein the following further step is performed:

estimating validation error of the model derived using the leave-one-out (LOO) cross validation technique, according to the formula;