Methods and apparatus to reduce computer-generated errors in computer-generated audience measurement data
An example apparatus includes a matrix processor in circuit with a probability generator to determine a first matrix representative of element-wise multiplication between a constraint matrix and a first transpose matrix of the estimated demographic impression distribution, the constraint matrix based on the reference demographic impression distribution and determine a second matrix by multiplying the first matrix with a second transpose matrix of the constraint matrix. The apparatus further includes an error determiner in circuit with the matrix processor, the error determiner to determine an error indicator value based on the second matrix, the error indicator value indicative of an error associated with the estimated demographic impression distribution, and a probability generator to generate, in response to the error indicator value satisfying a threshold, an accuracy-improved demographic impression distribution.
1. An apparatus comprising:
an impressions collector to:
log a plurality of impressions at a first server of a first entity based on receiving a plurality of first network communications at the first server of the first entity from first client devices and second client devices, the impressions indicative of accesses to media;
instruct the second client devices, via redirect network communications, to send third network communications to a second server of a database proprietor, the third network communications to be indicative of the accesses to the media at the second client devices;
generate a reference demographic impression distribution based on ones of the logged impressions at the first server corresponding to the first client devices, the reference demographic impression distribution representative of reference impression counts distributed across different demographic segments; and
access an inaccurate demographic impression distribution generated by the second server of the database proprietor, the inaccurate demographic impression distribution corresponding to second impressions logged by the second server based on the third network communications, and the inaccurate demographic impression distribution representative of first impression counts distributed across the different demographic segments;
a probability generator to determine an estimated demographic impression distribution based on the inaccurate demographic impression distribution, the estimated demographic impression distribution representative of second impression counts distributed across the different demographic segments;
a matrix processor in circuit with the probability generator, the matrix processor to:
determine a first matrix representative of element-wise multiplication between a constraint matrix and a first transpose matrix of the estimated demographic impression distribution, the constraint matrix based on the reference demographic impression distribution; and
determine a second matrix by multiplying the first matrix with a second transpose matrix of the constraint matrix;
an error determiner in circuit with the matrix processor, the error determiner to determine an error indicator value based on the second matrix, the error indicator value indicative of an error associated with the estimated demographic impression distribution;
the probability generator to generate, in response to the error indicator value satisfying a threshold, an accuracy-improved demographic impression distribution; and
a memory to store the accuracy-improved demographic impression distribution in a memory to improve an accuracy of the second server corresponding to the inaccurate demographic impression distribution.
2. The apparatus of claim 1 , wherein the plurality of impressions logged at the first server are based on audience members identifiable by the first server and based on corresponding audience member demographics.
3. The apparatus of claim 1 , wherein the second client devices include database proprietor identifiers recognizable by the second server of the database proprietor.
4. The apparatus of claim 1 , wherein the accuracy-improved demographic impression distribution represents an updated demographic impression distribution based on the estimated demographic impression distribution and the constraint matrix.
5. The apparatus of claim 1 , wherein the probability generator determines the estimated demographic impression distribution based on a weight.
6. The apparatus of claim 5 , wherein the weight is representative of a number of audience members using at least some of the second client devices.
7. The apparatus of claim 1 , wherein the matrix processor is to apply a weight to the estimated demographic impression distribution to determine the first matrix, the weight representative of a number of audience members using at least some of the second client devices.
8. The apparatus of claim 1 , wherein the probability generator is to, in response to the error determiner determining the error indicator value does not satisfy the threshold, generate a plurality of second estimated demographic impression distributions until the error determiner determines a second error indicator value corresponding to one of the second estimated demographic impression distributions that satisfies the threshold.
9. The apparatus of claim 1 , wherein the constraint matrix is representative of numerical impression limits for use in modeling the inaccurate demographic impression distribution.
10. The apparatus of claim 1 , wherein the error indicator value represents that there is a compliance error between constraint limits and a matrix in which the constraint matrix is multiplied by the estimated demographic impression distribution.
11. The apparatus of claim 1 , wherein the error indicator value is a Lagrange multiplier change value.
12. A method comprising:
logging a plurality of impressions at a first server of a first entity based on receiving a plurality of first network communications at the first server of the first entity from first client devices and second client devices, the impressions indicative of accesses to media;
instructing the second client devices, via redirect network communications, to send third network communications to a second server of a database proprietor, the third network communications to be indicative of the accesses to the media at the second client devices;
generating a reference demographic impression distribution based on ones of the logged impressions at the first server corresponding to the first client devices, the reference demographic impression distribution representative of reference impression counts distributed across different demographic segments;
accessing an inaccurate demographic impression distribution generated by the second server of the database proprietor, the inaccurate demographic impression distribution corresponding to second impressions logged by the second server based on the third network communications, and the inaccurate demographic impression distribution representative of first impression counts distributed across the different demographic segments;
determining an estimated demographic impression distribution based on the inaccurate demographic impression distribution, the estimated demographic impression distribution representative of second impression counts distributed across the different demographic segments;
determining a first matrix representative of element-wise multiplication between a constraint matrix and a first transpose matrix of the estimated demographic impression distribution, the constraint matrix based on the reference demographic impression distribution;
determining a second matrix by multiplying the first matrix with a second transpose matrix of the constraint matrix;
determining an error indicator value based on the second matrix, the error indicator value indicative of an error associated with the estimated demographic impression distribution;
generating, in response to the error indicator value satisfying a threshold, an accuracy-improved demographic impression distribution; and
storing the accuracy-improved demographic impression distribution in a memory to improve an accuracy of the second server corresponding to the inaccurate demographic impression distribution.
13. The method of claim 12 , wherein the plurality of impressions logged at the first server are based on audience members identifiable by the first server and based on corresponding audience member demographics.
14. The method of claim 12 , wherein the second client devices include database proprietor identifiers recognizable by the second server of the database proprietor.
15. The method of claim 12 , wherein the accuracy-improved demographic impression distribution represents an updated demographic impression distribution based on the estimated demographic impression distribution and the constraint matrix.
16. The method of claim 12 , further including determining the estimated demographic impression distribution based on a weight.
17. The method of claim 16 , wherein the weight is representative of a number of audience members using at least some of the second client devices.
18. The method of claim 12 , further including applying a weight to the estimated demographic impression distribution to determine the first matrix, the weight representative of a number of audience members using at least some of the second client devices.
19. The method of claim 12 , further including, in response to the error indicator value not satisfying the threshold, generating a plurality of second estimated demographic impression distributions until a second error indicator value corresponding to one of the second estimated demographic impression distributions satisfies the threshold.
20. The method of claim 12 , wherein the constraint matrix is representative of numerical impression limits for use in modeling the inaccurate demographic impression distribution.
21. The method of claim 12 , wherein the error indicator value represents that there is a compliance error between constraint limits and a matrix in which the constraint matrix is multiplied by the estimated demographic impression distribution.
22. The method of claim 12 , wherein the error indicator value is a Lagrange multiplier change value.
23. A non-transitory computer readable medium comprising computer readable instructions which, when executed, cause a processor to at least:
log a plurality of impressions at a first server of a first entity based on receiving a plurality of first network communications at the first server of the first entity from first client devices and second client devices, the impressions indicative of accesses to media;
instruct the second client devices, via redirect network communications, to send third network communications to a second server of a database proprietor, the third network communications to be indicative of the accesses to the media at the second client devices;
generate a reference demographic impression distribution based on ones of the logged impressions at the first server corresponding to the first client devices, the reference demographic impression distribution representative of reference impression counts distributed across different demographic segments;
access an inaccurate demographic impression distribution generated by the second server of the database proprietor, the inaccurate demographic impression distribution corresponding to second impressions logged by the second server based on the third network communications, and the inaccurate demographic impression distribution representative of first impression counts distributed across the different demographic segments;
determine an estimated demographic impression distribution based on the inaccurate demographic impression distribution, the estimated demographic impression distribution representative of second impression counts distributed across the different demographic segments;
determine a first matrix representative of element-wise multiplication between a constraint matrix and a first transpose matrix of the estimated demographic impression distribution, the constraint matrix based on the reference demographic impression distribution;
determine a second matrix by multiplying the first matrix with a second transpose matrix of the constraint matrix;
determine an error indicator value based on the second matrix, the error indicator value indicative of an error associated with the estimated demographic impression distribution;
generate, in response to the error indicator value satisfying a threshold, an accuracy-improved demographic impression distribution; and
store the accuracy-improved demographic impression distribution in a memory to improve an accuracy of the second server corresponding to the inaccurate demographic impression distribution.
24. The computer readable medium of claim 23 , wherein the plurality of impressions logged at the first server are based on audience members identifiable by the first server and based on corresponding audience member demographics.
25. The computer readable medium of claim 23 , wherein the second client devices include database proprietor identifiers recognizable by the second server of the database proprietor.
26. The computer readable medium of claim 23 , wherein the accuracy-improved demographic impression distribution represents an updated demographic impression distribution based on the estimated demographic impression distribution and the constraint matrix.
27. The computer readable medium of claim 23 , wherein the instructions are to cause the processor to determine the estimated demographic impression distribution based on a weight.
28. The computer readable medium of claim 27 , wherein the weight is representative of a number of audience members using at least some of the second client devices.
29. The computer readable medium of claim 23 , wherein the instructions are further to cause the processor to apply a weight to the estimated demographic impression distribution to determine the first matrix, the weight representative of a number of audience members using at least some of the second client devices.
30. The computer readable medium of claim 23 , wherein the instructions are further to cause the processor to, in response to determining the error indicator value does not satisfy the threshold, generate a plurality of second estimated demographic impression distributions until the processor determines a second error indicator value corresponding to one of the second estimated demographic impression distributions that satisfies the threshold.
31. The computer readable medium of claim 23 , wherein the constraint matrix is representative of numerical impression limits for use in modeling the inaccurate demographic impression distribution.
32. The computer readable medium of claim 23 , wherein the error indicator value represents that there is a compliance error between constraint limits and a matrix in which the constraint matrix is multiplied by the estimated demographic impression distribution.
33. The computer readable medium of claim 23 , wherein the error indicator value is a Lagrange multiplier change value.