Processor systems to estimate audience sizes and impression counts for different frequency intervals
Processor systems to estimate audience sizes and impression counts for different frequency intervals are disclosed. An example processor system includes a memory management unit (MMU) to assign requests from computing devices indicative of accesses to media to a first block of memory and to assign user-identified impression data corresponding to user-identified impressions to a second block of memory. The processor system including an arithmetic logic unit (ALU) to determine multipliers relating a first probability distribution for the user-identified impressions to a second probability distribution for census impressions. The multipliers based on probability constraints defined by weighted probabilities associated with the second probability distribution, where different ones of the probabilities weighted based on estimated populations for corresponding ones of the different demographics. The ALU to determine a plurality of census impression counts associated with the census impressions based on the multipliers.
1. A processor system, comprising:
memory;
first instructions in the processor system; and
processor circuitry to execute the first instructions to:
cause transmission of first network communications including cookies to be set on computing devices used to access media, the cookies to facilitate tracking of accesses to the media at the computing devices;
log census impressions at a first server of an audience measurement entity based on requests received from second network communications from computing devices, the requests indicative of the accesses to the media at the computing devices, the second network communications triggered by second instructions executed by at least one of browsers or applications that accessed the media at the computing devices, a total count of the requests corresponding to a total number of the census impressions associated with the media, a first portion of the census impressions corresponding to user-identified impressions and a second portion of the census impressions corresponding to unidentified impressions, the requests including cookie information associated with the cookies set on the computing devices, the cookie information insufficient by itself to indicate census impression counts for different impression frequency intervals associated with the census impressions;
cause transmission of redirect network communications to instruct the computing devices 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 computing devices;
store user-identified impression data corresponding to the user-identified impressions, the user-identified impressions obtained via a fourth network communication from the second server of the database proprietor, the user-identified impressions generated by the database proprietor based on data aggregated from the third network communications from the computing devices, the user-identified impressions associated with user-identified individuals for whom first demographic information is stored by the database proprietor, the user-identified impression data including a plurality of user-identified impression counts associated with corresponding ones of the impression frequency intervals, different ones of the user-identified individuals corresponding to audience members associated with different demographics;
determine multipliers relating a first probability distribution for the user-identified impressions to a second probability distribution for the census impressions, the multipliers based on census constraints defined by weighted probabilities associated with the second probability distribution, different ones of the probabilities weighted based on estimated populations for corresponding ones of the different demographics, determination of the multipliers to improve a computational efficiency of the processor system by eliminating a need to directly solve for all probabilities in the second probability distribution;
determine the census impression counts associated with the census impressions based on the multipliers, different ones of the census impression counts corresponding to different ones of the impression frequency intervals, the census impressions associated with media accessed by members of a population of an entire country; and
generate a report based on the different ones of the census impression counts.
2. The processor system of claim 1 , wherein the processor circuitry is to execute the first instructions to determine different ones of the census impressions according to the different demographics.
3. The processor system of claim 1 , wherein the processor circuitry is to execute the first instructions to determine the first probability distribution by identifying a distribution that satisfies a principle of maximum entropy with respect to the user-identified impressions subject to user-identified constraints defined by the user-identified impression data.
4. The processor system of claim 3 , wherein the processor circuitry is to execute the first instructions to determine the first probability distribution without directly calculating individual probabilities within the first probability distribution.
5. The processor system of claim 1 , wherein the processor circuitry is to execute the first instructions to:
store user-identified audience size data including different ones of a plurality of first unique audience sizes associated with different ones of the plurality of user-identified impression counts; and
determine, based on the multipliers, a plurality of second unique audience sizes corresponding to audience members associated with the census impression counts, different ones of the plurality of second unique audience sizes corresponding to different ones of the plurality of impression frequency intervals.
6. The processor system of claim 1 , wherein the multipliers are Lagrange multipliers.
7. The processor system of claim 1 , wherein the weighted probabilities associated with the second probability distribution correspond to a weighted KL-divergence.
8. A non-transitory computer readable medium comprising first instructions that, when executed, cause at least one processor to at least:
cause transmission of first network communications including cookies to be set on computing devices used to access media, the cookies to facilitate tracking of accesses to the media at the computing devices;
log census impressions at a first server of an audience measurement entity based on requests received from second network communications from the computing devices, the requests indicative of the accesses to the media at the computing devices, the second network communications triggered by second instructions executed by at least one of browsers or applications that accessed the media at the computing devices, a total count of the requests corresponding to a total number of the census impressions associated with the media, a first portion of the census impressions corresponding to user-identified impressions and a second portion of the census impressions corresponding to unidentified impressions, the requests including cookie information associated with the cookies set on the computing devices, the cookie information insufficient by itself to indicate census impression counts for different impression frequency intervals associated with the census impressions;
cause transmission of redirect network communications to instruct the computing devices 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 computing devices;
store user-identified impression data corresponding to the user-identified impressions, the user-identified impressions obtained via a fourth network communication from the second server of the database proprietor, the user-identified impressions generated by the database proprietor based on data aggregated from the third network communications, the user-identified impressions associated with user-identified individuals for whom first demographic information is stored by the database proprietor, the user-identified impression data including a plurality of user-identified impression counts associated with corresponding ones of the impression frequency intervals, different ones of the user-identified individuals corresponding to audience members associated with different demographics;
determine multipliers relating a first probability distribution for the user-identified impressions to a second probability distribution for the census impressions, the multipliers based on census constraints defined weighted probabilities associated with the second probability distribution, different ones of the probabilities weighted based on estimated populations for corresponding ones of the different demographics, determination of the multipliers to improve a computational efficiency of the at least one processor by eliminating a need to directly solve for all probabilities in the second probability distribution;
determine the census impression counts associated with the census impressions based on the multipliers, different ones of the census impression counts corresponding to different ones of the impression frequency intervals, the census impressions associated with media accessed by members of a population of an entire country; and
generate a report based on the different ones of the census impression counts.
9. The non-transitory computer readable medium of claim 8 , wherein the first instructions further cause the at least one processor to determine different ones of the census impressions according to the different demographics.
10. The non-transitory computer readable medium of claim 8 , wherein the first instructions further cause the at least one processor to determine the first probability distribution by identifying a distribution that satisfies a principle of maximum entropy with respect to the user-identified impressions subject to user-identified constraints defined by the user-identified impression data.
11. The non-transitory computer readable medium of claim 10 , wherein the first instructions further cause the at least one processor to determine the first probability distribution without directly calculating individual probabilities within the first probability distribution.
12. The non-transitory computer readable medium of claim 8 , wherein the first instructions further cause the at least one processor to:
store user-identified audience size data including different ones of a plurality of first unique audience sizes associated with different ones of the plurality of user-identified impression counts; and
determine, based on the multipliers, a plurality of second unique audience sizes corresponding to audience members associated with the census impression counts, different ones of the plurality of second unique audience sizes corresponding to different ones of the plurality of impression frequency intervals.
13. The non-transitory computer readable medium of claim 8 , wherein the multipliers are Lagrange multipliers.
14. The non-transitory computer readable medium of claim 8 , wherein the weighted probabilities associated with the second probability distribution correspond to a weighted KL-divergence.
15. A method, comprising:
transmitting first network communications including cookies to be set on computing devices used to access media, the cookies to facilitate tracking of accesses to the media at the computing devices;
logging, by executing first instructions with processor circuitry, census impressions at a first server of an audience measurement entity based on requests received from second network communications from the computing devices, the requests indicative of the accesses to the media at the computing devices, the second network communications triggered by second instructions executed by at least one of browsers or applications that accessed the media at the computing devices, a total count of the requests corresponding to a total number of the census impressions associated with the media, a first portion of the census impressions corresponding to user-identified impressions and a second portion of the census impressions corresponding to unidentified impressions, the requests including cookie information associated with the cookies set on the computing devices, the cookie information insufficient by itself to indicate census impression counts for different impression frequency intervals associated with the census impressions;
transmitting redirect network communications to instruct the computing devices 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 computing devices;
storing user-identified impression data corresponding to the user-identified impressions, the user-identified impressions obtained via a fourth network communication from the second server of the database proprietor, the user-identified impressions generated by the database proprietor based on data aggregated from the third network communications from the computing devices, the user-identified impressions associated with user-identified individuals for whom first demographic information is stored by the database proprietor, the user-identified impression data including a plurality of user-identified impression counts associated with corresponding ones of the impression frequency intervals, different ones of the user-identified individuals corresponding to audience members associated with different demographics;
determining, by executing the first instructions with the processor circuitry, multipliers relating a first probability distribution for the user-identified impressions to a second probability distribution for the census impressions, the multipliers based on census constraints defined by weighted probabilities associated with the second probability distribution, different ones of the probabilities weighted based on estimated populations for corresponding ones of the different demographics, the determining of the multipliers to improve a computational efficiency of the processor circuitry by eliminating a need to directly solve for all probabilities in the second probability distribution;
determining, by executing the first instructions with the processor circuitry, the census impression counts associated with the census impressions based on the multipliers, different ones of the census impression counts corresponding to different ones of the impression frequency intervals, the census impressions associated with media accessed by members of a population of an entire country; and
generating, by executing the first instructions with the processor circuitry, a report based on the different ones of the census impression counts.
16. The method of claim 15 , further including determining different ones of the census impressions according to the different demographics.
17. The method of claim 15 , further including determining the first probability distribution by identifying a distribution that satisfies a principle of maximum entropy with respect to the user-identified impressions subject to user-identified constraints defined by the user-identified impression data.
18. The method of claim 17 , further including determining the first probability distribution without directly calculating individual probabilities within the first probability distribution.
19. The method of claim 15 , further including:
storing user-identified audience size data including different ones of a plurality of first unique audience sizes associated with different ones of the plurality of user-identified impression counts; and
determining, based on the multipliers, a plurality of second unique audience sizes corresponding to audience members associated with the census impression counts, different ones of the plurality of second unique audience sizes corresponding to different ones of the plurality of impression frequency intervals.
20. The method of claim 15 , wherein the weighted probabilities associated with the second probability distribution correspond to a weighted KL-divergence.