Methods and apparatus to estimate audience sizes of media using deduplication based on vector of counts sketch data
Methods and apparatus to estimate audience sizes using deduplication based on vector of counts sketch data are disclosed. A system includes hardware circuitry to instantiate: coefficient analyzer circuitry to determine coefficient values of a polynomial based on (i) variances in values in a first vector of counts and a second vector of counts, (ii) a first cardinality of the first vector of counts, and (iii) a second cardinality of the second vector of counts; and overlap analyzer circuitry to: determine a real root of the polynomial; and report generator circuitry to estimate a deduplicated audience size based on (i) the estimate of the quantity of the second subscribers that are duplicates of the first subscribers and (ii) the first and second cardinalities. The system includes communication circuitry to transmit a network communication to a third party entity, the second network communication including a report based on the deduplicated audience size.
1. A computing system comprising a processor and a memory, the computing system configured to perform a set of acts comprising:
obtaining a first vector of counts indicative of digital impressions logged by a database proprietor, wherein the first vector of counts represents counts within a plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the database proprietor to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;
obtaining a second vector of counts indicative of digital impressions logged by an audience measurement entity, wherein the second vector of counts represents counts within the plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the audience measurement entity to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;
obtaining a first variance of the first vector of counts;
determining a second variance of the second vector of counts;
determining a covariance of the first vector of counts and the second vector of counts;
determining a number of duplications between the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first variance, the second variance, the covariance, a first cardinality of the digital impressions logged by the database proprietor, and a second cardinality of the digital impressions logged by the audience measurement entity;
determining a unique audience for a combination of the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first cardinality, the second cardinality, and the number of duplications; and
transmitting the unique audience to a third-party.
2. The computing system of claim 1 , wherein determining the number of duplications comprises:
determining coefficient values of a polynomial using the first variance, the second variance, the covariance, the first cardinality, and the second cardinality; and
determining a root of the polynomial so as to determine the number of duplications.
3. The computing system of claim 2 , wherein the impression identifiers comprise email addresses.
4. The computing system of claim 3 , wherein the set of acts further comprises logging the impressions logged by the audience measurement entity using an impression monitor system.
5. The computing system of claim 3 , wherein the digital impressions are exposures to a video.
6. The computing system of claim 3 , wherein the digital impressions are accesses to a website.
7. A method comprising:
obtaining, by a computing system, a first vector of counts indicative of digital impressions logged by a database proprietor, wherein the first vector of counts represents counts within a plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the database proprietor to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;
obtaining, by the computing system, a second vector of counts indicative of digital impressions logged by an audience measurement entity, wherein the second vector of counts represents counts within the plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the audience measurement entity to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;
obtaining, by the computing system, a first variance of the first vector of counts;
determining, by the computing system, a second variance of the second vector of counts;
determining, by the computing system, a covariance of the first vector of counts and the second vector of counts;
determining, by the computing system, a number of duplications between the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first variance, the second variance, the covariance, a first cardinality of the digital impressions logged by the database proprietor, and a second cardinality of the digital impressions logged by the audience measurement entity;
determining, by the computing system, a unique audience for a combination of the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first cardinality, the second cardinality, and the number of duplications; and
transmitting, by the computing system, the unique audience to a third-party.
8. The method of claim 7 , wherein determining the number of duplications comprises:
determining coefficient values of a polynomial using the first variance, the second variance, the covariance, the first cardinality, and the second cardinality; and
determining a root of the polynomial so as to determine the number of duplications.
9. The method of claim 8 , wherein the impression identifiers comprise email addresses.
10. The method of claim 9 , further comprising logging the impressions logged by the audience measurement entity using an impression monitor system.
11. The method of claim 9 , wherein the digital impressions are exposures to a video.
12. The method of claim 9 , wherein the digital impressions are accesses to a website.
13. A non-transitory computer readable medium having stored therein instructions which when executed by a computing system cause the computing system to perform a set of acts comprising:
obtaining a first vector of counts indicative of digital impressions logged by a database proprietor, wherein the first vector of counts represents counts within a plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the database proprietor to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;
obtaining a second vector of counts indicative of digital impressions logged by an audience measurement entity, wherein the second vector of counts represents counts within the plurality of bins and is created by: converting impression identifiers associated with the digital impressions logged by the audience measurement entity to respective hash values using a hash function, and mapping the hash values to respective bins of the plurality of bins;
obtaining a first variance of the first vector of counts;
determining a second variance of the second vector of counts;
determining a covariance of the first vector of counts and the second vector of counts;
determining a number of duplications between the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first variance, the second variance, the covariance, a first cardinality of the digital impressions logged by the database proprietor, and a second cardinality of the digital impressions logged by the audience measurement entity;
determining a unique audience for a combination of the digital impressions logged by the database proprietor and the digital impressions logged by the audience measurement entity using the first cardinality, the second cardinality, and the number of duplications; and
transmitting the unique audience to a third-party.
14. The non-transitory computer readable medium of claim 13 , wherein determining the number of duplications comprises:
determining coefficient values of a polynomial using the first variance, the second variance, the covariance, the first cardinality, and the second cardinality; and
determining a root of the polynomial so as to determine the number of duplications.
15. The non-transitory computer readable medium of claim 14 , wherein the impression identifiers comprise email addresses.
16. The non-transitory computer readable medium of claim 15 , wherein the set of acts further comprises logging the impressions logged by the audience measurement entity using an impression monitor system.
17. The non-transitory computer readable medium of claim 15 , wherein the digital impressions are exposures to a video.
18. The non-transitory computer readable medium of claim 15 , wherein the digital impressions are accesses to a website.