Methods and apparatus to estimate cardinality across multiple datasets represented using bloom filter arrays

A non-transitory computer-readable medium having stored therein instructions that, upon execution by one or more processors, cause a computing system to perform a set of acts comprising:

• receiving, via network communications, first and second Bloom filter arrays generated by respective first and second database proprietors, wherein each of the first and second Bloom filter arrays has a length defined by Bloom filter parameters, wherein the length provides a relative error in an audience size estimate no greater than a relative error at a confidence level, and wherein each of the first and second Bloom filter arrays is representative of respective first and second sets of users registered with the first and second database proprietors and corresponding media accesses;
• determining, an inclusion-exclusion expression that defines an audience size for a user group of interest, wherein terms in the inclusion-exclusion expression correspond to either a first cardinality of the first Bloom filter array or a second cardinality of a union of two or more of the first and second Bloom filter arrays and a third Bloom filter array, wherein the third Bloom filter array is representative of corresponding media access for a third set of users;
• estimating, based on the inclusion-exclusion expression, the audience size of the user group of interest that accounts for deduplication of users across the first, second, and third sets of users;
• and
• causing transmission of a report to another computing system based on the estimate of the audience size.

A method comprising:

• receiving, via network communications, first and second Bloom filter arrays generated by respective first and second database proprietors, wherein each of the first and second Bloom filter arrays has a length defined by Bloom filter parameters, wherein the length provides a relative error in an audience size estimate no greater than a relative error at a confidence level, and wherein each of the first and second Bloom filter arrays is representative of respective first and second sets of users registered with the first and second database proprietors and corresponding media accesses;
• determining, an inclusion-exclusion expression that defines an audience size for a user group of interest, wherein terms in the inclusion-exclusion expression correspond to either a first cardinality of the first Bloom filter array or a second cardinality of a union of two or more of the first and second Bloom filter arrays and a third Bloom filter array, wherein the third Bloom filter array is representative of corresponding media access for a third set of users;
• estimating, based on the inclusion-exclusion expression, the audience size of the user group of interest that accounts for deduplication of users across the first, second, and third sets of users;
• and
• causing transmission of a report to another computing system based on the estimate of the audience size.