Abstract: Methods and apparatus to estimate audience sizes using deduplication based on binomial sketch data are disclosed. An apparatus includes processor circuitry to instantiate coefficient analyzer circuitry to determine coefficient values of a polynomial based on (i) variances in values in the first sketch data and second sketch data, (ii) a first cardinality of the first sketch data, and (iii) a second cardinality of the second sketch data. The processor circuitry to instantiate overlap analyzer circuitry to determine a real root of the polynomial, the real root corresponding to the quantity of the second subscribers that are duplicates of the first subscribers. The processor circuitry to instantiate report generator circuitry to estimate a deduplicated audience size based on the estimate of the quantity of the second subscribers that are duplicates of the first subscribers and the first and second cardinalities.

Abstract: Methods and apparatus to estimate cardinality of users represented across multiple bloom filter arrays are disclosed. Examples includes processor circuitry to execute and/or instantiate instructions to generate a first composite Bloom filter array based on first and second Bloom filter arrays. The processor circuitry is to generate a final composite Bloom filter array based on the first composite Bloom filter array and a third Bloom filter array. Different ones of the first, second, and third Bloom filter arrays representative of different sets of users who accessed media. The first, second, and third Bloom filter arrays including differential privacy noise. The processor circuitry to estimate a cardinality of a union of the first, second, and third Bloom filter arrays based on the final composite Bloom filter array.

Abstract: 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.

Abstract: Methods and apparatus to estimate audience sizes using deduplication based on binomial sketch data are disclosed. An apparatus includes processor circuitry to instantiate coefficient analyzer circuitry to determine coefficient values of a polynomial based on (i) variances in values in the first sketch data and second sketch data, (ii) a first cardinality of the first sketch data, and (iii) a second cardinality of the second sketch data. The processor circuitry to instantiate overlap analyzer circuitry to determine a real root of the polynomial, the real root corresponding to the quantity of the second subscribers that are duplicates of the first subscribers. The processor circuitry to instantiate report generator circuitry to estimate a deduplicated audience size based on the estimate of the quantity of the second subscribers that are duplicates of the first subscribers and the first and second cardinalities.

Abstract: An example apparatus includes an audience size calculator circuitry to determine a first census-level audience size, and an impression count calculator circuitry to determine a first census-level impression count.

Abstract: Methods and apparatus to estimate audience sizes and durations for media accesses are disclosed. An example apparatus at least one memory, instructions, and processor circuitry to execute the instructions to select constraint equations corresponding to one or more events, the one or more events corresponding to a first audience and a second audience, the first audience to include the second audience, and determine, based on the constraint equations and an auxiliary equation, event audience sizes corresponding to the first audience and to the one or more events.

Abstract: Methods, apparatus, systems and articles of manufacture to estimate and deduplicate audiences are disclosed herein. An example apparatus includes a controller to determine a subunion of at least first and second marginal audiences of media based on of panel data and census data, the panel data including a panel impression count and a panel audience size, and the census data including a census impression count, an audience size calculator to determine a census audience size of the at least the first and second marginal audiences based on the panel impression count and the panel audience size and determine a subunion census audience size, the subunion census audience size corresponding to an overlap between the at least the first and second marginal audiences; and a report generator to generate a report including the census audience size and the subunion census audience size.

Abstract: 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.

Abstract: An example apparatus disclosed herein includes at least one memory, instructions, and at least one processor to execute the instructions to: receive first HyperLogLog (HLL) data from a first server of a first database proprietor and second HyperLogLog (HLL) data from a second server of a second database proprietor, the first HLL data including obfuscated first user impression data and the second HLL data including obfuscated second user impression data; generate union HLL data based on the first HLL data from the first database proprietor and the second HLL data from the second database proprietor by performing a union of data sets of the obfuscated first user impression data represented in the first HLL data and the obfuscated second user impression data represented in the second HLL data; and determine a total number of deduplicated unique audience members based on the union HLL data generated by the vector analyzer.

Abstract: Example technical solutions to determine census-level audience metrics across demographics are disclosed. Disclosed example apparatus include a distribution parameter solver to initialize distribution parameter values for a probability of an individual within a demographic being (i) included in a subscriber audience for the demographic and (ii) having a first impression duration, the subscriber audience having a first subscriber audience size. Disclosed example apparatus also include a divergence parameter solver to determine divergence parameter values between (i) the first subscriber audience size and the first impression duration and (ii) a census-level audience size and a second impression duration based on the initialized distribution parameter values.

Abstract: Methods and apparatus to estimate cardinality of users represented across multiple bloom filter arrays are disclosed. Examples includes processor circuitry to execute and/or instantiate instructions to generate a first composite Bloom filter array based on first and second Bloom filter arrays. The processor circuitry is to generate a final composite Bloom filter array based on the first composite Bloom filter array and a third Bloom filter array. Different ones of the first, second, and third Bloom filter arrays representative of different sets of users who accessed media. The first, second, and third Bloom filter arrays including differential privacy noise. The processor circuitry to estimate a cardinality of a union of the first, second, and third Bloom filter arrays based on the final composite Bloom filter array.

Abstract: Disclosed examples to estimate audience sizes of media include a coefficient generator to determine coefficient values for a polynomial based on normalized weighted sums of variances, a normalized weighted sum of covariances, and cardinalities corresponding to a first plurality of vectors of counts from a first database proprietor and a second plurality of vectors of counts from a second database proprietor, a real roots solver to determine a real root value of the polynomial, the real root value indicative of a number of audience members represented in the first plurality of vectors of counts that are also represented in the second plurality of vectors of counts, and an audience size generator to determine the audience size based on the real root value and the cardinalities of the first plurality of vectors of counts and the second plurality of vectors of counts.

Abstract: Disclosed examples to estimate audience sizes of media include a coefficient generator to determine coefficient values for a polynomial based on normalized weighted sums of variances, a normalized weighted sum of covariances, and cardinalities corresponding to a first plurality of vectors of counts from a first database proprietor and a second plurality of vectors of counts from a second database proprietor, a real roots solver to determine a real root value of the polynomial, the real root value indicative of a number of audience members represented in the first plurality of vectors of counts that are also represented in the second plurality of vectors of counts, and an audience size generator to determine the audience size based on the real root value and the cardinalities of the first plurality of vectors of counts and the second plurality of vectors of counts.

Abstract: Methods and apparatus to estimate cardinality across multiple datasets represented using Bloom filter arrays are disclosed. Disclosed examples include processor circuitry to execute and/or instantiate instructions to determine an inclusion-exclusion expression that defines an audience size for a user group of interest. Terms in the inclusion-exclusion expression corresponding to either a first cardinality of a first one of at least three Bloom filter arrays or a second cardinality of a union of two or more of the Bloom filter arrays. Different ones of the Bloom filter arrays representative of different sets of users who accessed media. The at least one processor further to estimate, based on the inclusion-exclusion expression, the audience size of the user group of interest.

Abstract: Methods, apparatus, systems and articles of manufacture to estimate and deduplicate audiences are disclosed herein. An example apparatus includes a controller to determine a subunion of at least first and second marginal audiences of media based on of panel data and census data, the panel data including a panel impression count and a panel audience size, and the census data including a census impression count, an audience size calculator to determine a census audience size of the at least the first and second marginal audiences based on the panel impression count and the panel audience size and determine a subunion census audience size, the subunion census audience size corresponding to an overlap between the at least the first and second marginal audiences; and a report generator to generate a report including the census audience size and the subunion census audience size.

Abstract: Methods and apparatus to estimate cardinality of users represented across multiple bloom filter arrays are disclosed. Examples includes processor circuitry to execute and/or instantiate instructions to generate a first composite Bloom filter array based on first and second Bloom filter arrays. The processor circuitry is to generate a final composite Bloom filter array based on the first composite Bloom filter array and a third Bloom filter array. Different ones of the first, second, and third Bloom filter arrays representative of different sets of users who accessed media. The first, second, and third Bloom filter arrays including differential privacy noise. The processor circuitry to estimate a cardinality of a union of the first, second, and third Bloom filter arrays based on the final composite Bloom filter array.

Abstract: Methods and apparatus to estimate cardinality across multiple datasets represented using Bloom filter arrays are disclosed. Disclosed examples include processor circuitry to execute and/or instantiate instructions to determine an inclusion-exclusion expression that defines an audience size for a user group of interest. Terms in the inclusion-exclusion expression corresponding to either a first cardinality of a first one of at least three Bloom filter arrays or a second cardinality of a union of two or more of the Bloom filter arrays. Different ones of the Bloom filter arrays representative of different sets of users who accessed media. The at least one processor further to estimate, based on the inclusion-exclusion expression, the audience size of the user group of interest.

Abstract: Methods, apparatus, systems and articles of manufacture to estimate and deduplicate audiences are disclosed herein. An example apparatus includes a controller to determine a subunion of at least first and second marginal audiences of media based on of panel data and census data, the panel data including a panel impression count and a panel audience size, and the census data including a census impression count, an audience size calculator to determine a census audience size of the at least the first and second marginal audiences based on the panel impression count and the panel audience size and determine a subunion census audience size, the subunion census audience size corresponding to an overlap between the at least the first and second marginal audiences; and a report generator to generate a report including the census audience size and the subunion census audience size.

Abstract: Methods and systems to estimate audience measurement metrics based on users represented in Bloom filter arrays are disclosed. An apparatus includes a communications interface to receive a first Bloom filter array from a first computer of a first database proprietor. The first Bloom filter array is representative of first users who accessed media. The first users are registered with the first database proprietor. The first Bloom filter array includes a first array of first elements. Values of respective ones of the first elements are either a 0 or a 1 based on whether quantities of the first users allocated to the respective ones of the first elements are even or odd. The apparatus further includes a Bloom filter array analyzer to estimate a first cardinality for the first Bloom filter array. The first cardinality is indicative of a total number of the first users who accessed the media.

Abstract: Methods and apparatus to generate corrected online audience measurement data are disclosed. An example apparatus includes programmable circuitry to at least receive, from a server of a database proprietor, a first audience count, a second audience count, and a third audience count, the first audience count indicative of a first number of impressions corresponding to first network communications, the second network communications from second computing devices, and the third audience count indicative of a third number of impressions corresponding to ones of the first network communications and ones of the second network communications attributed to the first media category and the second media category accessed by the first demographic group, the first audience count including a server-generated duplicated audience count generated by the server of the database proprietor, and calculate a deduplication factor for the first demographic group using the first, second, and third audience counts.