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, apparatus, systems, and articles of manufacture to virtually estimate cardinality with global registers are disclosed. An example apparatus includes processor circuitry to s assign subsets of a sample dataset to a shared global register array, the shared global register array having a first number of registers, the sample dataset selected from a reference dataset of media assets; identify a virtual register array from the shared global register array that includes data elements associated with a label value, the virtual register array including a second number of registers less than the first number of registers; determine a maximum rank value of the label value across the virtual register array; and calculate a cardinality estimate of the label value across the virtual register array based on the second number of registers and the maximum rank value.

Abstract: Disclosed examples determine a unique audience exposed to media while reducing memory resources of a computing device. Example instructions program programmable circuitry to log a plurality of impressions corresponding to media accessed at client devices; generate a first value based on a count of the impressions and a count of users of a database proprietor that accessed the media; generate a second value based on the first value and a count of demographic impressions logged by the database proprietor; and determine a unique audience size based on the second value.

Abstract: Methods, apparatus, systems, and articles of manufacture to perform computer-based monitoring of audiences of network-based media using information theory to estimate intermediate level unions are disclosed. An example apparatus to determine a deduplicated, census-based audience metric of media includes panel union calculator circuitry to calculate a threshold statistic corresponding to an intermediate union of a panel hierarchy, and census union calculator circuitry to calculate a deduplicated audience value corresponding to the intermediate union of the census hierarchy based on the threshold statistic.

Abstract: Methods and apparatus to estimate census-level audience sizes and duration data across dimensions and/or demographics are disclosed. An example apparatus includes constraint equation control circuitry to select at least one constraint equation corresponding to one or more events, the one or more events corresponding to first audience members and second audience members, the first audience members to include the second audience members, constraint parameter estimation circuitry to solve the at least one constraint equation to determine one or more constraint parameter values, the one or more constraint parameter values corresponding to the one or more events, and output generation circuitry to determine, based on one or more intermediate equations and the one or more constraint parameter values, an event audience size and an event duration corresponding to (a) the first audience members and (b) a combination of the one or more events and one or more demographics.

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, apparatus, systems, and articles of manufacture to perform computer-based monitoring of audiences of network-based media using information theory to estimate intermediate level unions are disclosed. An example apparatus to determine a deduplicated, census-based audience metric of media includes panel union calculator circuitry to calculate a threshold statistic corresponding to an intermediate union of a panel hierarchy, and census union calculator circuitry to calculate a deduplicated audience value corresponding to the intermediate union of the census hierarchy based on the threshold statistic.

Abstract: Methods and apparatus to estimate census level audience sizes, impression counts, and duration data are disclosed. Example instructions cause one or more processor to at least set up a system of equations based on first census data; select a census parameter value based on a constraint for census parameter selection, the constraint based on media access represented in panel data; iteratively solve for second census data that satisfies the system of equations using the panel data and the census parameter value, the second census data including an audience size value, an impression count value, and a duration value for a media item accessed by anonymous audience members in a demographic group; and generate a report including the second census data.

Abstract: An example apparatus includes an association controller to generate a tree structure association for a total audience size that accessed a plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size, a matrix generator to generate a matrix by selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item and storing the sum of probabilities value in an element of the matrix, and a commercial solver to estimate a deduplicated audience size of the total audience size using the matrix.

Abstract: Methods, apparatus, systems, and articles of manufacture to estimate cardinality of users represented in arbitrarily distributed bloom filter arrays are disclosed. A system includes a communication interface to: access a first Bloom filter array representative of first entries in a first database, the first entries allocated to ones of first elements in the first Bloom filter array based on a non-uniform distribution of outputs of a hash function applied to the first entries, and access a second Bloom filter array representative of second entries in a second database. The system also includes machine readable instructions to cause one or more processors to estimate a cardinality of a union of the first and second entries based on the non-uniform distribution of the outputs of the hash function.

Abstract: Disclosed examples determine constraints based on a structure of initial audience totals; for a number of iterations: select values for modified audience totals that satisfy the constraints, the modified audience totals corresponding respectively to the initial audience totals; and determine an output based on the values for the modified audience totals and the initial audience totals; select final values of the modified audience totals resulting from completion of the number of iterations, the final values of the modified audience totals to be logically consistent; and generate a report including the final values of the modified audience totals.

Abstract: A disclosed example includes at least one memory, programmable circuitry, and instructions to cause the programmable circuitry to increment a first value corresponding to a first position in a vector based on a first bit value representation, the first bit value representation corresponding to a first audience member identifier; increment a second value corresponding to a second position in the vector based on a second bit value representation, the second bit value representation corresponding to a second audience member identifier; estimate the second frequency moment of the media impression data using the vector; determine the variance of the second frequency moment; and based on the second frequency moment, schedule a query of the media impression data to be processed by a computer at a future time.

Abstract: Methods, apparatus, systems, and articles of manufacture to estimate cardinality of users represented in arbitrarily distributed bloom filter arrays are disclosed. An apparatus includes a communications interface to obtain a first Bloom filter array generated by a first computer of a first database proprietor and obtain a second Bloom filter array generated by a second computer of a second database proprietor. The apparatus includes a cardinality analyzer to estimate a total number of unique users included in a union of corresponding ones of the first and second users represented in the first and second Bloom filter arrays regardless of whether the first and second users are mapped, based on a first distribution or a second distribution different than the first distribution, to the corresponding first and second Bloom filter arrays.

Abstract: Methods, apparatus, systems, and articles of manufacture to estimate cardinality through ordered statistics are disclosed. In an example, an apparatus includes processor circuitry to selects a sample dataset from a first reference dataset of media assets and partitions the sample dataset into m mutually exclusive subsets of approximately equal size. The processor circuitry then estimates a ratio of a sample weighted average and empirical cumulative distribution of an approximately largest order statistic from at least one of the m subsets and generates an estimate of a total cardinality of the first reference dataset by multiplying the ratio by approximately m.

Abstract: Disclosed examples access data from a database, the data stored across multiple registers of the database; determine (a) a maximum rank for each of the multiple registers and (b) a maximum rank count for each of the multiple registers; determine a frequency distribution based on the maximum ranks and the maximum rank counts; and generate a report including at least one of the frequency distribution, the maximum ranks, or the maximum rank counts.

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, apparatus, systems, and articles of manufacture are disclosed to determine unique audience size via clustered data. An example apparatus includes memory, machine readable instructions, and processor circuitry to at least one of execute or instantiate the machine readable instructions. The example processor circuitry is to form a first matrix identifying matching and non-matching instances of first values of respective demographics of an audience of media and second values of the respective demographics. Also, the processor circuitry is to normalize the first matrix to generate an account sharing adjustment matrix. Additionally, the processor circuitry is to apply the account sharing adjustment matrix to a vector of one or more counts of impressions of the media to correct for one or more members of the audience that share a user account registered with a database proprietor, the one or more counts of the impressions corresponding to the respective demographics.

Abstract: A disclosed example includes at least one memory, programmable circuitry, and instructions to cause the programmable circuitry to increment a first value corresponding to a first position in a vector based on a first bit value representation, the first bit value representation corresponding to a first audience member identifier; increment a second value corresponding to a second position in the vector based on a second bit value representation, the second bit value representation corresponding to a second audience member identifier; estimate the second frequency moment of the media impression data using the vector; determine the variance of the second frequency moment; and based on the second frequency moment, schedule a query of the media impression data to be processed by a computer at a future time.

Abstract: Methods and apparatus for determining a unique audience exposed to media while reducing memory resources of a computing device are disclosed herein. An example apparatus includes memory; instructions in the apparatus; and processor circuitry to execute the instruction to, based on impression requests from a plurality of client devices via a network, log a plurality of impressions corresponding to media accessed at the client devices; generate a product by multiplying a count of the impressions by a square of a count of registered users of a database proprietor exposed to the media; generate a quotient by dividing the product by a count of demographic impressions logged by the database proprietor; and determine a unique audience size based on a square root of the quotient.

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.