Abstract: Example methods, apparatus, systems, and articles of manufacture are disclosed to estimate de-duplicated unknown total audience sizes based on partial information of known audiences. An example apparatus includes an association controller to generate a tree structure association corresponding to a union of first and second margins of time; and one or more commercial solvers to: perform parallel computations on a processor to determine multipliers by solving equations corresponding to the tree structure association, the multipliers corresponding to the first total audience size for the union, the second total audience size for the first margin, and the third total audience size for the second margin; and determine an estimate for the third total audience size for the second margin of time based on the multipliers.

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 methods, apparatus, systems, and articles of manufacture are disclosed to estimate de-duplicated unknown total audience sizes based on partial information of known audiences. An example apparatus includes an association controller to generate a tree structure association corresponding to a union of first and second margins of time; and one or more commercial solvers to: perform parallel computations on a processor to determine multipliers by solving equations corresponding to the tree structure association, the multipliers corresponding to the first total audience size for the union, the second total audience size for the first margin, and the third total audience size for the second margin; and determine an estimate for the third total audience size for the second margin of time based on the multipliers.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to generate measures of unique audiences for Internet-based media. An example apparatus disclosed herein includes at least one memory, instructions, and at least one processor.

Abstract: Methods, apparatus, and systems are disclosed for audience-based deduplication using vector-of-counts (VOC) central moments. An example system to determine an audience size for media based on vector of counts sketch data, the system including memory, programmable circuitry, and instructions to cause the programmable circuitry to apply a hash function to first vector of counts sketch data, second vector of counts sketch data, and third vector of counts sketch data to remove personally identifiable information, determine a first covariance matrix associated with intersection cardinalities of at least two of the first, second, or third vector of counts, determine a second covariance matrix associated with disjoint cardinalities of the at least two of the first, second, or third vector of counts, and determine the audience size based on the first covariance matrix or the second covariance matrix.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to estimate population reach from marginals. An example apparatus includes memory including computer readable instructions; and a processor to execute the instructions to: iteratively converge on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media; determine a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and iteratively converge on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to generate measures of unique audiences for Internet-based media. An example apparatus disclosed herein includes at least one memory, instructions, and at least one processor.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to generate measures of unique audiences for Internet-based media. An example apparatus disclosed herein includes at least one memory, instructions, and at least one processor.

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, apparatus, systems, and articles of manufacture are disclosed to estimate population reach from marginals. An example apparatus includes memory including computer readable instructions; and a processor to execute the instructions to: iteratively converge on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media; determine a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and iteratively converge on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to generate measures of unique audiences for Internet-based media.

Abstract: Example methods, apparatus, systems, and articles of manufacture are disclosed to estimate de-duplicated unknown total audience sizes based on partial information of known audiences. An example apparatus includes an association controller to generate a tree structure association corresponding to a union of first and second margins of time; and one or more commercial solvers to: perform parallel computations on a processor to determine multipliers by solving equations corresponding to the tree structure association, the multipliers corresponding to the first total audience size for the union, the second total audience size for the first margin, and the third total audience size for the second margin; and determine an estimate for the third total audience size for the second margin of time based on the multipliers.