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: Example methods, apparatus, systems, and articles of manufacture are disclosed to estimate population reach for different unions based on marginal ratings. An example apparatus includes a reach determiner to determine a population reach estimate of a union of time intervals for which media ratings data is available, the population reach estimate based on a pseudo universe estimate of a population audience corresponding to the union of the time intervals; a pseudo universe determiner to determine a pseudo universe estimate of a recorded audience corresponding to the union of the time intervals; determine the pseudo universe estimate of the population audience based on the pseudo universe estimate of the recorded audience; and iteratively update the pseudo universe estimate of the population audience to reduce an error; and a consistency checker to adjust the population reach estimate, the reach determiner to output the population reach estimate of the union.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to rectify false set top box tuning data. Disclosed examples methods include identifying in return path data a first group of set top boxes classified as likely to exhibit machine events in tuning data of the return path data more frequently than a second group of set top boxes represented in the return path data. Additionally, in some examples, the method includes determining whether the first group of set top boxes includes a machine event based on a pattern of the tuning data in the return path data for respective ones of the first group of set top boxes and improving an accuracy of return path data by rectifying the machine event.

Abstract: Example methods, apparatus, and articles of manufacture are disclosed to estimate population reach. An example apparatus includes processor circuitry to determine first multipliers corresponding to a panelist impression count and panelist audience size totals of at least one of a first margin of media, a second margin of the media, or a union of the first margin and the second margin, the first margin, the second margin, and the union included in a tree association; concurrently determine second multipliers using the tree association and the first multipliers; determine third multipliers corresponding to a total audience size exposed to the media at at least one of the first margin, the second margin, or the union based on the tree association using database proprietor impression totals; and determine, based on the third multipliers, an estimate for the population reach of the media for at least one of the first margin, the second margin, or the union.

Abstract: Methods and apparatus to determine reach with time dependent weights are disclosed. An example method disclosed herein includes determining a first subset of panelists exposed to media at a first time; determining a second subset of the panelists exposed to the media at a second time; applying a first plurality of weights to the first subset of panelists to generate first weighted exposures; applying a second plurality of weights to the second subset of the panelists to generate second weighted exposures; for a first panelist in the first and second subsets, determining a first cumulative weighted exposure by determining which of the first and second weighted exposures is largest for each of the first panelist; for a second panelist in one of the first and second subsets, determining a second cumulative weighted exposure by based on the weight applied to the second panelist; and determining a reach of the media for the first and second times by combining the first and second cumulative weighted exposures.

Abstract: A vehicle electric torque vectoring system includes a traction motor, a vectoring motor, gears, and a controller. The gears transfer torque from the propulsion and vectoring motors to wheels. The controller, responsive to a step change in an unmodified torque request for the vectoring motor and a predicted torque response of the vectoring motor being greater than the unmodified torque request, commands the vectoring motor to generate torque with a modified torque request less than the unmodified torque request. The controller further, responsive to the predicted torque response becoming less than the unmodified torque request, commands the vectoring motor to generate torque with the unmodified torque request.

Abstract: Methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to estimate and use duplication factors for audience measurement are disclosed. Example apparatus disclosed herein are to access first marginal ratings values that represent respective portions of a first population associated with corresponding ones of a plurality of media segments, estimate the duplication factor based on a difference between a sum of the first marginal ratings values and a largest one of the first marginal ratings values, access second marginal ratings values that represent respective portions of a second population associated with corresponding ones of the media segments, and output, based on the duplication factor and the second marginal ratings values, a reach value for a union of the media segments, the reach value to represent a number of unique individuals of the second population associated with at least one of the media segments.

Abstract: An example apparatus includes audience metrics collecting circuitry to access first audience metrics from a server, and access second audience metrics from the server, matrix building circuitry to build a matrix of the first audience metrics and the second audience metrics, missing values of the matrix corresponding to the second audience metrics, data transforming circuitry to transform the first audience metrics and the second audience metrics in the matrix, missing value calculating circuitry to determine imputed transformed values of the missing values using a recommender system, and the data transforming circuitry to recover imputed values of the missing values based on the imputed transformed values.

Abstract: Methods, systems, articles of manufacture, and apparatus are disclosed to map client specifications to standardized characteristics. An example apparatus includes a cluster identifier to cluster client databases into client clusters based on a threshold quantity of overlapping universal product codes (UPCs) between respective ones of the client databases, a characteristic analyzer to identify custom characteristics from the respective ones of the client clusters, ones of the custom characteristics having dissimilar nomenclature, and a graph builder to cluster the ones of the custom characteristics based on a similarity metric, and normalize the ones of the custom characteristics as a proxy characteristic, the proxy characteristic having a common nomenclature to represent the ones of the custom characteristics, the characteristic analyzer to enable improved product marketing analysis by replacing dissimilar nomenclature with the proxy characteristic.

Abstract: Ensemble classification algorithms having subclass resolution are disclosed. An example disclosed apparatus includes a fingerprint generator to generate a fingerprint of class probabilities of each of a plurality of samples, a distribution creator to create a distribution of the samples based on the generated fingerprints, and a distribution applicator to apply the distribution to a population to predict sub-class probabilities of each of the population.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to generate synthetic respondent level data. Example apparatus disclosed herein are to identify locations corresponding to monitored panelists, and when a first one of the identified locations corresponds to two or more affiliates, sum tuning minutes of the two or more affiliates. Disclosed example apparatus are also to generate an affiliate probability based on the sum, and convert first data of households in the first one of the locations to a candidate receivability session based on the affiliate probability. Disclosed apparatus are further to generate a seed panel, the seed panel to include at least one of the monitored panelists selected based on a population associated with return path data, and donate second data associated with a donor pool of first panelists to second panelists included in the seed panel, the second panelists associated with faulty media monitoring equipment.

Abstract: Methods, apparatus, systems, and articles of manufacture 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: In one aspect, a method includes (i) identifying a plurality of upcoming content-modification opportunities for a content-presentation device, each respective content-modification opportunity corresponding to a respective underlying advertisement that is available for replacement by a respective supplemental advertisement; (ii) using the identified upcoming content-modification opportunities as a basis for determining expected values for a plurality of supplemental advertisements; (iii) selecting a subset of supplemental advertisements from among the plurality of supplemental advertisements based on the subset having expected values above a threshold value; (iv) in advance of the upcoming content-modification opportunities, sending the subset of supplemental advertisements to be locally stored at the content-presentation device; and (v) upon occurrence of one of the content-modification opportunities, causing the content-presentation device to replace one of the respective underlying advertisements with one o

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 means for logging a plurality of impressions based on impression requests from a plurality of client devices, the plurality of impressions corresponding to media accessed at the client devices; means for obtaining counts, the obtaining means to: obtain a count of demographic impressions logged by a database proprietor; and obtain a count of registered users of the database proprietor exposed to the media; and means for determining a unique audience size by: multiplying a count of the plurality of impressions by a square of the count of the registered users to generate a product; dividing the product by the count of the demographic impressions to generate a quotient; and determining the unique audience size based on a square root of the quotient.

Abstract: Methods and apparatus to estimate demographics of a household are disclosed. An example method to determine demographics for non-panelist households includes calculating a first demographic constraint average and a second demographic constraint average based on a first demographic distribution of a first tuning event of a household and a second demographic distribution of a second tuning event of the household. The household is a non-panelist household. The example method also includes, based on the first demographic constraint average, determining a first likelihood of the household being associated with a first demographic constraint. The example method also includes, based on the second demographic constraint average, determining a second likelihood of the household being associated with a second demographic constraint. The example method also includes estimating a household characteristic of the household based on the first likelihood and the second likelihood.

Abstract: Example methods, apparatus, and articles of manufacture are disclosed to estimate population reach. An example apparatus includes an association controller to generate a tree association corresponding to a union of a first margin of media and a second margin of the media; and one or more commercial solvers to determine first multipliers by solving first equations corresponding to panelist impressions and panelist audience totals, the second margin, or the union; perform first parallel computations with a processor to determine second multipliers to solve second equations corresponding to the tree association using the first multipliers; discard the first multipliers; perform second parallel computations to determine third multipliers by solving third equations corresponding to the tree association using database proprietor impression totals; and determine an estimate for a population reach of the media for at least one of the first margin, the second margin, or the union based on the third multipliers.

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, apparatus, systems and articles of manufacture are disclosed that estimate the second frequency moment. An example apparatus includes a hashing generator to input a first audience member identifier and a second audience member identifier of the media impression data through a hashing function, an output of the hashing generator being a first bit-value representation of the first audience member identifier and a second bit-value representation of the second audience member identifier, a vector generator to increment first and second values of corresponding first and second positions in a vector based on the first and second bit-value representations, respectively, a second frequency moment generator to estimate the second frequency moment of the media impression data using the vector, and a comparator to, using the second frequency moment, determine whether a computer can complete a query request of the media impression data based on query processing constraints.

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, apparatus, systems, and articles of manufacture are disclosed to generate synthetic respondent level data. Example apparatus disclosed herein include means for generating a synthetic panel corresponding to a duration of time, the means for generating the synthetic panel to: generate a transition matrix corresponding to a first sub-duration of the duration of time and a second sub-duration of the duration of time,; generate, based on the transition matrix, a plurality of synthetic panelists and associated viewing data; remove first ones of the synthetic panelists associated with one or more weights that do not satisfy a threshold to generate the synthetic panel corresponding to the duration of time, the synthetic panel representative of audiences of media presented by a plurality of media devices during the duration of time; and generate synthetic respondent level data based on the viewing data associated with remaining second ones of the synthetic panelists.