Population Reach Estimation Using Tree Graph and Lagrange Multipliers
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Solution Overview
Problem
Traditional methods for estimating population reach across multiple media platforms face challenges due to over-counting and under-counting errors in server logs, and are computationally inefficient for large datasets, especially when calculating reach across numerous unions of media exposure.
Innovation Solution
The solution involves a tree graph association structure to represent media exposure data, using panelist and database proprietor impression data to calculate unique audiences through a system of equations that leverage Lagrange multipliers, allowing for parallel processing and efficient estimation of population reach across complex media unions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional server log techniques are used to monitor user access to Internet media, then implementation is simple and direct, but over-counting and under-counting errors occur and measurement precision deteriorates
Solution Approach 1:
The patent introduces an audience measurement entity (AME) as an intermediary between users and media servers. The AME receives impression requests from client devices, processes them through panelist data and database proprietor data, and generates accurate reach estimates. This intermediary structure eliminates direct reliance on error-prone server logs while maintaining measurement accuracy.
Solution Approach 2:
The patent replaces the mechanical server log counting system with a computational model using impression requests, panelist data, database proprietor data, and Lagrange multiplier-based equations. This substitution transforms the measurement from simple log counting to a sophisticated statistical estimation system that eliminates over-counting and under-counting errors.
2Productivity
If traditional numerical techniques are used to calculate population reach across multiple media platforms, then calculation methods are straightforward, but computational efficiency deteriorates for large datasets
Solution Approach 1:
The patent transforms the computational problem by changing parameters from direct enumeration of all possible media combinations to using Lagrange multipliers and system of equations. This parameter transformation reduces the computational complexity from exponential to polynomial time, enabling efficient processing of large datasets with multiple media platforms and unions.
Solution Approach 2:
The patent segments the computational task into distinct components: collecting impression requests, processing panelist data, processing database proprietor data, and solving the system of equations. This segmentation allows parallel processing and optimization of each component independently, significantly improving computational efficiency for large-scale audience measurement.
3Measurement precision
If comprehensive media exposure data is collected across multiple platforms, then population reach estimation accuracy improves, but memory and processing constraints worsen
Solution Approach 1:
The patent extracts only the essential data elements needed for reach estimation: impression requests containing media identifiers and timestamps, panelist identification data, and database proprietor impression counts. By extracting and processing only these critical elements rather than storing complete user behavior profiles, the system maintains measurement precision while reducing memory and processing requirements.
Data Source
AI summary
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.