Reach Calculation Efficiency via Entropy-Based Distribution Modeling
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Solution Overview
Problem
Traditional methods for calculating gross rating points (GRP) and reach metrics in market data analysis, such as the negative binomial distribution (NBD) model, fail to accurately account for unique impressions and can produce erroneous results, especially when sample sizes are low, leading to incorrect feasibility regions and the need for work-arounds like the Poisson distribution, which ignore original market data.
Innovation Solution
The proposed solution applies the principles of maximum entropy and minimum cross entropy to derive a distribution that best fits the market data, avoiding assumptions about the distribution shape and ensuring that the calculated GRP and reach values are consistent with empirical observations, using a market data evaluator system that includes engines for maximum entropy and minimum cross entropy to generate accurate reach values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the negative binomial distribution (NBD) model is used to calculate reach values, then the calculations can be performed with traditional methods, but the results become erroneous and unreliable, especially when sample sizes are low
Solution Approach 1:
The patent changes the fundamental parameters of the distribution model from negative binomial to Poisson distribution, and further refines it by applying entropy-based adjustments. This parameter change transforms the mathematical foundation of the calculation, allowing the system to maintain computational efficiency while dramatically improving the reliability of reach value calculations, especially in low sample size scenarios where traditional NBD fails.
Solution Approach 2:
The patent introduces an intermediary calculation step that uses entropy-based adjustments as a mediator between the Poisson distribution results and the final reach values. This intermediary layer corrects systematic biases in the traditional model without requiring a complete redesign of the calculation framework, thus maintaining productivity while enhancing reliability.
2Ease of operation
If work-arounds like the Poisson distribution are used to handle NBD limitations, then calculations can proceed in certain feasibility regions, but the original market data is ignored and results become independent of published GRP values
Solution Approach 1:
The patent implements a feedback mechanism where the calculated reach values are continuously adjusted based on their consistency with published GRP values. The entropy-based adjustment process provides feedback loops that ensure the final results remain anchored to the original market data and published metrics, preventing the loss of information that occurs when using standalone Poisson distribution without such feedback controls.
Solution Approach 2:
The patent performs preliminary calculations using the Poisson distribution framework, then applies subsequent entropy-based corrections as a second stage. This two-stage approach allows the system to benefit from the computational simplicity of Poisson while correcting its information-loss缺陷 through preliminary preservation and subsequent refinement of the original data relationships.
3Productivity
If traditional NBD model is applied, then reach calculations can be performed, but incorrect feasibility regions are produced leading to erroneous results
Solution Approach 1:
The patent fundamentally changes the distribution parameters from negative binomial to Poisson, and further refines them through entropy-based adjustments. This parameter transformation corrects the mathematical foundations that lead to incorrect feasibility regions, enabling the system to maintain broad calculation capability while dramatically improving the precision of feasibility region determination and eliminating erroneous results.
Data Source
AI summary
Methods, apparatus, systems and articles of manufacture are disclosed to improve reach calculation efficiency. An example method includes estimating, with a processor, a sample distribution of marketing data to generate a maximum entropy distribution, generating, with the processor, a geometric distribution based on estimating a minimum cross entropy of (a) the maximum entropy distribution and (b) the sample distribution of marketing data, and improving calculation efficiency of the public reach of the sample distribution of marketing data by generating, with the processor, conserved quantity expressions of the geometric distribution.