Constrained Linear Regression for Dynamic Sales Attribution
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Solution Overview
Problem
Traditional sales attribution models fail to dynamically adjust to changing market conditions and consumer behaviors, leading to inaccurate attribution of sales outcomes due to static coefficient assignments and lack of constraints on variables, oversimplifying the attribution process and potentially misleading decision-making.
Innovation Solution
A Constrained Linear Regression (CLR) model that initializes coefficients based on predefined criteria, applies operational bounds, and dynamically adjusts learning rates and multipliers to reflect current market dynamics, ensuring accurate attribution under fluctuating conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional linear regression models use static coefficients, then the model structure is simple and easy to implement, but the model cannot dynamically adjust to changing market conditions and consumer behaviors, leading to inaccurate attribution
Solution Approach 1:
The patent applies dynamics by transforming the static coefficient model into a dynamic one where coefficients are continuously updated through iterative optimization. The model transitions from fixed parameters to adaptive parameters that respond to changing market conditions, consumer behaviors, and sales data patterns in real-time, resolving the contradiction between model simplicity and adaptability.
Solution Approach 2:
The patent implements parameter changes by allowing model coefficients to vary dynamically through the optimization process. Instead of using fixed coefficients, the system continuously adjusts coefficient values based on incoming sales data and market conditions, enabling the model to adapt to changing environments while maintaining a relatively simple linear regression structure.
2Measurement precision
If traditional models use static coefficient assignment, then the model is computationally efficient and easy to operate, but it lacks constraints on variables and oversimplifies the attribution process
Solution Approach 1:
The patent applies feedback by implementing an iterative optimization process where the model continuously receives feedback from sales data and market conditions. The system computes gradients, updates coefficients, and refines attributions through multiple iterations, allowing the model to progressively improve attribution accuracy while maintaining operational simplicity through automated optimization routines.
3Measurement precision
If the model dynamically adjusts coefficients to reflect market dynamics, then attribution accuracy improves, but the computational complexity and optimization process become more complex
Solution Approach 1:
The patent applies preliminary action by pre-defining the optimization framework, gradient computation methods, and coefficient update rules before processing sales data. The system prepares the optimization architecture in advance, establishing the mathematical foundations and computational procedures that enable dynamic coefficient adjustment without requiring complex real-time decision-making during the attribution process.
Data Source
AI summary
The method comprises receiving one or more bounds for each coefficient of independent variables. Further, a steepness value is selected for controlling the velocity of weight updates for each coefficient. Subsequently, an update vector with a length equal to the number of independent variables may be created. Further, the method may comprise iterating until convergence. Each iteration may include computing a gradient for each independent variable based on the gradient, updating values of each coefficient based on the computed gradient, the computed multiplier, a learning rate, and the update vector. Further, the method involves monitoring the CLR optimization process for convergence based on whether a change in the value of the cost function is below a predefined threshold or a maximum number of iterations is reached. Further, the optimized CLR model may be utilized for at least one application within Revenue Growth Management (RGM).