Gamma Mixture Density Networks for WTP Estimation

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Solution Overview

Problem

Existing methods struggle to accurately estimate willingness-to-pay (WTP) distributions of individual products from historical sales data, especially when the data contains bundled offers, as they require disaggregated WTP distributions from aggregated buy and no-buy decisions.

Innovation Solution

The use of Gamma Mixture Density Networks (GMDNs) to estimate WTP distributions from both bundled and unbundled sales data. This involves training a GMDN model with historical sales data, where each product's WTP distribution is modeled as a mixture of gamma distributions, allowing for the estimation of bundle WTP distributions by convolving individual product distributions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If bundled sales data is used to estimate WTP distributions, then the model can handle real-world data scenarios, but the aggregated buy and no-buy decisions make it difficult to obtain disaggregated WTP distributions of individual products

Engineering Contradiction:

Improveability to handle bundled and unbundled sales dataVSAvoiddisaggregated WTP distribution information

Core Design Contradiction:

Adaptability or versatilityVSLoss of information

Solution Approach 1:

The patent segments the bundled WTP distribution into individual product WTP distributions by modeling each product's WTP as a separate gamma distribution. The GMDN model learns separate WTP parameters for each product within a bundle, allowing decomposition of the aggregated decision data into meaningful individual product-level insights.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent introduces WTP distributions as an intermediary representation between the observed aggregated buy/no-buy decisions and the underlying individual product valuations. By modeling WTP as a latent variable with specific distributional properties, the system infers individual product WTP from bundled purchase data without direct observation.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Productivity

If WTP distributions are estimated from aggregated bundled data, then the model can make predictions about customer choices, but the accuracy of disaggregated WTP estimation deteriorates

Engineering Contradiction:

Improveprediction capability for customer choiceVSAvoidaccuracy of disaggregated WTP distribution

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent changes the parameterization approach by using gamma distribution parameters (shape and rate) to represent WTP instead of relying on aggregated decision data alone. This parameter transformation enables precise estimation of individual product WTP distributions while maintaining the ability to predict bundled purchase decisions.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The GMDN model uses feedback from observed bundled purchase decisions to iteratively refine the estimated WTP distributions. The model adjusts its WTP parameter estimates based on the discrepancy between predicted and actual purchase behavior, improving measurement precision through continuous learning from aggregated data.

Inventive Principle:

Principle #23Feedback

3Measurement precision

If only unbundled sales data is used, then disaggregated WTP distributions can be obtained directly, but the model cannot accurately predict customer choices for new bundled offers

Engineering Contradiction:

Improvedisaggregated WTP distribution accuracyVSAvoidprediction capability for bundled offers

Core Design Contradiction:

Measurement precisionVSAdaptability or versatility

Solution Approach 1:

The patent creates a universal WTP estimation framework that handles both unbundled and bundled sales data through a single GMDN model. The model universally estimates WTP distributions for individual products while simultaneously enabling prediction of bundled offer choices, eliminating the need for separate models for different data types.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent merges the estimation of individual product WTP distributions with the prediction of bundled purchase decisions into a unified model framework. By combining these functions, the system leverages both unbundled and bundled data to achieve both precise WTP measurement and accurate bundled offer prediction.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS20250200596A1Estimating willingness-to-pay distributions from bundled and unbundled sales data using gamma mixture density networks

Publication Date: 2025.06.19 TATA CONSULTANCY SERVICES LTD

AI summary

The disclosure herein addresses estimating WTP distributions from bundled and unbundled sales data using GMDN model. The input samples are passed through the GMDN model to learn the plurality gamma mixture parameters. The learnt gamma mixture parameters are then used to evaluate the weighted CDF value at the offered price of the bundle and the bundle composition. The weighted CDF value is then used to predict the customer's choice based on the predefined threshold and estimates the revenue optimal price of the bundle composition. The disclosed GMDN model models the WTP distributions as the mixture of gamma distributions and learns the WTP distributions from the bundled and the unbundled sales with greater accuracy and excels in estimating the revenue optimal prices and the revenues of the products and the bundles.