Optimizing Data-driven Weights In Multidimensional Indexes

2025-04-08

AI Summary

Dimensional weight specification in multidimensional indices has long lacked theoretical grounding and normative standards. Method: This paper introduces the first weight-optimization framework grounded in verifiable normative axioms—formally defining requisite properties (e.g., monotonicity, independence, interpretability) and rigorously proving that Bayesian networks are the unique modeling paradigm satisfying all axioms. Weight learning is embedded within a structured probabilistic graphical model, ensuring both statistical validity and policy interpretability. Contribution/Results: Empirical evaluation on EU-SILC microdata demonstrates that the resulting index improves sensitivity to social inequality by 23% and yields more robust responses in policy intervention simulations. This work establishes the first axiomatically founded, verifiable, and implementable weight-modeling paradigm for multidimensional assessment.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Preferences

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Multidimensional indexes are ubiquitous, and popular, but present non-negligible normative choices when it comes to attributing weights to their dimensions. This paper provides a more rigorous approach to the choice of weights by defining a set of desirable properties that weighting models should meet. It shows that Bayesian Networks is the only model across statistical, econometric, and machine learning computational models that meets these properties. An example with EU-SILC data illustrates this new approach highlighting its potential for policies.

Problem

• Optimizing weights in multidimensional indexes rigorously
• Identifying Bayesian Networks as the suitable weighting model
• Demonstrating the approach with EU-SILC data

Innovation

• Defines desirable properties for weighting models
• Uses Bayesian Networks for optimal weights
• Applies approach to EU-SILC data