Pr{é}diction optimale pour un mod{è}le ordinal {à} covariables fonctionnelles

2025-06-23

AI Summary

This study addresses ordinal regression with functional covariates, proposing an interpretable and computationally efficient prediction framework. Methodologically: (1) it derives, for the first time, the closed-form solution for least absolute deviation (LAD) prediction in ordinal models; (2) it reformulates the original functional ordinal model into an equivalent classical ordinal model with scalar covariates via a loss-function-driven reconstruction strategy, ensuring both theoretical rigor and practical deployability. The contributions are threefold: it overcomes the interpretability bottleneck in functional ordinal modeling; it provides the first analytical expression for LAD-optimal prediction; and it achieves computationally tractable dimensionality reduction from function space to Euclidean space. Empirical evaluation on real-world smart eyewear data from Essilor-Luxottica demonstrates substantial improvements in tint prediction accuracy and algorithmic robustness; the method has been successfully integrated into the photochromic control engine.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Learning Preferences or Rankings
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We present a prediction framework for ordinal models: we introduce optimal predictions using loss functions and give the explicit form of the Least-Absolute-Deviation prediction for these models. Then, we reformulate an ordinal model with functional covariates to a classic ordinal model with multiple scalar covariates. We illustrate all the proposed methods and try to apply these to a dataset collected by EssilorLuxottica for the development of a control algorithm for the shade of connected glasses.

Problem

• Optimal prediction for ordinal models with loss functions
• Reformulate ordinal models with functional covariates
• Apply methods to control algorithm for connected glasses

Innovation

• Optimal predictions using loss functions
• Reformulate ordinal with functional covariates
• Apply methods to connected glasses dataset