Louis Berthier

Conformal prediction guarantees marginal coverage, but a pooled calibration quantile can hide systematic undercoverage across heterogeneous regions of the feature space. We introduce Self-Organized Conformal Prediction (SOCP), a calibration scheme that discovers input-space groups with an unsupervised Self-Organizing Map (SOM) trained without calibration data. At prediction time, the query’s best-matching unit (BMU) retrieves a calibration buffer from one cell, a fixed grid neighborhood, or a prototype enlargement (Regimes 1 to 3). When fixed neighborhoods are too sparse, Regime 3 adds cells by prototype distance, using a global budget selected from training cell occupancies and the planned calibration size before any calibration score is observed. The predictor and nonconformity score remain unchanged. Cell-only retrieval has exact cell-conditional validity, and each fixed union of cells has exact retrieved-set validity. Interpreting a neighborhood threshold at its central cell incurs an explicit Kolmogorov-Smirnov (KS) bias term. Across ten regression and classification benchmarks, SOCP lowers the mean weighted coverage gap (WCovGap) relative to pooled split conformal prediction (SCP) on all ten datasets. The mean relative change is -14.8%, with a mean increase of 3.0% in output size. Under fixed-neighborhood retrieval, SO calibration lowers mean WCovGap across ten seeds in 43 of 50 score and dataset comparisons, while SO-SCP lowers it for every dataset at all three tested external partition granularities. These results provide local group calibration without supervised partitions or predictor retraining, while the diagnostics make the cost and limits of locality explicit.

This paper introduces torchsom, an open-source Python library that provides a reference implementation of the Self-Organizing Map (SOM) in PyTorch. This package offers three main features: (i) dimensionality reduction, (ii) clustering, and (iii) friendly data visualization. It relies on a PyTorch backend, enabling (i) fast and efficient training of SOMs through GPU acceleration, and (ii) easy and scalable integration with the PyTorch ecosystem. torchsom also follows the scikit-learn API for ease of use and extensibility. The library is released under the Apache 2.0 license with 90% test coverage, and its source code and documentation are available at https://github.com/michelin/TorchSOM.

In rubber mixing, the nominal quality grade of a compound is largely governed by the production recipe and understood by experienced operators. However, batches manufactured within the same grade may exhibit quality fluctuations whose origins are difficult to interpret due to the combined effects of recipe settings, raw material characteristics, process variables, equipment conditions, and environmental factors. This work addresses an upstream offline analysis problem aimed at extracting model-supported process insights into within-grade quality variability from high-dimensional industrial production records. The proposed framework uses predictive modeling as an analytical backbone for robust feature selection, explainability, interaction analysis, and uncertainty-aware interpretation. It combines Ranked Frequency Feature Selection (RFFS) with synthetic variables, SHapley Additive exPlanations (SHAP)-based global, local, and pairwise interaction explainability, and multi-split Conformal Prediction (CP)-based Uncertainty Quantification (UQ). The framework is evaluated on a large-scale Michelin rubber-mixing dataset comprising 35,125 records and 316 input variables, including Production Recipe Settings (PRS), Process Variables (PV), Weather Conditions (WC), and Raw Material Characteristics (RMC). The feature-selection strategy is evaluated with four ranking operators and four predictive backbones. With eXtreme Gradient Boosting (XGBoost), it retains 20 variables, corresponding to a 94% input-space reduction, with a test MSE of 0.233 compared with 0.234 for all variables. SHAP provides model-based explanations of influential variables, threshold-like response patterns, and interactions, while multi-split CP provides prediction intervals with near-nominal marginal coverage and subgroup diagnostics that reveal undercoverage. An open-data execution on the public UCI Superconductivity dataset makes the workflow inspectable without proprietary data. The framework provides an offline, explainable, and uncertainty-aware methodology for supporting high-level process management activities, such as variable prioritization, process investigation, and quality-improvement studies.