Publications
Peer-reviewed articles, preprints, and open-source software in uncertainty quantification, adaptive learning, and interpretable machine learning.
My work sits at the intersection of uncertainty quantification, adaptive learning, and interpretability for industrial machine learning. Preprints are available on arXiv; for talks and posters, see the Talks and Seminars pages.
2026
- Self-Organized Conformal Prediction: Reducing Regional Coverage Gaps with Unsupervised Group DiscoveryAdvances in Neural Information Processing Systems (NeurIPS), 2026Accepted, to appear
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.
@inproceedings{berthier2026selforganized_cp, title = {Self-Organized Conformal Prediction: Reducing Regional Coverage Gaps with Unsupervised Group Discovery}, author = {Berthier, Louis and Shokry, Ahmed and Moreaud, Maxime and Ramelet, Guillaume and Dieuleveut, Aymeric}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, year = {2026}, eprint = {2606.29403}, archiveprefix = {arXiv}, primaryclass = {stat.ML}, note = {Accepted, to appear}, url = {https://arxiv.org/abs/2606.29403}, } - torchsom: The Reference PyTorch Library for Self-Organizing MapsJournal of Machine Learning Research, 2026
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.
@article{berthier2025torchsom, title = {torchsom: The Reference PyTorch Library for Self-Organizing Maps}, author = {Berthier, Louis and Shokry, Ahmed and Moreaud, Maxime and Ramelet, Guillaume and Moulines, Eric}, journal = {Journal of Machine Learning Research}, volume = {27}, number = {190}, pages = {1--17}, year = {2026}, url = {https://jmlr.org/papers/v27/25-2467.html}, } - Adaptive Soft Sensing: A Just-in-Time Approach with Self-Organizing Maps and Online Feature SelectionIEEE International Conference on Emerging Technologies and Factory Automation (ETFA), 2026
ML-based soft sensors are essential in chemical manufacturing, where real-time quality measurements are often unavailable. Among existing approaches, JITL is widely adopted for its ability to model nonlinear, multimodal, and locally varying behavior, especially in batch processes. However, JITL-based soft sensors remain difficult to scale to industrial systems characterized by high-dimensional data, limited interpretability, and time-varying operating conditions driven by process drifts. To overcome these limitations, this work proposes a novel, adaptive JITL soft-sensor framework tailored for large-scale, evolving industrial environments. First, a SOM is adopted as a topology-preserving latent-space representation to embed both historical and query samples. This projection preserves local neighborhood relationships and reveals latent data structures, enabling effective selection of relevant training samples based on process topology rather than point-wise distance calculations in the original data space. Second, a real-time SHAP-based Feature Selection mechanism identifies and updates the most influential process variables, ensuring continuous interpretability and adaptation. The proposed methodology is validated on a real industrial rubber production line at Michelin. Experimental results demonstrate substantial improvements, reducing mean squared error (MSE) by up to 61.1% and raising the coefficient of determination (R2) from -0.14 to 0.56 compared to global learning baselines.
@inproceedings{berthier2026etfa_adaptive_soft_sensing, title = {Adaptive Soft Sensing: A Just-in-Time Approach with Self-Organizing Maps and Online Feature Selection}, author = {Berthier, Louis and Shokry, Ahmed and Moreaud, Maxime and Ramelet, Guillaume and Moulines, Eric}, booktitle = {2026 IEEE 31st International Conference on Emerging Technologies and Factory Automation (ETFA)}, year = {2026}, pages = {1--10}, doi = {10.1109/ETFA68377.2026.11725271}, address = {Västerås, Sweden}, organization = {IEEE}, } - Explainable Offline Process Analytics for Within-Grade Quality Variability in Industrial Rubber MixingLouis Berthier, Ahmed Shokry, Maxime Moreaud, Guillaume Ramelet, Sylvain Desroziers, and Eric MoulinesDigital Chemical Engineering, 2026Accepted, to appear
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.
@article{berthier2026explainable_offline_analytics, title = {Explainable Offline Process Analytics for Within-Grade Quality Variability in Industrial Rubber Mixing}, author = {Berthier, Louis and Shokry, Ahmed and Moreaud, Maxime and Ramelet, Guillaume and Desroziers, Sylvain and Moulines, Eric}, journal = {Digital Chemical Engineering}, year = {2026}, publisher = {Elsevier}, note = {Accepted, to appear}, }
2025
- Software
torchsom: The Reference PyTorch Library for Self-Organizing MapsLouis Berthier2025@software{berthier2025torchsom_software, author = {Berthier, Louis}, title = {torchsom: The Reference PyTorch Library for Self-Organizing Maps}, year = {2025}, version = {1.3.1}, url = {https://github.com/michelin/TorchSOM}, } - Knowledge Discovery in Large-Scale Batch Processes through Explainable Boosted Models and Uncertainty Quantification: Application to Rubber MixingEuropean Symposium on Computer Aided Process Engineering (ESCAPE 35), 2025
Rubber mixing (RM) is a vital batch process producing high-quality composites, which serve as input material for manufacturing different types of final products, such as tires. Due to its complexity, this process faces two main challenges regarding the final quality: i) lack of online measurement and ii) limited comprehension of the influence of the different factors involved in the process. While data-driven and machine learning (ML) based soft-sensing methods have been widely applied to address the first challenge, the second challenge, to the best of the author’s knowledge, has not yet been addressed in the rubber industry. This work presents a data-driven method for extracting knowledge and providing explainability in the quality prediction in RM processes. The method centers on an XGBoost model while leveraging high-dimensional data collected over extended time periods from one of Michelins complex mixing processes. First, a recursive feature elimination-based procedure is used for selecting relevant features, which reduces the number of input features used for building the ML model by 82% while improving its predictive performance by 17%. Secondly, SHapley Additive exPlanations (SHAP) techniques are employed to explain the ML models predictions through global and local analyses of feature interactions. The selected quality-related variables can be leveraged to improve process control and supervision. Finally, an uncertainty quantification (UQ) module, based on Split Conformal Prediction (SCP), is combined with the ML model, providing confidence intervals with 90% coverage and empirically verified theoretical guarantees. This module ensures prediction reliability and robustness in real applications.
@inproceedings{berthier2025knowledge_discovery_rubber_mixing, title = {Knowledge Discovery in Large-Scale Batch Processes through Explainable Boosted Models and Uncertainty Quantification: Application to Rubber Mixing}, author = {Berthier, Louis and Shokry, Ahmed and Moulines, Eric and Ramelet, Guillaume and Desroziers, Sylvain}, booktitle = {35th European Symposium on Computer Aided Process Engineering (ESCAPE 35)}, series = {Systems and Control Transactions}, volume = {4}, pages = {1518--1523}, year = {2025}, doi = {10.69997/sct.183525}, url = {https://doi.org/10.69997/sct.183525}, } - Detecting fast-ripples on both micro- and macro-electrodes in epilepsy: A wavelet-based CNN detectorLudovic Gardy, Jonathan Curot, Luc Valton, Louis Berthier, Emmanuel J. Barbeau, and Christophe HurterJournal of Neuroscience Methods, 2025
Background: Fast-ripples (FR) are short ( 10 ms) high-frequency oscillations (HFO) between 200 and 600 Hz that are helpful in epilepsy to identify the epileptogenic zone. Our aim is to propose a new method to detect FR that had to be efficient for intracerebral EEG (iEEG) recorded from both usual clinical macro-contacts (millimeter scale) and microwires (micrometer scale). New Method: Step 1 of the detection method is based on a convolutional neural network (CNN) trained using a large database of > 11,000 FR recorded from the iEEG of 38 patients with epilepsy from both macro-contacts and microwires. The FR and non-FR events were fed to the CNN as normalized time-frequency maps. Step 2 is based on feature-based control techniques in order to reject false positives. In step 3, the human is reinstated in the decision-making process for final validation using a graphical user interface. Results: WALFRID achieved high performance on the realistically simulated data with sensitivity up to 99.95 % and precision up to 96.51 %. The detector was able to adapt to both macro and micro-EEG recordings. The real data was used without any pre-processing step such as artefact rejection. The precision of the automatic detection was of 57.5. Step 3 helped eliminating remaining false positives in a few minutes per subject. Comparison with Existing Methods: WALFRID performed as well or better than 6 other existing methods. Conclusion: Since WALFRID was created to mimic the work-up of the neurologist, clinicians can easily use, understand, interpret and, if necessary, correct the output.
@article{gardy2025fast_ripples, title = {Detecting fast-ripples on both micro- and macro-electrodes in epilepsy: A wavelet-based CNN detector}, author = {Gardy, Ludovic and Curot, Jonathan and Valton, Luc and Berthier, Louis and Barbeau, Emmanuel J. and Hurter, Christophe}, journal = {Journal of Neuroscience Methods}, volume = {415}, pages = {110350}, year = {2025}, publisher = {Elsevier}, doi = {10.1016/j.jneumeth.2024.110350}, }
2023
- 2DSBG: A 2D Semi Bi-Gaussian Filter Adapted for Adjacent and Multi-Scale Line Feature DetectionIEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023
Existing filtering techniques fail to precisely detect adjacent line features in multi-scale applications. In this paper, a new filter composed of a bi-Gaussian and a semi-Gaussian kernel is proposed, capable of highlighting complex linear structures such as ridges and valleys of different widths, with noise robustness. Experiments have been performed on a set of both synthetic and real images containing adjacent line features. The obtained results show the performance of the new technique in comparison to the main existing filtering methods.
@inproceedings{magnier2023_2dsbg, title = {2DSBG: A 2D Semi Bi-Gaussian Filter Adapted for Adjacent and Multi-Scale Line Feature Detection}, author = {Magnier, Baptiste and Shokouh, Ghulam Sakhi and Berthier, Louis and Pie, Marcel and Ruggiero, Adrien}, booktitle = {ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {1--5}, year = {2023}, organization = {IEEE}, doi = {10.1109/ICASSP49357.2023.10095570}, }
Under review and in preparation
- Under ReviewBeyond Anytime: Mask-Valid Conformal Prediction2026
When conformal prediction is deployed over sequential batches, practitioners need coverage guarantees that localize to flexible evaluation windows, renew after failures, and do not require past test labels. We introduce mask-valid conformal prediction, a framework that interpolates between marginal and anytime guarantees through binary monitoring masks. We formalize two desiderata, restart validity and calibration-data measurability, identify a class of feasible threshold policies satisfying both, and show that the design of cost-optimal schedules reduces to an optimization problem with linear constraints. When costs are forecasted rather than known in advance, we propose a replanning procedure and bound its hindsight suboptimality in terms of forecast errors. In the anytime setting, under a parametric statistical model, we show that feasible threshold schedules remain informative for polynomially many steps in the calibration size, whereas e-processes can collapse to uninformative prediction sets after only logarithmically many. Experiments on classification and regression tasks validate the framework.
@unpublished{berthier2026masked_cp, title = {Beyond Anytime: Mask-Valid Conformal Prediction}, author = {Hegazy, Mahmoud and Berthier, Louis and Jordan, Michael I. and Dieuleveut, Aymeric}, year = {2026}, } - Under ReviewWhere Should Locality Enter Conformal Prediction?Louis Berthier and Eric Moulines2026
On a fixed partition, score normalization pools calibration scores after cellwise scaling, whereas Mondrian calibration estimates a threshold within each cell. With limited labeled data, we compare their coverage risk (the mean squared deviation of realized cell coverage from its target) and evaluate set size separately. Our main result quantifies the cost of estimating empirical quantiles independently within cells before pooling, relative to Mondrian calibration using all the same labels. Under stratified sampling, averaging score normalization’s linearized coverage error over within-cell fitting-calibration splits gives all-label Mondrian’s linear error, a Rao-Blackwell relation. With at least two cells, the variance gap is explicit and strictly positive, without equal normalized densities or matching fitting and calibration proportions. Direct L² remainder bounds and covariance bounds give two nonasymptotic routes to compare full coverage risks. The bounds are numerically informative in controlled models. Separate certified risk calculations for specified laws establish Mondrian’s advantage with 20 observations per role and cell. Small-sample reversals remain possible. Simulations at equal label budgets support the comparison, including with unequal normalized densities. In an exploratory comparison on twelve datasets, unadjusted paired intervals favor all-label Mondrian in 91 of 192 dataset-allocation designs and normalization in none. These results favor all-label Mondrian for coverage risk when empirical cell quantiles are fitted independently.
@unpublished{berthier2026where_locality_cp, title = {Where Should Locality Enter Conformal Prediction?}, author = {Berthier, Louis and Moulines, Eric}, year = {2026}, } - In PreparationA Unified Online Framework for Adaptive Soft Sensing in High-Dimensional Batch Processes2026
Adaptive soft sensing is crucial for real-time quality prediction in high-dimensional batch manufacturing processes, where evolving process dynamics, sensor degradation, and multi-mode operation render conventional static models ineffective. Existing adaptive strategies, including moving-window (MW), ensemble (ENS), and just-in-time learning (JITL), have been predominantly evaluated in isolation on low-dimensional benchmarks. At the same time, traditional distance metrics and static feature selection fail to address high-dimensional, time-varying industrial conditions. This work introduces a unified online framework integrating three key contributions: (i) topology-aware data retrieval via self-organizing maps (SOMs), which compute similarity on a learned grid of denoised prototype vectors rather than in raw sensor space, (ii) dual feature selection mechanisms combining explicit online SHAP-based Feature Selection (SFS) with implicit ensemble diversity, and (iii) comprehensive comparison of five adaptive strategies. Illustrated on an industrial large-scale rubber-mixing dataset with 35,125 observations, 167 features, and three sub-quality indicators across a short-term horizon of one month and a half and a long-term horizon of one year, the framework demonstrates that tree-based models outperform shallow neural networks like multilayer perceptron (MLP), with XGBoost (XGB) ahead of CatBoost (CTB) in nearly all configurations. All adaptive strategies substantially outperform static baselines, with hybrid approaches balancing short-term reactivity and long-term memory, achieving accurate, interpretable, and computationally feasible quality prediction for real-time industrial deployment even in the presence of process drifts.
@unpublished{berthier2026unified_online_soft_sensing, title = {A Unified Online Framework for Adaptive Soft Sensing in High-Dimensional Batch Processes}, author = {Berthier, Louis and Shokry, Ahmed and Moreaud, Maxime and Ramelet, Guillaume and Moulines, Eric}, year = {2026}, }