arXiv subjects

Nicolas Vayatis

Publications and source records attributed to Nicolas Vayatis.

At least 19 recordsLinked to original sources

arXiv2026

A Model for Imbalanced Label Aggregation: A Focus on Minority-Class Detection

We study imbalanced crowdsourcing with a focus on class-dependent annotator accuracy, a setting that, to the best of our knowledge, remains relatively underexplored despite its importance in real-world inspection systems where the labels of greatest operational importance are also the rarest ones. In this setting, annotators may be reliable on both classes, unreliable on both classes, majority-class specialists, or minority-class specialists. Existing models only partially address this problem: they either capture class-dependent errors but ignore item difficulty, or they model item difficulty without capturing class-dependent errors. To fill this gap for imbalanced datasets in crowdsourcing, we introduce a generative aggregation model combining item difficulty with class-dependent annotator competence. The model allows both annotator abilities and item difficulties to vary across classes. We then revisit Condorcet's Jury Theorem in the class-imbalanced setting. We also show that majority voting asymptotically preserves the underlying class proportion. We evaluate our model on $33$ real-world crowdsourcing datasets, covering multiclass tasks such as images and text, as well as two large-scale regimes: large-scale annotation datasets, with many annotations per item, and large-scale item datasets, with a large number of annotated instances. Across these diverse settings, our model consistently achieves the highest minority recall while remaining competitive in balanced accuracy, making it particularly relevant when rare-label recovery is the primary objective.

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arXiv2026

Parallel gradient boosting for flexible estimation of conditional distributions

Boosting is one of the most successful learning techniques for standard classification and regression tasks. Its extension to multi-output prediction problems has found an increasing number of applications in recent years. Among them is the prediction of entire conditional distributions rather than single functionals, which can often be framed as a multi-output regression problem, for example multiple quantile regression. Addressing such problems with classical implementations of boosting is computationally challenging, because usually one base model is trained for each target at every iteration. More efficient variants of boosting have been proposed to speed up training, but they tend to be tied to specific loss functions and classes of base learners, usually decision trees. In this work, we study a modification of the gradient boosting algorithm, which we call parallel gradient boosting, designed to circumvent all these limitations. The core idea is to use a common descent direction for all training observations. By doing so, only one base model is needed at each iteration, regardless of the number of targets, which allows for considerable performance gains. We establish sufficient conditions for the convergence of the algorithm, whose practical use is introduced via the multiple quantile regression setting. We show that in such a setting, it provides predictions of similar quality to state-of-the-art boosting libraries such as XGBoost, while being faster by several orders of magnitude. Then, we evaluate the properties of the resulting conditional distribution estimator, which is shown empirically to outperform other nonparametric and semiparametric estimators, especially in high-dimensional settings and in the presence of mixed and/or missing covariates.

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arXiv2026

GLOBe: A Modular Global Optimization library

Open-source libraries are have a catalytic role in research pipelines, where new methods must be compared against up-to-date baselines. We present the GLobal Optimization Benchmark (GLOBe) modular Python library that unifies classical and recent continuous global optimization algorithms, including decision-based and mathematically founded particle-based methods, in a single framework. A central contribution of GLOBe is its modular architecture, which factors common algorithmic patterns into reusable familyl evel components and enables plugins to be implemented once and makes them available to all algorithms in the corresponding family. This modular design leverages recent advances in mathematical formalization of global optimization, where structural commonalities across algorithms have been identified and used to develop broadly applicable, formally grounded algorithmic features. The C++ backend relies on Eigen 5 for efficient linear algebra. GLOBe presently includes 14 optimizers, 19 analytical benchmarks along with a random function generator, and an integrated toolkit for direct algorithm comparison.

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arXiv2026

Accelerating Full-Scale Nonlinear Model Predictive Control via Surrogate Dynamics Optimization

Driven by advances in hardware and software technologies, nonlinear model predictive control (NMPC) has gained increasing adoption in both industry and academia over the past decades. However, its practical deployment is often limited by the computational cost of simulating the embedded process model, especially for high-dimensional, multi-time-scale, or nonlinear systems commonly found in real-world applications. Thus, this paper introduces Surrogate Dynamics Optimization (SDO), a warm-start framework for full-scale NMPC to address the limitation of standard initialization strategies. The approach relies on a machine learning surrogate model to solve a lightweight auxiliary problem that approximates the original one. The methodology is reproducible and compatible with inhouse simulation and optimization tools, a key consideration in industrial contexts. Data efficiency of SDO, as well as the impact of surrogate design on the overall performance, are evaluated through a non-trivial simulation case study: 24-hour optimal load-following control of a pressurized water reactor. The results show consistent improvements in NMPC convergence speed within a fixed computational budget, while reducing training data generation costs by two orders of magnitude compared to behavior cloning.

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arXiv2026

Optimal Fair Aggregation of Crowdsourced Noisy Labels using Demographic Parity Constraints

As acquiring reliable ground-truth labels is usually costly, or infeasible, crowdsourcing and aggregation of noisy human annotations is the typical resort. Aggregating subjective labels, though, may amplify individual biases, particularly regarding sensitive features, raising fairness concerns. Nonetheless, fairness in crowdsourced aggregation remains largely unexplored, with no existing convergence guarantees and only limited post-processing approaches for enforcing $\varepsilon$-fairness under demographic parity. We address this gap by analyzing the fairness s of crowdsourced aggregation methods within the $\varepsilon$-fairness framework, for Majority Vote and Optimal Bayesian aggregation. In the small-crowd regime, we derive an upper bound on the fairness gap of Majority Vote in terms of the fairness gaps of the individual annotators. We further show that the fairness gap of the aggregated consensus converges exponentially fast to that of the ground-truth under interpretable conditions. Since ground-truth itself may still be unfair, we generalize a state-of-the-art multiclass fairness post-processing algorithm from the continuous to the discrete setting, which enforces strict demographic parity constraints to any aggregation rule. Experiments on synthetic and real datasets demonstrate the effectiveness of our approach and corroborate the theoretical insights.

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arXiv2025

Enhancing Nuclear Reactor Core Simulation through Data-Based Surrogate Models

In recent years, there has been an increasing need for Nuclear Power Plants (NPPs) to improve flexibility in order to match the rapid growth of renewable energies. The Operator Assistance Predictive System (OAPS) developed by Framatome addresses this problem through Model Predictive Control (MPC). In this work, we aim to improve MPC methods through data-driven simulation schemes. Thus, from a set of nonlinear stiff ordinary differential equations (ODEs), this paper introduces two surrogate models acting as alternative simulation schemes to enhance nuclear reactor core simulation. We show that both data-driven and physics-informed models can rapidly integrate complex dynamics, with a very low computational time (up to 1000x time reduction).

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arXiv2025

A Unifying Framework for Global Optimization: From Theory to Formalization

We introduce an abstract measure___theoretic framework that serves as a tool to rigorously study stochastic iterative global optimization algorithms as a unified class. The framework is formulated in terms of probability kernels, which, via the Ionescu--Tulcea theorem, induce probability measures on the space of sequences of algorithm iterations, endowed with two intuitive properties. This framework answers the need for a general, implementation___independent formalism in the analysis of such algorithms, providing a starting point for formalizing global optimization results in proof-assistants. To illustrate the relevance of our tool, we show that common algorithms fit naturally in the framework, and we also use it to give a rigorous proof of a general consistency theorem for stochastic iterative global optimization algorithms (Proposition 3 of (Malherbe, et al., 2017). This proof and the entire framework are formalized in the Lean proof assistant. This formalization both ensures the correctness of the definitions and proofs, and provides a basis for future machine-assisted formalizations in the field.

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arXiv2025

OneBatchPAM: A Fast and Frugal K-Medoids Algorithm

This paper proposes a novel k-medoids approximation algorithm to handle large-scale datasets with reasonable computational time and memory complexity. We develop a local-search algorithm that iteratively improves the medoid selection based on the estimation of the k-medoids objective. A single batch of size m << n provides the estimation, which reduces the required memory size and the number of pairwise dissimilarities computations to O(mn), instead of O(n^2) compared to most k-medoids baselines. We obtain theoretical results highlighting that a batch of size m = O(log(n)) is sufficient to guarantee, with strong probability, the same performance as the original local-search algorithm. Multiple experiments conducted on real datasets of various sizes and dimensions show that our algorithm provides similar performances as state-of-the-art methods such as FasterPAM and BanditPAM++ with a drastically reduced running time.

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arXiv2024

A Pre-Trained Graph-Based Model for Adaptive Sequencing of Educational Documents

Massive Open Online Courses (MOOCs) have greatly contributed to making education more accessible. However, many MOOCs maintain a rigid, one-size-fits-all structure that fails to address the diverse needs and backgrounds of individual learners. Learning path personalization aims to address this limitation, by tailoring sequences of educational content to optimize individual student learning outcomes. Existing approaches, however, often require either massive student interaction data or extensive expert annotation, limiting their broad application. In this study, we introduce a novel data-efficient framework for learning path personalization that operates without expert annotation. Our method employs a flexible recommender system pre-trained with reinforcement learning on a dataset of raw course materials. Through experiments on semi-synthetic data, we show that this pre-training stage substantially improves data-efficiency in a range of adaptive learning scenarios featuring new educational materials. This opens up new perspectives for the design of foundation models for adaptive learning.

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arXiv2024

LIPO+: Frugal Global Optimization for Lipschitz Functions

In this paper, we propose simple yet effective empirical improvements to the algorithms of the LIPO family, introduced in [Malherbe2017], that we call LIPO+ and AdaLIPO+. We compare our methods to the vanilla versions of the algorithms over standard benchmark functions and show that they converge significantly faster. Finally, we show that the LIPO family is very prone to the curse of dimensionality and tends quickly to Pure Random Search when the dimension increases. We give a proof for this, which is also formalized in Lean mathematical language. Source codes and a demo are provided online.

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arXiv2024

Collaborative non-parametric two-sample testing

This paper addresses the multiple two-sample test problem in a graph-structured setting, which is a common scenario in fields such as Spatial Statistics and Neuroscience. Each node $v$ in fixed graph deals with a two-sample testing problem between two node-specific probability density functions (pdfs), $p_v$ and $q_v$. The goal is to identify nodes where the null hypothesis $p_v = q_v$ should be rejected, under the assumption that connected nodes would yield similar test outcomes. We propose the non-parametric collaborative two-sample testing (CTST) framework that efficiently leverages the graph structure and minimizes the assumptions over $p_v$ and $q_v$. Our methodology integrates elements from f-divergence estimation, Kernel Methods, and Multitask Learning. We use synthetic experiments and a real sensor network detecting seismic activity to demonstrate that CTST outperforms state-of-the-art non-parametric statistical tests that apply at each node independently, hence disregard the geometry of the problem.

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arXiv2024

Stein Boltzmann Sampling: A Variational Approach for Global Optimization

In this paper, we present a flow-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the Stein Variational Gradient Descent (SVGD) algorithm to sequentially and deterministically move those particles in order to approximate a target distribution whose mass is concentrated around promising areas of the domain of the optimized function. The target is chosen to be a properly parametrized Boltzmann distribution. For the purpose of global optimization, we adapt the generic SVGD theoretical framework allowing to address more general target distributions over a compact subset of $\mathbb{R}^d$, and we prove SBS's asymptotic convergence. In addition to the main SBS algorithm, we present two variants: the SBS-PF that includes a particle filtering strategy, and the SBS-HYBRID one that uses SBS or SBS-PF as a continuation after other particle- or distribution-based optimization methods. A detailed comparison with state-of-the-art methods on benchmark functions demonstrates that SBS and its variants are highly competitive, while the combination of the two variants provides the best trade-off between accuracy and computational cost.

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arXiv2023

Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization

Quantifying the difference between two probability density functions, $p$ and $q$, using available data, is a fundamental problem in Statistics and Machine Learning. A usual approach for addressing this problem is the likelihood-ratio estimation (LRE) between $p$ and $q$, which -- to our best knowledge -- has been investigated mainly for the offline case. This paper contributes by introducing a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations $(x_t \sim p, x'_t \sim q)$ are observed over time. The non-parametric nature of our approach has the advantage of being agnostic to the forms of $p$ and $q$. Moreover, we capitalize on the recent advances in Kernel Methods and functional minimization to develop an estimator that can be efficiently updated online. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.

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arXiv2023

A framework for paired-sample hypothesis testing for high-dimensional data

The standard paired-sample testing approach in the multidimensional setting applies multiple univariate tests on the individual features, followed by p-value adjustments. Such an approach suffers when the data carry numerous features. A number of studies have shown that classification accuracy can be seen as a proxy for two-sample testing. However, neither theoretical foundations nor practical recipes have been proposed so far on how this strategy could be extended to multidimensional paired-sample testing. In this work, we put forward the idea that scoring functions can be produced by the decision rules defined by the perpendicular bisecting hyperplanes of the line segments connecting each pair of instances. Then, the optimal scoring function can be obtained by the pseudomedian of those rules, which we estimate by extending naturally the Hodges-Lehmann estimator. We accordingly propose a framework of a two-step testing procedure. First, we estimate the bisecting hyperplanes for each pair of instances and an aggregated rule derived through the Hodges-Lehmann estimator. The paired samples are scored by this aggregated rule to produce a unidimensional representation. Second, we perform a Wilcoxon signed-rank test on the obtained representation. Our experiments indicate that our approach has substantial performance gains in testing accuracy compared to the traditional multivariate and multiple testing, while at the same time estimates each feature's contribution to the final result.

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arXiv2023

Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy Maximization

This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard approaches when used out-of-distribution (Ovadia et al., 2019; Liu et al., 2021). Considering that this issue is mainly related to a lack of weight diversity, we claim that standard methods sample in "over-restricted" regions of the weight space due to the use of "over-regularization" processes, such as weight decay and zero-mean centered Gaussian priors. We propose to solve the problem by adopting the maximum entropy principle for the weight distribution, with the underlying idea to maximize the weight diversity. Under this paradigm, the epistemic uncertainty is described by the weight distribution of maximal entropy that produces neural networks "consistent" with the training observations. Considering stochastic neural networks, a practical optimization is derived to build such a distribution, defined as a trade-off between the average empirical risk and the weight distribution entropy. We develop a novel weight parameterization for the stochastic model, based on the singular value decomposition of the neural network's hidden representations, which enables a large increase of the weight entropy for a small empirical risk penalization. We provide both theoretical and numerical results to assess the efficiency of the approach. In particular, the proposed algorithm appears in the top three best methods in all configurations of an extensive out-of-distribution detection benchmark including more than thirty competitors.

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arXiv2023

Deep Anti-Regularized Ensembles provide reliable out-of-distribution uncertainty quantification

We consider the problem of uncertainty quantification in high dimensional regression and classification for which deep ensemble have proven to be promising methods. Recent observations have shown that deep ensemble often return overconfident estimates outside the training domain, which is a major limitation because shifted distributions are often encountered in real-life scenarios. The principal challenge for this problem is to solve the trade-off between increasing the diversity of the ensemble outputs and making accurate in-distribution predictions. In this work, we show that an ensemble of networks with large weights fitting the training data are likely to meet these two objectives. We derive a simple and practical approach to produce such ensembles, based on an original anti-regularization term penalizing small weights and a control process of the weight increase which maintains the in-distribution loss under an acceptable threshold. The developed approach does not require any out-of-distribution training data neither any trade-off hyper-parameter calibration. We derive a theoretical framework for this approach and show that the proposed optimization can be seen as a "water-filling" problem. Several experiments in both regression and classification settings highlight that Deep Anti-Regularized Ensembles (DARE) significantly improve uncertainty quantification outside the training domain in comparison to recent deep ensembles and out-of-distribution detection methods. All the conducted experiments are reproducible and the source code is available at \url{https://github.com/antoinedemathelin/DARE}.

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arXiv2023

A Bipartite Ranking Approach to the Two-Sample Problem

The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention, especially because the information acquisition processes at work in the Big Data era often involve various sources, poorly controlled, leading to datasets possibly exhibiting a strong sampling bias. While classic methods relying on the computation of a discrepancy measure between the empirical distributions face the curse of dimensionality, we develop an alternative approach based on statistical learning and extending rank tests, capable of detecting small departures from the null assumption in the univariate case when appropriately designed. Overcoming the lack of natural order on $\mathbb{R}^d$ when $d\geq 2$, it is implemented in two steps. Assigning to each of the samples a label (positive vs. negative) and dividing them into two parts, a preorder on $\mathbb{R}^d$ defined by a real-valued scoring function is learned by means of a bipartite ranking algorithm applied to the first part and a rank test is applied next to the scores of the remaining observations to detect possible differences in distribution. Because it learns how to project the data onto the real line nearly like (any monotone transform of) the likelihood ratio between the original multivariate distributions would do, the approach is not much affected by the dimensionality, ignoring ranking model bias issues, and preserves the advantages of univariate rank tests. Nonasymptotic error bounds are proved based on recent concentration results for two-sample linear rank-processes and an experimental study shows that the approach promoted surpasses alternative methods standing as natural competitors.

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arXiv2023

Online Centralized Non-parametric Change-point Detection via Graph-based Likelihood-ratio Estimation

Consider each node of a graph to be generating a data stream that is synchronized and observed at near real-time. At a change-point $\tau$, a change occurs at a subset of nodes $C$, which affects the probability distribution of their associated node streams. In this paper, we propose a novel kernel-based method to both detect $\tau$ and localize $C$, based on the direct estimation of the likelihood-ratio between the post-change and the pre-change distributions of the node streams. Our main working hypothesis is the smoothness of the likelihood-ratio estimates over the graph, i.e connected nodes are expected to have similar likelihood-ratios. The quality of the proposed method is demonstrated on extensive experiments on synthetic scenarios.

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