arXiv subjects

Stephan Clémençon

Publications and source records attributed to Stephan Clémençon.

At least 19 recordsLinked to original sources

arXiv2026

Fast and Efficient Asynchronous Gossip Algorithm for Robust and Non-Smooth Convex Decentralized Learning

Asynchronous primal-dual methods for decentralized non-smooth convex optimization often require each node to maintain $\mathcal{O}(d)$ auxiliary variables, where $d$ is its degree. This dependence on degree increases memory requirements and can amplify the effects of stale information, especially in dense networks. Motivated by the challenge of frugal memory management in decentralized learning, we introduce Goal-PD, an asynchronous gossip-based primal-dual algorithm that maintains only two variables per node, regardless of the node's degree. We establish almost-sure convergence of Goal-PD to a minimizer of the underlying optimization problem, and prove linear convergence when the objective functions are piecewise linear-quadratic. For decentralized mean estimation, we show that pairwise averaging is a special case of Goal-PD, which establishes a direct link between the proposed primal-dual framework and classical gossip. Experiments on synthetic and real datasets over various network topologies, with non-smooth objectives including median estimation, show that Goal-PD converges faster than existing asynchronous baselines while requiring significantly less memory by design.

cs.LG↗

arXiv2026

On Pairwise Quantile Regression - Statistical Guarantees and Applications

Quantile regression provides a powerful tool for summarizing the conditional distribution of a real-valued random variable (r.v.) of interest $Y$ as a function of covariates $Z$ in cases where it shows a large dispersion with high probability, going beyond the situation where standard least square regression is informative/predictive. This article aims to extend this methodology to the pairwise setting, where the variable to be explained is a similarity score between two independent observations (e.g., pixelated ID photos used as input to biometric systems), and the explanatory variables consist of the pair of covariates attached to these observations, such as age or hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for $U$-processes, we prove generalization bounds and identify mild conditions under which fast learning rates can be achieved. Confirming the probabilistic analysis, experiments based on simulation data also provide solid empirical evidence of the validity of the methodology promoted here for pairwise quantile regression. Finally, its usefulness from an application perspective is demonstrated by a detailed study aimed at analyzing errors in similarity scoring for facial recognition.

stat.ML↗

arXiv2026

TimeSAE: Causal Sparse Decoding for Faithful Explanations of Black-Box Time Series Models

As black box models and pretrained models gain traction in time series applications, understanding and explaining their predictions becomes increasingly vital, especially in high-stakes domains where interpretability and trust are essential. However, most of the existing methods involve only in-distribution explanation, and do not generalize outside the training support, which requires the learning capability of generalization. In this work, we aim to provide a framework to explain black-box models for time series data through the dual lenses of Sparse Autoencoders (SAEs) and causality. We show that many current explanation methods are sensitive to distributional shifts, limiting their effectiveness in real-world scenarios. Building on the concept of Sparse Autoencoder, we introduce TimeSAE, a framework for black-box model explanation. We conduct extensive evaluations of TimeSAE on both synthetic and real-world time series datasets, comparing it to leading baselines. The results, supported by both quantitative metrics and qualitative insights, show that TimeSAE provides more faithful and robust explanations. Our code is available in an easy-to-use library TimeSAE-Lib: https://oublalkhalid.github.io/TimeSAE/

cs.LG↗

arXiv2026

Doing well with less! On Sampling Techniques for Empirical Pairwise Loss Estimation/Minimization

Many machine learning problems, including similarity learning, ranking, and clustering, rely on empirical pairwise loss functions whose quadratic computational cost quickly becomes prohibitive at scale. We demonstrate how a frugal approach that retains only a fraction of the available information on pairs can achieve estimation or optimization performance comparable to that obtained by using all pairs, by leveraging survey sampling techniques. A central finding, supported by both theory and experiments, is that such sampling plans must target pairs directly rather than individual observations. In particular, for pairwise losses between high-dimensional vectors such as embeddings in vision or graph learning, assigning higher inclusion probabilities to informative pairs using suitable auxiliary information yields performance close to full pairwise evaluation, providing a principled and theoretically grounded trade-off between accuracy and computational cost.

stat.ML↗

arXiv2026

Decentralized Ranking Aggregation via Gossip: Convergence and Robustness

The concept of ranking aggregation plays a central role in preference analysis, and numerous algorithms for calculating median rankings, often originating in social choice theory, have been documented in the literature, offering theoretical guarantees in a centralized setting, \textit{i.e.}, when all the ranking data to be aggregated can be brought together in a single computing unit. For many technologies (\textit{e.g.} peer-to-peer networks, IoT, multi-agent systems), extending the ability to calculate consensus rankings with guarantees of convergence and resilience to potential contamination in a decentralized setting, when preference data is initially distributed across a communicating network, remains a major methodological challenge. Indeed, in recent years, the literature on decentralized computation has mainly focused on computing or optimizing statistics such as arithmetic means using gossip algorithms. The purpose of this article is precisely to study how to achieve reliable and resilient consensus on collective rankings in a decentralized setting, thereby raising new questions, robustness to corrupted nodes, and scalability through reduced communication costs in particular. The approach proposed and analyzed here relies on the robustness guarantees offered by random gossip communication, which allows autonomous agents to compute a global ranking consensus using local interactions only, without coordination or a central authority.

cs.LG↗

arXiv2026

Weak Signals and Heavy Tails: Learning Theory meets Extreme Value Analysis

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing multivariate extreme value theory and statistical learning theory together in a common, nonparametric and nonasymptotic framework makes it possible to design and analyze new methods for exploiting the scarce information located in distribution tails in these purposes. This article reviews recently proved theoretical tools for establishing guarantees for supervised or unsupervised algorithms learning from a fraction of extreme data. These are mainly exponential maximal deviation inequalities tailored to low-probability regions and concentration results for stochastic processes empirically describing the behavior of multivariate extreme observations, their dependence structure in particular. Under appropriate assumptions of regular variation, several illustrative applications in multivariate settings are then examined: classification, regression, anomaly detection, model selection via cross-validation. For these, generalization results are established inspired by the classical bounds in statistical learning theory. In the same spirit, it is also shown how to adapt the popular high-dimensional Lasso technique in the context of extreme values for the covariates with generalization guarantees.

math.ST↗

arXiv2026

On Gossip Algorithms for Machine Learning with Pairwise Objectives

In the IoT era, information is more and more frequently picked up by connected smart sensors with increasing, though limited, storage, communication and computation abilities. Whether due to privacy constraints or to the structure of the distributed system, the development of statistical learning methods dedicated to data that are shared over a network is now a major issue. Gossip-based algorithms have been developed for the purpose of solving a wide variety of statistical learning tasks, ranging from data aggregation over sensor networks to decentralized multi-agent optimization. Whereas the vast majority of contributions consider situations where the function to be estimated or optimized is a basic average of individual observations, it is the goal of this article to investigate the case where the latter is of pairwise nature, taking the form of a U -statistic of degree two. Motivated by various problems such as similarity learning, ranking or clustering for instance, we revisit gossip algorithms specifically designed for pairwise objective functions and provide a comprehensive theoretical framework for their convergence. This analysis fills a gap in the literature by establishing conditions under which these methods succeed, and by identifying the graph properties that critically affect their efficiency. In particular, a refined analysis of the convergence upper and lower bounds is performed.

cs.LG↗

arXiv2026

Active Bipartite Ranking with Smooth Posterior Distributions

In this article, bipartite ranking, a statistical learning problem involved in many applications and widely studied in the passive context, is approached in a much more general \textit{active setting} than the discrete one previously considered in the literature. While the latter assumes that the conditional distribution is piece wise constant, the framework we develop permits in contrast to deal with continuous conditional distributions, provided that they fulfill a Hölder smoothness constraint. We first show that a naive approach based on discretisation at a uniform level, fixed \textit{a priori} and consisting in applying next the active strategy designed for the discrete setting generally fails. Instead, we propose a novel algorithm, referred to as smooth-rank and designed for the continuous setting, which aims to minimise the distance between the ROC curve of the estimated ranking rule and the optimal one w.r.t. the $\sup$ norm. We show that, for a fixed confidence level $ε>0$ and probability $δ\in (0,1)$, smooth-rank is PAC$(ε,δ)$. In addition, we provide a problem dependent upper bound on the expected sampling time of smooth-rank and establish a problem dependent lower bound on the expected sampling time of any PAC$(ε,δ)$ algorithm. Beyond the theoretical analysis carried out, numerical results are presented, providing solid empirical evidence of the performance of the algorithm proposed, which compares favorably with alternative approaches.

stat.ML↗

arXiv2026

Beyond Kemeny Medians: Consensus Ranking Distributions Definition, Properties and Statistical Learning

In this article we develop a new method for summarizing a ranking distribution, \textit{i.e.} a probability distribution on the symmetric group $\mathfrak{S}_n$, beyond the classical theory of consensus and Kemeny medians. Based on the notion of \textit{local ranking median}, we introduce the concept of \textit{consensus ranking distribution} ($\crd$), a sparse mixture model of Dirac masses on $\mathfrak{S}_n$, in order to approximate a ranking distribution with small distortion from a mass transportation perspective. We prove that by choosing the popular Kendall $τ$ distance as the cost function, the optimal distortion can be expressed as a function of pairwise probabilities, paving the way for the development of efficient learning methods that do not suffer from the lack of vector space structure on $\mathfrak{S}_n$. In particular, we propose a top-down tree-structured statistical algorithm that allows for the progressive refinement of a CRD based on ranking data, from the Dirac mass at a Kemeny median at the root of the tree to the empirical ranking data distribution itself at the end of the tree's exhaustive growth. In addition to the theoretical arguments developed, the relevance of the algorithm is empirically supported by various numerical experiments.

stat.ML↗

arXiv2025

Robust Distributed Estimation: Extending Gossip Algorithms to Ranking and Trimmed Means

This paper addresses the problem of robust estimation in gossip algorithms over arbitrary communication graphs. Gossip algorithms are fully decentralized, relying only on local neighbor-to-neighbor communication, making them well-suited for situations where communication is constrained. A fundamental challenge in existing mean-based gossip algorithms is their vulnerability to malicious or corrupted nodes. In this paper, we show that an outlier-robust mean can be computed by globally estimating a robust statistic. More specifically, we propose a novel gossip algorithm for rank estimation, referred to as \textsc{GoRank}, and leverage it to design a gossip procedure dedicated to trimmed mean estimation, coined \textsc{GoTrim}. In addition to a detailed description of the proposed methods, a key contribution of our work is a precise convergence analysis: we establish an $\mathcal{O}(1/t)$ rate for rank estimation and an $\mathcal{O}(1 / {t})$ rate for trimmed mean estimation, where by $t$ is meant the number of iterations. Moreover, we provide a breakdown point analysis of \textsc{GoTrim}. We empirically validate our theoretical results through experiments on diverse network topologies, data distributions and contamination schemes.

stat.ML↗

arXiv2025

On Regression in Extreme Regions

We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical regression on a subsample of observations with continuous labels that are the furthest away from the origin, focusing specifically on their angular components. The underlying assumptions of our approach are grounded in the theory of multivariate regular variation, a cornerstone of extreme value theory. We address the stylized problem of nonparametric least squares regression with predictors chosen from a Vapnik-Chervonenkis class. This work contributes to a broader initiative to develop statistical learning theoretical foundations for supervised learning strategies that enhance performance on the supposedly heavy tails of covariates. Previous efforts in this area have focused exclusively on binary classification on extreme covariates. Although the continuous target setting necessitates different techniques and regularity assumptions, our main results echo findings from earlier studies. We quantify the predictive performance on tail regions in terms of excess risk, presenting it as a finite sample risk bound with a clear bias-variance decomposition. Numerical experiments with simulated and real data illustrate our theoretical findings.

stat.ML↗

arXiv2025

Asynchronous Gossip Algorithms for Rank-Based Statistical Methods

As decentralized AI and edge intelligence become increasingly prevalent, ensuring robustness and trustworthiness in such distributed settings has become a critical issue-especially in the presence of corrupted or adversarial data. Traditional decentralized algorithms are vulnerable to data contamination as they typically rely on simple statistics (e.g., means or sum), motivating the need for more robust statistics. In line with recent work on decentralized estimation of trimmed means and ranks, we develop gossip algorithms for computing a broad class of rank-based statistics, including L-statistics and rank statistics-both known for their robustness to outliers. We apply our method to perform robust distributed two-sample hypothesis testing, introducing the first gossip algorithm for Wilcoxon rank-sum tests. We provide rigorous convergence guarantees, including the first convergence rate bound for asynchronous gossip-based rank estimation. We empirically validate our theoretical results through experiments on diverse network topologies.

stat.ML↗

arXiv2025

Feature Impact Analysis on Top Long-Jump Performances with Quantile Random Forest and Explainable AI Techniques

Biomechanical features have become important indicators for evaluating athletes' techniques. Traditionally, experts propose significant features and evaluate them using physics equations. However, the complexity of the human body and its movements makes it challenging to explicitly analyze the relationships between some features and athletes' final performance. With advancements in modern machine learning and statistics, data analytics methods have gained increasing importance in sports analytics. In this study, we leverage machine learning models to analyze expert-proposed biomechanical features from the finals of long jump competitions in the World Championships. The objectives of the analysis include identifying the most important features contributing to top-performing jumps and exploring the combined effects of these key features. Using quantile regression, we model the relationship between the biomechanical feature set and the target variable (effective distance), with a particular focus on elite-level jumps. To interpret the model, we apply SHapley Additive exPlanations (SHAP) alongside Partial Dependence Plots (PDPs) and Individual Conditional Expectation (ICE) plots. The findings reveal that, beyond the well-documented velocity-related features, specific technical aspects also play a pivotal role. For male athletes, the angle of the knee of the supporting leg before take-off is identified as a key factor for achieving top 10% performance in our dataset, with angles greater than 169°contributing significantly to jump performance. In contrast, for female athletes, the landing pose and approach step technique emerge as the most critical features influencing top 10% performances, alongside velocity. This study establishes a framework for analyzing the impact of various features on athletic performance, with a particular emphasis on top-performing events.

cs.LG↗

arXiv2025

Polar Coordinate-Based 2D Pose Prior with Neural Distance Field

Human pose capture is essential for sports analysis, enabling precise evaluation of athletes' movements. While deep learning-based human pose estimation (HPE) models from RGB videos have achieved impressive performance on public datasets, their effectiveness in real-world sports scenarios is often hindered by motion blur, occlusions, and domain shifts across different pose representations. Fine-tuning these models can partially alleviate such challenges but typically requires large-scale annotated data and still struggles to generalize across diverse sports environments. To address these limitations, we propose a 2D pose prior-guided refinement approach based on Neural Distance Fields (NDF). Unlike existing approaches that rely solely on angular representations of human poses, we introduce a polar coordinate-based representation that explicitly incorporates joint connection lengths, enabling a more accurate correction of erroneous pose estimations. Additionally, we define a novel non-geodesic distance metric that separates angular and radial discrepancies, which we demonstrate is better suited for polar representations than traditional geodesic distances. To mitigate data scarcity, we develop a gradient-based batch-projection augmentation strategy, which synthesizes realistic pose samples through iterative refinement. Our method is evaluated on a long jump dataset, demonstrating its ability to improve 2D pose estimation across multiple pose representations, making it robust across different domains. Experimental results show that our approach enhances pose plausibility while requiring only limited training data. Code is available at: https://github.com/QGAN2019/polar-NDF.

cs.CV↗

arXiv2025

Anomaly Detection based on Markov Data: A Statistical Depth Approach

The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth functions permit to generalize the notions of quantiles and (signed) ranks for observations in $\mathbb{R}^d$ with $d>1$, as well as statistical procedures based on such quantities. Here we develop a general theoretical framework for evaluating the depth of a Markov sample path and recovering it statistically from an estimate of its transition probability with (non-) asymptotic guarantees. We also detail some of its applications, focusing particularly on unsupervised anomaly detection. Beyond the theoretical analysis carried out, numerical experiments are displayed, providing empirical evidence of the relevance of the novel concept we introduce here to quantify the degree of abnormality of Markov paths of variable length.

math.ST↗

arXiv2025

Tail Index Estimation for Discrete Heavy-Tailed Distributions

It is the purpose of this paper to investigate the issue of estimating the regularity index $β>0$ of a discrete heavy-tailed r.v. $S$, \textit{i.e.} a r.v. $S$ valued in $\mathbb{N}^*$ such that $\mathbb{P}(S>n)=L(n)\cdot n^{-β}$ for all $n\geq 1$, where $L:\mathbb{R}^*_+\to \mathbb{R}_+$ is a slowly varying function. As a first go, we consider the situation where inference is based on independent copies $S_1,\; \ldots,\; S_n$ of the generic variable $S$. Just like the popular Hill estimator in the continuous heavy-tail situation, the estimator $\widehatβ$ we propose can be derived by means of a suitable reformulation of the regularly varying condition, replacing $S$'s survivor function by its empirical counterpart. Under mild assumptions, a non-asymptotic bound for the deviation between $\widehatβ$ and $β$ is established, as well as limit results (consistency and asymptotic normality). Beyond the i.i.d. case, the inference method proposed is extended to the estimation of the regularity index of a regenerative $β$-null recurrent Markov chain. Since the parameter $β$ can be then viewed as the tail index of the (regularly varying) distribution of the return time of the chain $X$ to any (pseudo-) regenerative set, in this case, the estimator is constructed from the successive regeneration times. Because the durations between consecutive regeneration times are asymptotically independent, we can prove that the consistency of the estimator promoted is preserved. In addition to the theoretical analysis carried out, simulation results provide empirical evidence of the relevance of the inference technique proposed.

math.ST↗

arXiv2024

Flexible Parametric Inference for Space-Time Hawkes Processes

Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can accurately capture. This paper aims to develop a fast and flexible parametric inference technique to recover the parameters of the kernel functions involved in the intensity function of a space-time Hawkes process based on such data. Our statistical approach combines three key ingredients: 1) kernels with finite support are considered, 2) the space-time domain is appropriately discretized, and 3) (approximate) precomputations are used. The inference technique we propose then consists of a $\ell_2$ gradient-based solver that is fast and statistically accurate. In addition to describing the algorithmic aspects, numerical experiments have been carried out on synthetic and real spatio-temporal data, providing solid empirical evidence of the relevance of the proposed methodology.

stat.ML↗

arXiv2024

A Statistical Learning View of Simple Kriging

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory of statistical learning does not apply directly and guarantees of the generalization capacity of predictive rules learned from such data are left to establish. We analyze here the simple Kriging task from a statistical learning perspective, i.e. by carrying out a nonparametric finite-sample predictive analysis. Given $d\geq 1$ values taken by a realization of a square integrable random field $X=\{X_s\}_{s\in S}$, $S\subset \mathbb{R}^2$, with unknown covariance structure, at sites $s_1,\; \ldots,\; s_d$ in $S$, the goal is to predict the unknown values it takes at any other location $s\in S$ with minimum quadratic risk. The prediction rule being derived from a training spatial dataset: a single realization $X'$ of $X$, independent from those to be predicted, observed at $n\geq 1$ locations $σ_1,\; \ldots,\; σ_n$ in $S$. Despite the connection of this minimization problem with kernel ridge regression, establishing the generalization capacity of empirical risk minimizers is far from straightforward, due to the non independent and identically distributed nature of the training data $X'_{σ_1},\; \ldots,\; X'_{σ_n}$ involved in the learning procedure. In this article, non-asymptotic bounds of order $O_{\mathbb{P}}(1/\sqrt{n})$ are proved for the excess risk of a plug-in predictive rule mimicking the true minimizer in the case of isotropic stationary Gaussian processes, observed at locations forming a regular grid in the learning stage. These theoretical results are illustrated by various numerical experiments, on simulated data and on real-world datasets.

stat.ML↗