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.

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 $\mathcal{O}(\log(t)/t)$ 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.

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.

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.

Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremes

Motivated by the increasing availability of data of functional nature, we develop a general probabilistic and statistical framework for extremes of regularly varying random elements $X$ in $L^2[0,1]$. We place ourselves in a Peaks-Over-Threshold framework where a functional extreme is defined as an observation $X$ whose $L^2$-norm $\|X\|$ is comparatively large. Our goal is to propose a dimension reduction framework resulting into finite dimensional projections for such extreme observations. Our contribution is double. First, we investigate the notion of Regular Variation for random quantities valued in a general separable Hilbert space, for which we propose a novel concrete characterization involving solely stochastic convergence of real-valued random variables. Second, we propose a notion of functional Principal Component Analysis (PCA) accounting for the principal `directions' of functional extremes. We investigate the statistical properties of the empirical covariance operator of the angular component of extreme functions, by upper-bounding the Hilbert-Schmidt norm of the estimation error for finite sample sizes. Numerical experiments with simulated and real data illustrate this work.

On Regression in Extreme Regions

In the classic regression problem, the value of a real-valued random variable $Y$ is to be predicted based on the observation of a random vector $X$, taking its values in $\mathbb{R}^d$ with $d\geq 1$ say. The statistical learning problem consists in building a predictive function $\hat{f}:\mathbb{R}^d\to \mathbb{R}$ based on independent copies of the pair $(X,Y)$ so that $Y$ is approximated by $\hat{f}(X)$ with minimum error in the mean-squared sense. Motivated by various applications, ranging from environmental sciences to finance or insurance, special attention is paid here to the case of extreme (i.e. very large) observations $X$. Because of their rarity, they contribute in a negligible manner to the (empirical) error and the predictive performance of empirical quadratic risk minimizers can be consequently very poor in extreme regions. In this paper, we develop a general framework for regression in the extremes. It is assumed that $X$'s conditional distribution given $Y$ belongs to a non parametric class of heavy-tailed probability distributions. It is then shown that an asymptotic notion of risk can be tailored to summarize appropriately predictive performance in extreme regions of the input space. It is also proved that minimization of an empirical and non asymptotic version of this 'extreme risk', based on a fraction of the largest observations solely, yields regression functions with good generalization capacity. In addition, numerical results providing strong empirical evidence of the relevance of the approach proposed are displayed.

On Medians of (Randomized) Pairwise Means

Tournament procedures, recently introduced in Lugosi & Mendelson (2016), offer an appealing alternative, from a theoretical perspective at least, to the principle of Empirical Risk Minimization in machine learning. Statistical learning by Median-of-Means (MoM) basically consists in segmenting the training data into blocks of equal size and comparing the statistical performance of every pair of candidate decision rules on each data block: that with highest performance on the majority of the blocks is declared as the winner. In the context of nonparametric regression, functions having won all their duels have been shown to outperform empirical risk minimizers w.r.t. the mean squared error under minimal assumptions, while exhibiting robustness properties. It is the purpose of this paper to extend this approach in order to address other learning problems, in particular for which the performance criterion takes the form of an expectation over pairs of observations rather than over one single observation, as may be the case in pairwise ranking, clustering or metric learning. Precisely, it is proved here that the bounds achieved by MoM are essentially conserved when the blocks are built by means of independent sampling without replacement schemes instead of a simple segmentation. These results are next extended to situations where the risk is related to a pairwise loss function and its empirical counterpart is of the form of a $U$-statistic. Beyond theoretical results guaranteeing the performance of the learning/estimation methods proposed, some numerical experiments provide empirical evidence of their relevance in practice.

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, the flagship problem in Geostatistics: the values of a square integrable random field $X=\{X_s\}_{s\in S}$, $S\subset \mathbb{R}^2$, with unknown covariance structure are to be predicted with minimum quadratic risk, based upon observing a single realization of the spatial process at a finite number of locations $s_1,\; \ldots,\; s_n$ 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 i.i.d. nature of the spatial data $X_{s_1},\; \ldots,\; X_{s_n}$ involved. In this article, nonasymptotic bounds of order $O_{\mathbb{P}}(1/n)$ 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. These theoretical results, as well as the role played by the technical conditions required to establish them, are illustrated by various numerical experiments and hopefully pave the way for further developments in statistical learning based on spatial data.

Improving the quality control of seismic data through active learning

In image denoising problems, the increasing density of available images makes an exhaustive visual inspection impossible and therefore automated methods based on machine-learning must be deployed for this purpose. This is particulary the case in seismic signal processing. Engineers/geophysicists have to deal with millions of seismic time series. Finding the sub-surface properties useful for the oil industry may take up to a year and is very costly in terms of computing/human resources. In particular, the data must go through different steps of noise attenuation. Each denoise step is then ideally followed by a quality control (QC) stage performed by means of human expertise. To learn a quality control classifier in a supervised manner, labeled training data must be available, but collecting the labels from human experts is extremely time-consuming. We therefore propose a novel active learning methodology to sequentially select the most relevant data, which are then given back to a human expert for labeling. Beyond the application in geophysics, the technique we promote in this paper, based on estimates of the local error and its uncertainty, is generic. Its performance is supported by strong empirical evidence, as illustrated by the numerical experiments presented in this article, where it is compared to alternative active learning strategies both on synthetic and real seismic datasets.

Functional Anomaly Detection: a Benchmark Study

The increasing automation in many areas of the Industry expressly demands to design efficient machine-learning solutions for the detection of abnormal events. With the ubiquitous deployment of sensors monitoring nearly continuously the health of complex infrastructures, anomaly detection can now rely on measurements sampled at a very high frequency, providing a very rich representation of the phenomenon under surveillance. In order to exploit fully the information thus collected, the observations cannot be treated as multivariate data anymore and a functional analysis approach is required. It is the purpose of this paper to investigate the performance of recent techniques for anomaly detection in the functional setup on real datasets. After an overview of the state-of-the-art and a visual-descriptive study, a variety of anomaly detection methods are compared. While taxonomies of abnormalities (e.g. shape, location) in the functional setup are documented in the literature, assigning a specific type to the identified anomalies appears to be a challenging task. Thus, strengths and weaknesses of the existing approaches are benchmarked in view of these highlighted types in a simulation study. Anomaly detection methods are next evaluated on two datasets, related to the monitoring of helicopters in flight and to the spectrometry of construction materials namely. The benchmark analysis is concluded by recommendation guidance for practitioners.