arXiv subjects

Olivier Wintenberger

Publications and source records attributed to Olivier Wintenberger.

At least 19 recordsLinked to original sources

arXiv2026

Moments for self-normalized partial sums

We consider a regularly varying stationary sequence of random variables (Xt) with tail index ___ < 2. For these sequences we study the joint convergence of sums, `p- type moduli and maxima. We focus on ratio statistics, including the studentized sums and sums normalized by the corresponding maxima, and study the existence of moments for the limit ratios. We consider particular examples of processes (Xt) whose limit ratios possess all moments. But, in contrast to the latter situation, there also exist sequences (Xt) where certain moments of the limit ratio are in___nite. This phenomenon results from extremal clusters in the sequence.

math.PR↗

arXiv2026

Contribution of expert aggregation to temperature prediction part i

Many Numerical Weather Prediction models and their associated Post-Processed Models are available. Combining all of these predictions in an optimal way is however not straightforward. This can be achieved thanks to Expert Aggregation (EA) which has many advantages, such as being online, being adaptive to model changes and having theoretical guarantees. In this paper, we propose a method for making deterministic temperature predictions with EA. We used Exponentially Weighted Average, MLprod and MLpol and Bernstein Online Aggregation. Hence, we combine and outperform the forecasts of the raw and post-processed Integrated Forecasting System (IFS), forecasts of Application of Research to Operations at Mesoscale (AROME), Action de Recherche Petite Echelle Grande Echelle (ARPEGE) and quantiles of the post processed Pr{é}vision d'Ensemble ARPEGE (PEARP). We also compare the different EA strategies in various settings and show that they outperform the National Blend of Models. Finally, we discuss certain limitations.

math.OC↗

arXiv2026

Contribution of expert aggregation to temperature prediction part II: Second order bounds with sleeping experts

In this paper we improve on the temperature predictions made with (online) Expert Aggregation (EA) [Cesa-Bianchi and Lugosi, 2006] in Part I. In particular, we make the aggregation more reactive, whilst maintaining at least the same root mean squared error and reducing the number of large errors. We have achieved this by using the Sleeping Expert Framework (SEF) [Freund et al., 1997, Devaine et al., 2013], which allows the more efficient use of biased experts (bad on average but which may be good at some point). To deal with the fact that, unlike in Devaine et al. [2013], we do not know in advance when to use these biased experts, we resorted to gradient boosted regression trees [Chen and Guestrin, 2016] and provide regret bounds against sequences of experts [Mourtada and Maillard, 2017] which take into account this uncertainty. We applied this in a fully online way on BOA [Wintenberger, 2024], an adaptive aggregation with second order regret bounds, which had the best results in Part I. Finally, we made a meta-aggregation with the EA follow the leader. This chooses whether or not to use the SEF in order to limit the possible noise added by the SEF.

math.OC↗

arXiv2026

Assessing Extrapolation of Peaks Over Thresholds with Martingale Testing

We present the winning strategy for the EVA2025 Data Challenge, which aimed to estimate the probability of extreme precipitation events. These events occurred at most once in the dataset making the challenge fundamentally one of extrapolating extreme values. Given the scarcity of extreme events, we argue that a simple, robust modeling approach is essential. We adopt univariate models instead of multivariate ones and model Peaks Over Thresholds using Extreme Value Theory. Specifically, we fit an exponential distribution to model exceedances of the target variable above a high quantile (after seasonal adjustment). The novelty of our approach lies in using martingale testing to evaluate the extrapolation power of the procedure and to agnostically select the level of the high quantile. While this method has several limitations, we believe that framing extrapolation as a game opens the door to other agnostic approaches in Extreme Value Analysis.

stat.ME↗

arXiv2026

A duration-augmented binary Markov chain for rainfall occurrence with long dry spells

Simulating realistic wet and dry spells is central in weather generators and climate-impact studies. While finite-order Markov chains are standard, they often fail to reproduce persistent dry conditions due to their inherent subexponential decay. We model rainfall occurrence by introducing a duration-augmented binary Markov chain. We establish a link with alternating renewal chains, enabling flexible parametric modelling of wet and dry spell duration distribution. We model those using two regime-adapted specifications from the general class of extended Generalized Pareto Distributions, yielding flexible tail behaviour across various climates. We use estimation methods adapted to each specification. Our model is applied to around 200 stations in the South of Europe spanning diverse Mediterranean and continental climates. We compare this framework to standard Markov models in characterising persistence and high-quantile extrapolation. The approach is generic, extending naturally to multi-state settings or other binary sequence applications in environmental statistics.

stat.ME↗

arXiv2026

High-Probability Minimax Adaptive Estimation in Besov Spaces via Online-to-Batch

We study nonparametric regression over Besov spaces from noisy observations under sub-exponential noise, aiming to achieve minimax-optimal guarantees on the integrated squared error that hold with high probability and adapt to the unknown noise level. To this end, we propose a wavelet-based online learning algorithm that dynamically adjusts to the observed gradient noise by adaptively clipping it at an appropriate level, eliminating the need to tune parameters such as the noise variance or gradient bounds. As a by-product of our analysis, we derive high-probability adaptive regret bounds that scale with the $\ell_1$-norm of the competitor. Finally, in the batch statistical setting, we obtain adaptive and minimax-optimal estimation rates for Besov spaces via a refined online-to-batch conversion. This approach carefully exploits the structure of the squared loss in combination with self-normalized concentration inequalities.

math.ST↗

arXiv2026

Geometry-Aware Optimal Transport: Fast Intrinsic Dimension and Wasserstein Distance Estimation

Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization error is governed by the intrinsic dimension of our data. Therefore, the true bottleneck is the knowledge and control of the sampling error. In this work, we tackle this issue by introducing novel estimators for both sampling error and intrinsic dimension. The key finding is a simple, tuning-free estimator of $\text{OT}_c(ρ, \hatρ)$ that utilizes the semi-dual OT functional and, remarkably, requires no OT solver. Furthermore, we derive a fast intrinsic dimension estimator from the multi-scale decay of our sampling error estimator. This framework unlocks significant computational and statistical advantages in practice, enabling us to (i) quantify the convergence rate of the discretization error, (ii) calibrate the entropic regularization of Sinkhorn divergences to the data's intrinsic geometry, and (iii) introduce a novel, intrinsic-dimension-based Richardson extrapolation estimator that strongly debiases Wasserstein distance estimation. Numerical experiments demonstrate that our geometry-aware pipeline effectively mitigates the discretization error bottleneck while maintaining computational efficiency.

stat.ML↗

arXiv2025

Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport

Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while still benefiting from the acceleration provided by regularization, a natural solver would adaptively decrease the regularization as it approaches the solution. Although some algorithms heuristically implement this idea, their theoretical guarantees and the extent of their acceleration compared to using a fixed regularization remain largely open. In the setting of semi-discrete OT, where the source measure is continuous and the target is discrete, we prove that decreasing the regularization can indeed accelerate convergence. To this end, we introduce DRAG: Decreasing (entropic) Regularization Averaged Gradient, a stochastic gradient descent algorithm where the regularization decreases with the number of optimization steps. We provide a theoretical analysis showing that DRAG benefits from decreasing regularization compared to a fixed scheme, achieving an unbiased $\mathcal{O}(1/t)$ sample and iteration complexity for both the OT cost and the potential estimation, and a $\mathcal{O}(1/\sqrt{t})$ rate for the OT map. Our theoretical findings are supported by numerical experiments that validate the effectiveness of DRAG and highlight its practical advantages.

stat.ML↗

arXiv2025

Stochastic Optimization in Semi-Discrete Optimal Transport: Convergence Analysis and Minimax Rate

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $μ$ is transported to a discrete target measure $ν$, with particular attention to the OT map approximation. In this setting, Stochastic Gradient Descent (SGD) based solvers have demonstrated strong empirical performance in recent machine learning applications, yet their theoretical guarantee to approximate the OT map is an open question. In this work, we answer it positively by providing both computational and statistical convergence guarantees of SGD. Specifically, we show that SGD methods can estimate the OT map with a minimax convergence rate of $\mathcal{O}(1/\sqrt{n})$, where $n$ is the number of samples drawn from $μ$. To establish this result, we study the averaged projected SGD algorithm, and identify a suitable projection set that contains a minimizer of the objective, even when the source measure is not compactly supported. Our analysis holds under mild assumptions on the source measure and applies to MTW cost functions,whic include $\|\cdot\|^p$ for $p \in (1, \infty)$. We finally provide numerical evidence for our theoretical results.

math.ST↗

arXiv2025

Online (Non-)Convex Learning via Tempered Optimism

Optimistic Online Learning aims to exploit experts conveying reliable information to predict the future. However, such implicit optimism may be challenged when it comes to practical crafting of such experts. A fundamental example consists in approximating a minimiser of the current problem and use it as expert. In the context of dynamic environments, such an expert only conveys partially relevant information as it may lead to overfitting. To tackle this issue, we introduce in this work the \emph{optimistically tempered} (OT) online learning framework designed to handle such imperfect experts. As a first contribution, we show that tempered optimism is a fruitful paradigm for Online Non-Convex Learning by proposing simple, yet powerful modification of Online Gradient and Mirror Descent. Second, we derive a second OT algorithm for convex losses and third, evaluate the practical efficiency of tempered optimism on real-life datasets and a toy experiment.

cs.LG↗

arXiv2025

Power comparison of sequential testing by betting procedures

In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which coincide asymptotically with the null (e.g. vanishing mean) while still allowing to reject in finite time. Introducing variance constraints, we show that the alternative can be broaden while keeping power guarantees for certain second-order testing procedures. We also compare different test procedures in multidimensional setting using characteristics of the rejection times. Finally, we extend our analysis to other functionals as well as testing and comparing forecasters. Our results are illustrated with numerical simulations including bounded mean testing and comparison of forecasters.

math.ST↗

arXiv2025

Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting

Nonlinear and delayed effects of covariates often render time series forecasting challenging. To this end, we propose a novel forecasting framework based on ridge regression with signature features calculated on sliding windows. These features capture complex temporal dynamics without relying on learned or hand-crafted representations. Focusing on the discrete-time setting, we establish theoretical guarantees, namely universality of approximation and stationarity of signatures. We introduce an efficient sequential algorithm for computing signatures on sliding windows. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge.

stat.ME↗

arXiv2025

Minimax Adaptive Online Nonparametric Regression over Besov Spaces

We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular prediction rules, modeled by Besov spaces $B\_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s > \tfrac{d}{p}$. We introduce an adaptive wavelet-based algorithm that performs sequential prediction without prior knowledge of $(s,p,q)$, and establish minimax-optimal regret bounds against any comparator in $B\_{pq}^s$. We further design a locally adaptive extension capable of dynamically tracking spatially inhomogeneous smoothness. This adaptive mechanism adjusts the resolution of the predictions over both time and space, yielding refined regret bounds in terms of local regularity. Consequently, in heterogeneous environments, our adaptive guarantees can significantly surpass those obtained by standard global methods.

math.ST↗

arXiv2025

Sample-Path Large Deviations for Functionals of Poisson Cluster Processes

We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and the offspring distributions governing the propagation mechanism. These findings can also be interpreted as hidden regular variation of the cluster processes' functionals, extending the results in Dombry et al. (2022) to cluster processes with heavy-tailed characteristics, including mixed Binomial Poisson cluster processes and Hawkes processes. Notably, by restricting to the adequate subspace of measures on D([0, 1], R+), and applying the correct normalization and scaling to the paths of the centered cumulative functional, the limit measure concentrates on paths with multiple large jumps.

math.PR↗

arXiv2025

Asymptotic Normality of Infinite Centered Random Forests -Application to Imbalanced Classification

Many classification tasks involve imbalanced data, in which a class is largely underrepresented. Several techniques consists in creating a rebalanced dataset on which a classifier is trained. In this paper, we study theoretically such a procedure, when the classifier is a Centered Random Forests (CRF). We establish a Central Limit Theorem (CLT) on the infinite CRF with explicit rates and exact constant. We then prove that the CRF trained on the rebalanced dataset exhibits a bias, which can be removed with appropriate techniques. Based on an importance sampling (IS) approach, the resulting debiased estimator, called IS-ICRF, satisfies a CLT centered at the prediction function value. For high imbalance settings, we prove that the IS-ICRF estimator enjoys a variance reduction compared to the ICRF trained on the original data. Therefore, our theoretical analysis highlights the benefits of training random forests on a rebalanced dataset (followed by a debiasing procedure) compared to using the original data. Our theoretical results, especially the variance rates and the variance reduction, appear to be valid for Breiman's random forests in our experiments.

stat.ML↗

arXiv2025

Infinite random forests for imbalanced classification tasks

We study predictive probability inference in classification tasks using random forests under class imbalance. We focus on two simplified variants of Breiman's algorithm, namely subsampling Infinite Random Forests (IRFs) and under-sampling IRFs, and establish their asymptotic normality. In the under-sampling setting, training data from both classes are resampled to achieve balance, which enhances minority class representation but introduces a biased model. To correct this, we propose a debiasing procedure based on Importance Sampling (IS) using odds ratios. We instantiate our results using 1-Nearest Neighbor (1-NN) classifiers as base learners in the IRFs and prove the nearly minimax optimality of the approach for Lipschitz continuous objectives. We also show that the IS bagged 1-NN estimator matches the convergence rate of its subsampled counterpart while attaining lower asymptotic variance in most cases. Our theoretical findings are supported by simulation studies, highlighting the empirical benefits of the proposed approach.

math.ST↗

arXiv2025

On the asymptotics of extremal lp-blocks cluster inference

Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks. Examples of cluster statistics are the extremal index, cluster size probabilities, and other cluster indices. The purpose of our work is twofold. First, we state the asymptotic normality of block estimators for cluster inference based on consecutive observations with large lp-norms, for p < 0. The case p=$α$, where $α$ > 0 is the tail index of the time series, has specific nice properties thus we analyze the asymptotic of blocks estimators when approximating $α$ using the Hill estimator. Second, we verify the conditions we require on classical models such as linear models and solutions of stochastic recurrence equations. Regarding linear models, we prove that the asymptotic variance of classical index cluster-based estimators is null as first conjectured in Hsing T. [26]. We illustrate our findings on simulations.

math.PR↗

arXiv2025

Tail asymptotics and precise large deviations for some Poisson cluster processes

We study the tail asymptotics of two functionals (the maximum and the sum of the marks) of a generic cluster in two sub-models of the marked Poisson cluster process, namely the renewal Poisson cluster process and the Hawkes process. Under the hypothesis that the governing components of the processes are regularly varying, we extend results due to [18] and [5] notably, relying on Karamata's Tauberian Theorem to do so. We use these asymptotics to derive precise large deviation results in the fashion of [30] for the above-mentioned processes.

math.PR↗