arXiv subjects

Raphaël Huser

Publications and source records attributed to Raphaël Huser.

At least 19 recordsLinked to original sources

arXiv2026

Uncertainty and Explainability in Deep Rough Volatility: A Neural Information-Theoretic Posterior Approach

Deep learning has substantially accelerated the calibration of complex stochastic-volatility models, but neural point calibration alone does not capture the uncertainty remaining after an implied-volatility (IV) surface has been observed. We develop a simulation-based inference framework for rough Heston (rHeston) calibration that learns the posterior distribution of the model parameters conditional on an IV surface. Using neural ratio estimation, we obtain calibrated posterior samples that can be propagated through heteroscedastic neural surrogate pricers for path-dependent exotic options. The resulting posterior-predictive distributions combine residual parameter uncertainty with conditional surrogate uncertainty and yield uncertainty-aware price intervals. We further introduce Hellinger-SHAP, an information-theoretic explainability method for posterior inference. Rather than attributing a single parameter point estimate, it applies local-background Kernel SHAP to a posterior-information functional measuring contraction from the prior to the posterior. This identifies maturity--moneyness regions associated with posterior information gain for individual rHeston parameters. In a simulation study, posterior-predictive intervals provide calibrated or conservative coverage across forward-start, barrier, and realized-variance claims, while point plug-in prices can be materially unreliable for selected contract regimes. Together, the UQ and XAI analyses provide a transparent framework for uncertainty-aware neural calibration and downstream exotic pricing under the specified prior-predictive model.

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arXiv2026

Neural Conditional Simulation for Complex Spatial Processes

A key objective in spatial statistics is to simulate from the distribution of a spatial process at a selection of unobserved locations conditional on observations (i.e., a predictive distribution) to enable spatial prediction and uncertainty quantification. However, exact conditional simulation from this predictive distribution is intractable or inefficient for many spatial process models. In this paper, we propose neural conditional simulation (NCS), a general method for spatial conditional simulation that is based on neural diffusion models. Specifically, using spatial masks, we implement a conditional score-based diffusion model that evolves Gaussian noise into samples from a predictive distribution when given a partially observed spatial field and spatial process parameters as inputs. The diffusion model relies on a neural network that only requires unconditional samples from the spatial process for training. Once trained, the diffusion model is amortized with respect to the observations in the partially observed field, the number and locations of those observations, and the spatial process parameters, and can therefore be used to conditionally simulate from a broad class of predictive distributions without retraining the neural network. We assess the NCS-generated simulations against simulations from the true conditional distribution of a Gaussian process model, and against Markov chain Monte Carlo (MCMC) simulations from a Brown--Resnick process model for spatial extremes. In the latter case, we show that it is more efficient and accurate to conditionally simulate using NCS than classical MCMC techniques. We also demonstrate the use of NCS to predict spatial extremes in the Red Sea. We conclude that NCS enables efficient and accurate conditional simulation from spatial predictive distributions that are challenging to sample from using traditional methods.

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arXiv2026

Separation-based causal discovery for extremes

Structural causal models (SCMs), with an underlying directed acyclic graph (DAG), provide a powerful analytical framework to describe the interaction mechanisms in large-scale complex systems. However, when the system exhibits extreme events, the governing mechanisms can change dramatically, and SCMs with a focus on rare events are needed. We propose a new class of SCMs, called XSCMs, which leverage transformed-linear algebra to model causal relationships among extreme values. Similar to traditional SCMs, we prove that XSCMs satisfy the causal Markov and causal faithfulness properties with respect to partial tail (un)correlatedness. This enables estimation of the underlying DAG for extremes using separation-based tests, and makes many state-of-the-art constraint-based causal discovery algorithms directly applicable. We further consider the problem of undirected graph estimation for relationships among tail-dependent (and potentially heavy-tailed) data. The effectiveness of our method, compared to alternative approaches, is validated through simulation studies on large-scale systems with up to 50 variables, and in a well-studied application to river discharge data from the Danube basin. Finally, we apply the framework to investigate complex market-wide relationships in China's derivatives market.

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arXiv2026

Neural Parameter Estimation with Incomplete Data

Advances in artificial intelligence (AI) and deep learning have led to neural networks being used to generate lightning-speed answers to complex science questions, paintings in the style of Monet, or stories like those of Twain. Leveraging their computational speed and flexibility, neural networks are also being used to facilitate fast, likelihood-free statistical inference. However, it is not straightforward to use neural networks with data that for various reasons are incomplete, which precludes their use in many applications. A recently proposed approach to remedy this issue uses an appropriately padded data vector and a vector that encodes the missingness pattern as input to a neural network. While computationally efficient, this "masking" approach is not robust to the missingness mechanism and can result in statistically inefficient inferences. Here, we propose an alternative approach that is based on the Monte Carlo expectation-maximization (EM) algorithm. Our EM approach is likelihood-free, substantially faster than the conventional EM algorithm as it does not require numerical optimization at each iteration, and more statistically efficient than the masking approach. This research addresses a prototypical problem that asks how improvements could be made in AI by introducing Bayesian statistical thinking. We compare the two approaches to missingness using simulated incomplete data from a variety of spatial models. The utility of the methodology is shown on Arctic sea-ice data, analyzed using a novel hidden Potts model with an intractable likelihood.

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arXiv2025

Forecasting the Term Structure of Interest Rates with SPDE-Based Models

The Dynamic Nelson--Siegel (DNS) model is a widely used framework for term structure forecasting. We propose a novel extension that models DNS residuals as a Gaussian random field, capturing dependence across both time and maturity. The residual field is represented via a stochastic partial differential equation (SPDE), enabling flexible covariance structures and scalable Bayesian inference through sparse precision matrices. We consider a range of SPDE specifications, including stationary, non-stationary, anisotropic, and nonseparable models. The SPDE--DNS model is estimated in a Bayesian framework using the integrated nested Laplace approximation (INLA), jointly inferring latent DNS factors and the residual field. Empirical results show that the SPDE-based extensions improve both point and probabilistic forecasts relative to standard benchmarks. When applied in a mean--variance bond portfolio framework, the forecasts generate economically meaningful utility gains, measured as performance fees relative to a Bayesian DNS benchmark under monthly rebalancing. Importantly, incorporating the structured SPDE residual substantially reduces cross-maturity and intertemporal dependence in the remaining measurement error, bringing it closer to white noise. These findings highlight the advantages of combining DNS with SPDE-driven residual modeling for flexible, interpretable, and computationally efficient yield curve forecasting.

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arXiv2025

Intrinsic Whittle--Matérn fields and sparse spatial extremes

Intrinsic Gaussian fields are used in many areas of statistics as models for spatial or spatio-temporal dependence, or as priors for latent variables. However, there are two major gaps in the literature: first, the number and flexibility of existing intrinsic models are very limited; second, theory, fast inference, and software are currently underdeveloped for intrinsic fields. We tackle these challenges by introducing the new flexible class of intrinsic Whittle--Matérn Gaussian random fields obtained as the solution to a stochastic partial differential equation (SPDE). Exploiting sparsity resulting from finite-element approximations, we develop fast estimation and simulation methods for these models. We demonstrate the benefits of this intrinsic SPDE approach for the important task of kriging under extrapolation settings. Leveraging the connection of intrinsic fields to spatial extreme value processes, we translate our theory to an SPDE approach for Brown--Resnick processes for sparse modeling of spatial extreme events. This new paradigm paves the way for efficient inference in unprecedented dimensions. To demonstrate the wide applicability of our new methodology, we apply it in two very different areas: a longitudinal study of renal function data, and the modeling of marine heat waves using high-resolution sea surface temperature data.

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arXiv2025

deepspat: An R package for modeling nonstationary spatial and spatio-temporal Gaussian and extremes data through deep deformations

Nonstationarity in spatial and spatio-temporal processes is ubiquitous in environmental datasets, but is not often addressed in practice, due to a scarcity of statistical software packages that implement nonstationary models. In this article, we introduce the R software package deepspat, which allows for modeling, fitting and prediction with nonstationary spatial and spatio-temporal models applied to Gaussian and extremes data. The nonstationary models in our package are constructed using a deep multi-layered deformation of the original spatial or spatio-temporal domain, and are straightforward to implement. Model parameters are estimated using gradient-based optimization of customized loss functions with tensorflow, which implements automatic differentiation. The functionalities of the package are illustrated through simulation studies and an application to Nepal temperature data.

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arXiv2025

Nonlinear Coherence for Vector Time Series: Defining Region-to-Region Functional Brain Connectivity

Alterations in functional brain connectivity characterize neurodegenerative disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD). As a non-invasive and cost-effective technique, electroencephalography (EEG) is gaining increasing attention for its potential to identify reliable biomarkers for early detection and differential diagnosis of AD and FTD. Considering the behavioral similarities of signals from adjacent EEG channels, we propose a new spectral dependence measure, the nonlinear vector coherence (NVC), to capture beyond-linear interactions between oscillations of two multivariate time series observed from distinct brain regions. This addresses the limitations of conventional channel-to-channel approaches and defines a more natural region-to-region connectivity framework in the frequency domain. As a result, the NVC measure offers a new approach to investigate dependence between brain regions, which then enables to identify altered functional connectivity dynamics associated with AD and FTD. We further introduce a rank-based inference procedure that enables fast and distribution-free estimation of the proposed measure, as well as a fully nonparametric test for spectral independence. The empirical performance of our proposed inference methodology is demonstrated through extensive numerical experiments. An application to resting-state EEG data reveals that our novel NVC measure uncovers distinct and diagnostically meaningful connectivity patterns which effectively discriminate healthy individuals from those with AD and FTD.

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arXiv2025

Neural Bayes estimation and selection for complex bivariate extremal dependence models

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for several models available in the multivariate extremes literature, particularly for the most flexible tail models, including those that interpolate between the two key dependence classes of `asymptotic dependence' and `asymptotic independence'. We focus on approaches that leverage neural networks to approximate Bayes estimators. In particular, we explore the properties of neural Bayes estimators for parameter inference for several flexible but computationally expensive models to fit, with a view to aiding their routine implementation. Owing to the absence of likelihood evaluation in the inference procedure, classical information criteria such as the Bayesian information criterion cannot be used to select the most appropriate model. Instead, we propose using neural networks as neural Bayes classifiers for model selection. Our goal is to provide a toolbox for simple, fast fitting and comparison of complex extreme-value dependence models, where the best model is selected for a given data set and its parameters subsequently estimated using neural Bayes estimation. We apply our classifiers and estimators to analyse the pairwise extremal behaviour of changes in horizontal geomagnetic field fluctuations at three different locations.

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arXiv2025

Simulation-based inference via telescoping ratio estimation for trawl processes

The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics. While such models are often easy to simulate from, parameter estimation remains challenging. Simulation-based inference (SBI) offers a promising way forward, but existing methods typically require large training datasets or complex architectures and frequently yield confidence (credible) regions that fail to attain their nominal values, raising doubts on the reliability of estimates for the very features that motivate the use of these models. To address these challenges, we propose a fast and accurate, sample-efficient SBI framework for amortized posterior inference applicable to intractable stochastic processes. The proposed approach relies on two main steps: first, we learn the posterior density by decomposing it sequentially across parameter dimensions. Then, we use Chebyshev polynomial approximations to efficiently generate independent posterior samples, enabling accurate inference even when Markov chain Monte Carlo methods mix poorly. We further develop novel diagnostic tools for SBI in this context, as well as post-hoc calibration techniques; the latter not only lead to performance improvements of the learned inferential tool, but also to the ability to reuse it directly with new time series of varying lengths, thus amortizing the training cost. We demonstrate the method's effectiveness on trawl processes, a class of flexible infinitely divisible models that generalize univariate Gaussian processes, applied to energy demand data.

stat.ML↗

arXiv2025

Joint modeling of low and high extremes using a multivariate extended generalized Pareto distribution

In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to droughts, while heavy rainfall may generate large floods, and both of these extreme scenarios can have major impacts on the safety of people and infrastructure, as well as agricultural or other economic sectors. In the univariate case, the extended generalized Pareto distribution (eGPD) was specifically developed to accurately model low, moderate, and high precipitation intensities, while bypassing the threshold selection procedure usually conducted in extreme-value analyses. In this work, we extend this approach to the multivariate case. The proposed multivariate eGPD has the following appealing properties: (1) its marginal distributions behave like univariate eGPDs; (2) its lower and upper joint tails comply with multivariate extreme-value theory, with key parameters separately controlling dependence in each joint tail; and (3) the model allows for fast simulation and is thus amenable to simulation-based inference. We propose estimating model parameters by leveraging modern neural approaches, where a neural network, once trained, can provide point estimates, credible intervals, or full posterior approximations in a fraction of a second. Our new methodology is illustrated by application to daily rainfall times series data from the Netherlands. The proposed model is shown to provide satisfactory marginal and dependence fits from low to high quantiles.

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arXiv2025

Causal Spatial Quantile Regression

Treatment effects in a wide range of economic, environmental, and epidemiological applications often vary across space, and understanding the heterogeneity of causal effects across space and outcome quantiles is a critical challenge in spatial causal inference. To effectively capture spatial heterogeneity in distributional treatment effects, we propose a novel semiparametric neural network-based causal framework leveraging deep spatial quantile regression and then construct a plug-in estimator for spatial quantile treatment effects (SQTE). This framework incorporates an efficient adjustment procedure to mitigate the impact of spatial hidden confounders. Extensive simulations across various scenarios demonstrate that our methodology can accurately estimate SQTE, even with the presence of spatial hidden confounders. Additionally, the spatial confounding adjustment procedure effectively reduces neighborhood spatial patterns in the residuals. We apply this method to assess the spatially varying quantile treatment effects of maternal smoking on newborn birth weight in North Carolina, United States. Our findings consistently show negative effects across all birth weight quantiles, with particularly severe impacts observed in the lower quantile regions.

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arXiv2025

The Efficient Tail Hypothesis: An Extreme Value Perspective on Market Efficiency

In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in financial markets where data often exhibit both positive and negative extremal dependence. To this end, we construct regular variation models on the entirety of $\mathbb{R}^d$ and develop a bivariate measure for asymmetry in the strength of extremal dependence between adjacent orthants. Our directional tail dependence (DTD) measure allows us to define the Efficient Tail Hypothesis (ETH) -- an analogue of the Efficient Market Hypothesis -- for the extremal behaviour of the market. Asymptotic results for estimators of DTD are described, and we discuss testing of the ETH via permutation-based methods and present novel tools for visualization. Empirical study of China's futures market leads to a rejection of the ETH and we identify potential profitable investment opportunities. To promote the research of microstructure in China's derivatives market, we open-source our high-frequency data, which are being collected continuously from multiple derivative exchanges.

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arXiv2025

Club Exco: clustering brain extreme communities from multi-channel EEG data

Current methods for clustering brain networks over time often rely on cross-dependence measures computed from the entire range of EEG signals, which can obscure information specific to extreme neural activity. To overcome this, we introduce Club Exco, a novel clustering method grounded in extreme value theory, designed to detect brain communities with co-occurring high-amplitude EEG events. By focusing on tail behavior, Club Exco isolates extreme-value synchrony across channels, offering new insights into seizure dynamics. We apply Club Exco to neonatal EEG recordings from 30 patients (13 seizure-free and 17 with clinically confirmed seizures). Our method identifies robust ``brain extreme communities'' and constructs Extreme Connectivity Persistence matrices that summarize how often channels exhibit synchronous extremes across time. Seizure patients exhibit more persistent and variable clustering among non-adjacent regions, suggesting seizure propagation, while non-seizure patients show more consistent clustering in anatomically adjacent regions. Compared to coherence-based methods (e.g., Hierarchical Cluster Coherence procedure), Club Exco captures distinct, seizure-associated connectivity patterns, especially in high-amplitude segments. These results highlight Club Exco's potential to characterize extreme neural events and inform clinical understanding of seizure localization and spread.

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arXiv2025

Generative modelling of multivariate geometric extremes using normalising flows

Leveraging the recently emerging geometric approach to multivariate extremes and the flexibility of normalising flows on the hypersphere, we propose a principled deep-learning-based methodology that enables accurate joint tail extrapolation in all directions. We exploit theoretical links between intrinsic model parameters defined as functions on hyperspheres to construct models ranging from high flexibility to parsimony, thereby enabling the efficient modelling of multivariate extremes displaying complex dependence structures in higher dimensions with reasonable sample sizes. We use the generative feature of normalising flows to perform fast probability estimation for arbitrary Borel risk regions via an efficient Monte Carlo integration scheme. The good properties of our estimators are demonstrated via a simulation study in up to ten dimensions. We apply our methodology to the analysis of low and high extremes of wind speeds. In particular, we find that our methodology enables probability estimation for non-trivial extreme events in relation to electricity production via wind turbines and reveals interesting structure in the underlying data.

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arXiv2025

Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks

Neural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Although they are appealing to use with spatial models, where estimation is often a computational bottleneck, neural Bayes estimators in spatial applications have, to date, been restricted to data collected over a regular grid. These estimators are also currently dependent on a prescribed set of spatial locations, which means that the neural network needs to be re-trained for new data sets; this renders them impractical in many applications and impedes their widespread adoption. In this work, we employ graph neural networks to tackle the important problem of parameter point estimation from data collected over arbitrary spatial locations. In addition to extending neural Bayes estimation to irregular spatial data, our architecture leads to substantial computational benefits, since the estimator can be used with any configuration or number of locations and independent replicates, thus amortising the cost of training for a given spatial model. We also facilitate fast uncertainty quantification by training an accompanying neural Bayes estimator that approximates a set of marginal posterior quantiles. We illustrate our methodology on Gaussian and max-stable processes. Finally, we showcase our methodology on a data set of global sea-surface temperature, where we estimate the parameters of a Gaussian process model in 2161 spatial regions, each containing thousands of irregularly-spaced data points, in just a few minutes with a single graphics processing unit.

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arXiv2024

Flexible and efficient emulation of spatial extremes processes via variational autoencoders

Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. In this paper, we aim to push the boundaries on computation and modeling of high-dimensional spatial extremes via integrating a new spatial extremes model that has flexible and non-stationary dependence properties in the encoding-decoding structure of a variational autoencoder called the XVAE. The XVAE can emulate spatial observations and produce outputs that have the same statistical properties as the inputs, especially in the tail. Our approach also provides a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while outperforming many spatial extremes models with a stationary dependence structure. Lastly, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16703 grid cells. We demonstrate how to use XVAE to identify regions susceptible to marine heatwaves under climate change and examine the spatial and temporal variability of the extremal dependence structure.

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arXiv2024

Neural Methods for Amortized Inference

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimization libraries and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software, and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

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