arXiv subjects

Eugénie Terreaux

Publications and source records attributed to Eugénie Terreaux.

7 recordsLinked to original sources

arXiv2026

A Robust Framework for Model Order Selection in Correlated Large-Dimensional CES Noise

This paper addresses model order selection under large-dimensional, correlated, non-Gaussian noise. Sources are assumed to be embedded in additive Complex Elliptically Symmetric (CES) noise with an unknown Toeplitz-structured scatter matrix. We propose a two-stage robust framework: (i) a noise-whitening step based on a Toeplitz-rectified $M$-estimator of the scatter matrix, and (ii) signal subspace rank inference via large-dimensional Random Matrix Theory (RMT). Almost sure consistency of the proposed estimators is established, together with explicit RMT eigenvalue upper bounds separating signal from noise components, in the regime where the observation dimension $m$ and the sample size $N$ grow proportionally. Three estimation branches are derived, based respectively on the sample covariance matrix (SCM), Maronna's $M$-estimator, and the distribution-free Tyler $M$-estimator for whitening. The methodology is validated on synthetic data, real hyperspectral images, EEG recordings, and financial data, with significant gains over AIC and unwhitened methods.

stat.ME↗

arXiv2026

Backbone-Equated Diffusion OOD via Sparse Internal Snapshots

Fair comparison between diffusion-based OOD detectors is challenging, as conclusions can vary with backbone choice, corruption parameterization, and test-time budget. We address this issue through a Mutualized Backbone-Equated (MBE) protocol that aligns canonical corruption levels and logical test-time cost across diffusion backbones. Within this setting, we introduce Canonical Feature Snapshots (CFS), a family of detectors that probes a frozen diffusion backbone using only a tiny number of native internal activations at canonical low-noise levels. On a controlled CIFAR-scale benchmark, the strongest one-forward CFS variant is CFS(1x2), while an even smaller decoder-only variant remains highly competitive. This shows that much of the relative-OOD signal exposed by frozen diffusion backbones is concentrated in a small number of sparse internal states, rather than requiring full denoising trajectories or high-capacity downstream heads. We further provide a local diagnostic theory explaining these observations through conditional encoder-decoder complementarity, diagonal-score separation, and low-noise corruption stability. The official implementation is available at https://github.com/RouzAY/cfs-diffusion-ood/.

cs.LG↗

arXiv2026

GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models

Diffusion models learn a time-indexed score field $\mathbf{s}_θ(\mathbf{x}_t,t)$ that often inherits approximate equivariances (flips, rotations, circular shifts) from in-distribution (ID) data and convolutional backbones. Most diffusion-based out-of-distribution (OOD) detectors exploit score magnitude or local geometry (energies, curvature, covariance spectra) and largely ignore equivariances. We introduce Group-Equivariant Posterior Consistency (GEPC), a training-free probe that measures how consistently the learned score transforms under a finite group $\mathcal{G}$, detecting equivariance breaking even when score magnitude remains unchanged. At the population level, we propose the ideal GEPC residual, which averages an equivariance-residual functional over $\mathcal{G}$, and we derive ID upper bounds and OOD lower bounds under mild assumptions. GEPC requires only score evaluations and produces interpretable equivariance-breaking maps. On OOD image benchmark datasets, we show that GEPC achieves competitive or improved AUROC compared to recent diffusion-based baselines while remaining computationally lightweight. On high-resolution synthetic aperture radar imagery where OOD corresponds to targets or anomalies in clutter, GEPC yields strong target-background separation and visually interpretable equivariance-breaking maps. Code is available at https://github.com/RouzAY/gepc-diffusion/.

cs.LG↗

arXiv2026

DopplerGLRTNet for Radar Off-Grid Detection

Off-grid targets whose Doppler (or angle) does not lie on the discrete processing grid can severely degrade classical normalized matched-filter (NMF) detectors: even at high SNR, the detection probability may saturate at operationally relevant low false-alarm rates. A principled remedy is the continuous-parameter GLRT, which maximizes a normalized correlation over the parameter domain; however, dense scanning increases test-time cost and remains sensitive to covariance mismatch through whitening. We propose DopplerGLRTNet, an amortized off-grid GLRT: a lightweight regressor predicts the continuous Doppler within a resolution cell from the whitened observation, and the detector outputs a single GLRT/NMF-like score given by the normalized matched-filter energy at the predicted Doppler. Monte Carlo simulations in Gaussian and compound-Gaussian clutter show that DopplerGLRTNet mitigates off-grid saturation, approaches dense-scan performance at a fraction of its cost, and improves robustness to covariance estimation at the same empirically calibrated Pfa.

eess.SP↗

arXiv2026

Out-of-Distribution Radar Detection with Complex VAEs: Theory, Whitening, and ANMF Fusion

We investigate the detection of weak complex-valued signals immersed in non-Gaussian, range-varying interference, with emphasis on maritime radar scenarios. The proposed methodology exploits a Complex-valued Variational AutoEncoder (CVAE) trained exclusively on clutter-plus-noise to perform Out-Of-Distribution detection. By operating directly on in-phase / quadrature samples, the CVAE preserves phase and Doppler structure and is assessed in two configurations: (i) using unprocessed range profiles and (ii) after local whitening, where per-range covariance estimates are obtained from neighboring profiles. Using extensive simulations together with real sea-clutter data from the CSIR maritime dataset, we benchmark performance against classical and adaptive detectors (MF, NMF, AMF-SCM, ANMF-SCM, ANMF-Tyler). In both configurations, the CVAE yields a higher detection probability Pd at matched false-alarm rate Pfa, with the most notable improvements observed under whitening. We further integrate the CVAE with the ANMF through a weighted log-p fusion rule at the decision level, attaining enhanced robustness in strongly non-Gaussian clutter and enabling empirically calibrated Pfa control under H0. Overall, the results demonstrate that statistical normalization combined with complex-valued generative modeling substantively improves detection in realistic sea-clutter conditions, and that the fused CVAE-ANMF scheme constitutes a competitive alternative to established model-based detectors.

stat.ML↗

arXiv2018

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation: Application to the Maximum Variety Portfolio

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but the same improvements apply also in the other optimisation problems such as the Minimum Variance Portfolio. We assume that the most important information (or the latent factors) are embedded in correlated Elliptical Symmetric noise extending classical Gaussian assumptions. We propose here to focus on a recent method of model order selection allowing to efficiently estimate the subspace of main factors describing the market. This non-standard model order selection problem is solved through Random Matrix Theory and robust covariance matrix estimation. The proposed procedure will be explained through synthetic data and be applied and compared with standard techniques on real market data showing promising improvements.

stat.AP↗

arXiv2017

Robust Model Order Selection in Large Dimensional Elliptically Symmetric Noise

This paper deals with model order selection in context of correlated noise. More precisely, one considers sources embedded in an additive Complex Elliptically Symmetric (CES) noise, with unknown parameters. The main difficultly for estimating the model order lies into the noise correlation, namely the scatter matrix of the corresponding CES distribution. In this work, to tackle that problem, one adopts a two-step approach: first, we develop two different methods based on a Toeplitz-structured model for estimating this unknown scatter matrix and for whitening the correlated noise. Then, we apply Maronna's $M$-estimators on the whitened signal to estimate the covariance matrix of the "decorrelated" signal in order to estimate the model order. The proposed methodology is based both on robust estimation theory as well as large Random Matrix Theory, and original results are derived, proving the efficiency of this methodology. Indeed, the main theoretical contribution is to derive consistent robust estimators for the covariance matrix of the signal-plus-correlated noise in a large dimensional regime and to propose efficient methodology to estimate the rank of signal subspace. Finally, as shown in the analysis, these results show a great improvement compared to the state-of-the-art, on both simulated and real hyperspectral images.

stat.ME↗