Publications
Publications in reversed chronological order. Generated by jekyll-scholar.
2025
- Journal articleDistribution-Free Uncertainty Quantification for Inverse Problems: Application to Weak Lensing Mass MappingLeterme, Hubert, Fadili, Jalal, and Starck, Jean-LucAstronomy & Astrophysics (in press) Jan 2025
In inverse problems, distribution-free uncertainty quantification (UQ) aims to obtain error bars with coverage guarantees that are independent of any prior assumptions about the data distribution. In the context of mass mapping, uncertainties could lead to errors that affects our understanding of the underlying mass distribution, or could propagate to cosmological parameter estimation, thereby impacting the precision and reliability of cosmological models. Current surveys, such as Euclid or Rubin, will provide new weak lensing datasets of very high quality. Accurately quantifying uncertainties in mass maps is therefore critical to perform reliable cosmological parameter inference. In this paper, we extend the conformalized quantile regression (CQR) algorithm, initially proposed for scalar regression, to inverse problems. We compare our approach with another distribution-free approach based on risk-controlling prediction sets (RCPS). Both methods are based on a calibration dataset, and offer finite-sample coverage guarantees that are independent of the data distribution. Furthermore, they are applicable to any mass mapping method, including blackbox predictors. In our experiments, we apply UQ on three mass-mapping method: the Kaiser-Squires inversion, iterative Wiener filtering, and the MCALens algorithm. Our experiments reveal that RCPS tends to produce overconservative confidence bounds with small calibration sets, whereas CQR is designed to avoid this issue. Although the expected miscoverage rate is guaranteed to stay below a user-prescribed threshold regardless of the mass mapping method, selecting an appropriate reconstruction algorithm remains crucial for obtaining accurate estimates, especially around peak-like structures, which are particularly important for inferring cosmological parameters. Additionally, the choice of mass mapping method influences the size of the error bars.
2024
- PreprintGalaxy-Point Spread Function Correlations as a Probe of Weak-Lensing Systematics with UNIONS DataGuerrini, Sacha, Kilbinger, Martin, Leterme, Hubert, Guinot, Axel and 5 more authorsSubmitted to Astronomy & Astrophysics (arXiv:2412.14666) Dec 2024
Weak gravitational lensing requires precise measurements of galaxy shapes and therefore an accurate knowledge of the PSF model. The latter can be a source of systematics that affect the shear two-point correlation function. A key stake of weak lensing analysis is to forecast the systematics due to the PSF. Correlation functions of galaxies and the PSF, the so-called {}rho\- and {}tau\-statistics, are used to evaluate the level of systematics coming from the PSF model and PSF corrections, and contributing to the two-point correlation function used to perform cosmological inference. Our goal is to introduce a fast and simple method to estimate this level of systematics and assess its agreement with state-of-the-art approaches. We introduce a new way to estimate the covariance matrix of the {}tau\-statistics using analytical expressions. The covariance allows us to estimate parameters directly related to the level of systematics associated with the PSF and provides us with a tool to validate the PSF model used in a weak-lensing analysis. We apply those methods to data from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). We show that the semi-analytical covariance yields comparable results than using covariances obtained from simulations or jackknife resampling. It requires less computation time and is therefore well suited for rapid comparison of the systematic level obtained from different catalogs. We also show how one can break degeneracies between parameters with a redefinition of the {}tau\-statistics. The methods developed in this work will be useful tools in the analysis of current weak-lensing data but also of Stage IV surveys such as Euclid, LSST or Roman. They provide fast and accurate diagnostics on PSF systematics that are crucial to understand in the context of cosmic shear studies.
- Conference paperFrom CNNs to Shift-Invariant Twin Models Based on Complex WaveletsIn 2024 32nd European Signal Processing Conference (EUSIPCO) Aug 2024
We propose a novel antialiasing method to increase shift invariance in convolutional neural networks (CNNs). More precisely, we replace the conventional combination "real-valued convolutions + max pooling" ({}mathbb R\Max) by "complex-valued convolutions + modulus" ({}mathbb C\Mod), which produce stable feature representations for band-pass filters with well-defined orientations. In a recent work, we proved that, for such filters, the two operators yield similar outputs. Therefore, {}mathbb C\Mod can be viewed as a stable alternative to {}mathbb R\Max. To separate band-pass filters from other freely-trained kernels, in this paper, we designed a "twin" architecture based on the dual-tree complex wavelet packet transform, which generates similar outputs as standard CNNs with fewer trainable parameters. In addition to improving stability to small shifts, our experiments on AlexNet and ResNet showed increased prediction accuracy on natural image datasets such as ImageNet and CIFAR10. Furthermore, our approach outperformed recent antialiasing methods based on low-pass filtering by preserving high-frequency information, while reducing memory usage.
2023
- Doctoral ThesisA Complex Wavelet Approach for Shift-Invariant Convolutional Neural NetworksLeterme, HubertJun 2023
Despite significant advancements in computer vision over the past decade, convolutional neural networks (CNNs) still suffer from a lack of mathematical understanding. In particular, stability properties with respect to small transformations such as translations, rotations, scaling or deformations are only partially understood. While there is a broad literature on this topic, some gaps remain, specifically with regard to the combined effect of convolution and max pooling layers in producing near shift-invariant feature representations. This property is of utmost importance for classification, since two shifted versions of a single input image are expected to receive the same label. It is well-known that subsampled convolutions with band-pass filters are prone to producing unstable image representations when inputs are shifted by a few pixels. The first contribution of this thesis consists in proving that a nonlinear max pooling operator can partially restore shift invariance. By applying results from the wavelet theory, and adopting a probabilistic point of view, we reveal a similarity between the max pooling of real-valued convolutions, as implemented in conventional architectures, and the modulus of complex-valued convolutions, for which a measure of shift invariance is established. However, for specific filter frequencies, this similarity is lost, and CNNs become unstable to translations. This phenomenon, known as aliasing, can be avoided by employing additional low-pass filters in strategic locations of the network architecture, as several authors have done in recent years. While their methods effectively increase both shift invariance and prediction accuracy, they come at the cost of significant loss of high-frequency information. As a second contribution, we present a novel antialiasing method which, unlike previous methods, preserves this information. Relying on our theoretical study, the key idea is to exploit the properties of complex convolutions to guarantee near-shift invariance for any filter frequency. By adding an imaginary part to high-frequency kernels and replacing the max pooling layer with a simple modulus operator, we empirically evidence an increase in the network’s stability and a lower error rate compared to previous approaches based on low-pass filtering. In conclusion, the aim of this thesis is twofold: improving the mathematical understanding of CNNs from the perspective of shift invariance, and improving the tradeoff between stability and information preserving, based on our theoretical contribution which is grounded in wavelet theory. Our findings thus have the potential to positively impact various applications of computer vision, especially in fields that require theoretical guarantees.
2022
- PreprintOn the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural NetworksarXiv:2209.11740 Sep 2022
In this paper, we aim to improve the mathematical interpretability of convolutional neural networks for image classification. When trained on natural image datasets, such networks tend to learn parameters in the first layer that closely resemble oriented Gabor filters. By leveraging the properties of discrete Gabor-like convolutions, we prove that, under specific conditions, feature maps computed by the subsequent max pooling operator tend to approximate the modulus of complex Gabor-like coefficients, and as such, are stable with respect to certain input shifts. We then compute a probabilistic measure of shift invariance for these layers. More precisely, we show that some filters, depending on their frequency and orientation, are more likely than others to produce stable image representations. We experimentally validate our theory by considering a deterministic feature extractor based on the dual-tree wavelet packet transform, a particular case of discrete Gabor-like decomposition. We demonstrate a strong correlation between shift invariance on the one hand and similarity with complex modulus on the other hand.
2021
- Workshop paperModélisation Parcimonieuse de CNNs Avec Des Paquets d’Ondelettes Dual-TreeIn ORASIS, Sep 2021
We propose to improve the mathematical interpretability of convolutional neural networks (CNNs) for image classification. In this purpose, we replace the first layers of existing models such as AlexNet or ResNet by an operator containing the dual-tree wavelet packet transform, i.e., a redundant decomposition using complex and oriented waveforms. Our experiments show that these modified networks behave very similarly to the original models once trained. The goal is then to study this operator from a theoretical point of view and to identify potential optimizations. We want to analyze its main properties such as directional selectivity, stability with respect to small shifts and rotations, thus retaining discriminant information while decreasing intra-class variability. This work is a step toward a more complete description of CNNs using well-defined mathematical operators, characterized by a small number of arbitrary parameters, making them easier to interpret.