FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used frameworks such as Plug-and-Play (PnP) algorithms. In this work, we introduce Fixed-points of Restoration (FiRe) priors as a new framework for expanding the notion of priors in PnP to general restoration models beyond traditional denoising models. The key insight behind FiRe is that natural images emerge as fixed points of the composition of a degradation operator with the corresponding restoration model. This enables us to derive an explicit formula for our implicit prior by quantifying invariance of images under this composite operation. Adopting this fixed-point perspective, we show how various restoration networks can effectively serve as priors for solving inverse problems. The FiRe framework further enables ensemble-like combinations of multiple restoration models as well as acquisition-informed restoration networks, all within a unified optimization approach. Experimental results validate the effectiveness of FiRe across various inverse problems, establishing a new paradigm for incorporating pretrained restoration models into PnP-like algorithms.

sbi reloaded: a toolkit for simulation-based inference workflows

Scientists and engineers use simulators to model empirically observed phenomena. However, tuning the parameters of a simulator to ensure its outputs match observed data presents a significant challenge. Simulation-based inference (SBI) addresses this by enabling Bayesian inference for simulators, identifying parameters that match observed data and align with prior knowledge. Unlike traditional Bayesian inference, SBI only needs access to simulations from the model and does not require evaluations of the likelihood-function. In addition, SBI algorithms do not require gradients through the simulator, allow for massive parallelization of simulations, and can perform inference for different observations without further simulations or training, thereby amortizing inference. Over the past years, we have developed, maintained, and extended $\texttt{sbi}$, a PyTorch-based package that implements Bayesian SBI algorithms based on neural networks. The $\texttt{sbi}$ toolkit implements a wide range of inference methods, neural network architectures, sampling methods, and diagnostic tools. In addition, it provides well-tested default settings but also offers flexibility to fully customize every step of the simulation-based inference workflow. Taken together, the $\texttt{sbi}$ toolkit enables scientists and engineers to apply state-of-the-art SBI methods to black-box simulators, opening up new possibilities for aligning simulations with empirically observed data.

Analysis and Synthesis Denoisers for Forward-Backward Plug-and-Play Algorithms

In this work we study the behavior of the forward-backward (FB) algorithm when the proximity operator is replaced by a sub-iterative procedure to approximate a Gaussian denoiser, in a Plug-and-Play (PnP) fashion. In particular, we consider both analysis and synthesis Gaussian denoisers within a dictionary framework, obtained by unrolling dual-FB iterations or FB iterations, respectively. We analyze the associated minimization problems as well as the asymptotic behavior of the resulting FB-PnP iterations. In particular, we show that the synthesis Gaussian denoising problem can be viewed as a proximity operator. For each case, analysis and synthesis, we show that the FB-PnP algorithms solve the same problem whether we use only one or an infinite number of sub-iteration to solve the denoising problem at each iteration. To this aim, we show that each "one sub-iteration" strategy within the FB-PnP can be interpreted as a primal-dual algorithm when a warm-restart strategy is used. We further present similar results when using a Moreau-Yosida smoothing of the global problem, for an arbitrary number of sub-iterations. Finally, we provide numerical simulations to illustrate our theoretical results. In particular we first consider a toy compressive sensing example, as well as an image restoration problem in a deep dictionary framework.

SKADA-Bench: Benchmarking Unsupervised Domain Adaptation Methods with Realistic Validation

Unsupervised Domain Adaptation (DA) consists of adapting a model trained on a labeled source domain to perform well on an unlabeled target domain with some data distribution shift. While many methods have been proposed in the literature, fair and realistic evaluation remains an open question, particularly due to methodological difficulties in selecting hyperparameters in the unsupervised setting. With SKADA-Bench, we propose a framework to evaluate DA methods and present a fair evaluation of existing shallow algorithms, including reweighting, mapping, and subspace alignment. Realistic hyperparameter selection is performed with nested cross-validation and various unsupervised model selection scores, on both simulated datasets with controlled shifts and real-world datasets across diverse modalities, such as images, text, biomedical, and tabular data with specific feature extraction. Our benchmark highlights the importance of realistic validation and provides practical guidance for real-life applications, with key insights into the choice and impact of model selection approaches. SKADA-Bench is open-source, reproducible, and can be easily extended with novel DA methods, datasets, and model selection criteria without requiring re-evaluating competitors. SKADA-Bench is available on GitHub at https://github.com/scikit-adaptation/skada-bench.

Unmixing Noise from Hawkes Process to Model Learned Physiological Events

Physiological signal analysis often involves identifying events crucial to understanding biological dynamics. Traditional methods rely on handcrafted procedures or supervised learning, presenting challenges such as expert dependence, lack of robustness, and the need for extensive labeled data. Data-driven methods like Convolutional Dictionary Learning (CDL) offer an alternative but tend to produce spurious detections. This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections. Leveraging marked Hawkes processes, UNHaP distinguishes between events of interest and spurious ones. By treating the event detection output as a mixture of structured and unstructured events, UNHaP efficiently unmixes these processes and estimates their parameters. This approach significantly enhances the understanding of event distributions while minimizing false detection rates.

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.

S-JEPA: towards seamless cross-dataset transfer through dynamic spatial attention

Motivated by the challenge of seamless cross-dataset transfer in EEG signal processing, this article presents an exploratory study on the use of Joint Embedding Predictive Architectures (JEPAs). In recent years, self-supervised learning has emerged as a promising approach for transfer learning in various domains. However, its application to EEG signals remains largely unexplored. In this article, we introduce Signal-JEPA for representing EEG recordings which includes a novel domain-specific spatial block masking strategy and three novel architectures for downstream classification. The study is conducted on a 54~subjects dataset and the downstream performance of the models is evaluated on three different BCI paradigms: motor imagery, ERP and SSVEP. Our study provides preliminary evidence for the potential of JEPAs in EEG signal encoding. Notably, our results highlight the importance of spatial filtering for accurate downstream classification and reveal an influence of the length of the pre-training examples but not of the mask size on the downstream performance.

Equivariant plug-and-play image reconstruction

Plug-and-play algorithms constitute a popular framework for solving inverse imaging problems that rely on the implicit definition of an image prior via a denoiser. These algorithms can leverage powerful pre-trained denoisers to solve a wide range of imaging tasks, circumventing the necessity to train models on a per-task basis. Unfortunately, plug-and-play methods often show unstable behaviors, hampering their promise of versatility and leading to suboptimal quality of reconstructed images. In this work, we show that enforcing equivariance to certain groups of transformations (rotations, reflections, and/or translations) on the denoiser strongly improves the stability of the algorithm as well as its reconstruction quality. We provide a theoretical analysis that illustrates the role of equivariance on better performance and stability. We present a simple algorithm that enforces equivariance on any existing denoiser by simply applying a random transformation to the input of the denoiser and the inverse transformation to the output at each iteration of the algorithm. Experiments on multiple imaging modalities and denoising networks show that the equivariant plug-and-play algorithm improves both the reconstruction performance and the stability compared to their non-equivariant counterparts.

Meta-Prior: Meta learning for Adaptive Inverse Problem Solvers

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However, real-world imaging challenges often lack ground truth data, rendering traditional supervised approaches ineffective. Moreover, for each new imaging task, a new model needs to be trained from scratch, wasting time and resources. To overcome these limitations, we introduce a novel approach based on meta-learning. Our method trains a meta-model on a diverse set of imaging tasks that allows the model to be efficiently fine-tuned for specific tasks with few fine-tuning steps. We show that the proposed method extends to the unsupervised setting, where no ground truth data is available. In its bilevel formulation, the outer level uses a supervised loss, that evaluates how well the fine-tuned model performs, while the inner loss can be either supervised or unsupervised, relying only on the measurement operator. This allows the meta-model to leverage a few ground truth samples for each task while being able to generalize to new imaging tasks. We show that in simple settings, this approach recovers the Bayes optimal estimator, illustrating the soundness of our approach. We also demonstrate our method's effectiveness on various tasks, including image processing and magnetic resonance imaging.

PAVI: Plate-Amortized Variational Inference

Given observed data and a probabilistic generative model, Bayesian inference searches for the distribution of the model's parameters that could have yielded the data. Inference is challenging for large population studies where millions of measurements are performed over a cohort of hundreds of subjects, resulting in a massive parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that efficiently tackle large population studies. Our main idea is to share the parameterization and learning across the different i.i.d. variables in a generative model, symbolized by the model's \textit{plates}. We name this concept \textit{plate amortization}. Contrary to off-the-shelf stochastic VI, which slows down inference, plate amortization results in orders of magnitude faster to train variational distributions. Applied to large-scale hierarchical problems, PAVI yields expressive, parsimoniously parameterized VI with an affordable training time. This faster convergence effectively unlocks inference in those large regimes. We illustrate the practical utility of PAVI through a challenging Neuroimaging example featuring 400 million latent parameters, demonstrating a significant step towards scalable and expressive Variational Inference.