Classical first-order optimization methods for imaging inverse problems scale poorly with image resolution. Wavelet based multilevel strategies can accelerate convergence under strong blur, but their fixed coarse-to-fine schedules lose effectiveness in moderate-blur or noise-dominated regimes. In this work, we propose an adaptive multiresolution block coordinate Forward-Backward algorithm for image restoration. Multiresolution block selection is driven by the local magnitude of the proximal update via a stochastic non-smooth Gauss-Southwell rule applied to the wavelet decomposition of the image. This adaptive selection strategy dynamically balances updates across scales, emphasizing coarse or fine blocks according to the degradation regime. As a result, the proposed method automatically adapts to varying blur and noise levels without relying on a predefined hierarchical update scheme.

Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the problem. The theoretical and practical performance of BCD relies heavily on the rules defining the choice of the blocks to be updated at each iteration. We propose a new deterministic BCD framework that allows for very flexible updates, while guaranteeing state-of-the-art convergence guarantees on non-smooth nonconvex optimization problems. While encompassing several update rules from the literature, this framework allows for priority on updates of particular blocks and correlations in the block selection between iterations, which is not permitted under the classical convergent stochastic framework. This flexibility is leveraged in the context of multilevel optimization algorithms and, in particular, in multilevel image restoration problems, where the efficiency of the approach is illustrated.

Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spectral clustering requires the computation of the spectral decomposition of the Laplacian matrix, which is not applicable for large graphs with a large number of communities. This work introduces PASCO, an overlay that accelerates clustering algorithms. Our method consists of three steps: (1) We compute several independent small graphs representing the input graph by applying an efficient and structure-preserving coarsening algorithm. (2) A clustering algorithm is run in parallel onto each small graph and provides several partitions of the initial graph. (3) These partitions are aligned and combined with an optimal transport method to output the final partition. The PASCO framework is based on two key contributions: a novel global algorithm structure designed to enable parallelization and a fast, empirically validated graph coarsening algorithm that preserves structural properties. We demonstrate the strong performance of PASCO in terms of computational efficiency, structural preservation, and output partition quality, evaluated on both synthetic and real-world graph datasets.

Pairwise temporal interactions between entities can be represented as temporal networks, which code the propagation of processes such as epidemic spreading or information cascades, evolving on top of them. The largest outcome of these processes is directly linked to the structure of the underlying network. Indeed, a node of a network at a given time cannot affect more nodes in the future than it can reach via time-respecting paths. This set of nodes reachable from a source defines an out-component, which identification is costly. In this paper, we propose an efficient matrix algorithm to tackle this issue and show that it outperforms other state-of-the-art methods. Secondly, we propose a hashing framework to coarsen large temporal networks into smaller proxies on which out-components are more easily estimated, and then recombined to obtain the initial components. Our graph hashing solution has implications in privacy respecting representation of temporal networks.

This paper presents a multilevel algorithm specifically designed for radio-interferometric imaging in astronomy. The proposed algorithm is used to solve the uSARA (unconstrained Sparsity Averaging Reweighting Analysis) formulation of this image restoration problem. Multilevel algorithms rely on a hierarchy of approximations of the objective function to accelerate its optimization. In contrast to the usual multilevel approaches where this hierarchy is derived in the parameter space, here we construct the hierarchy of approximations in the observation space. The proposed approach is compared to a reweighted forward-backward procedure, which is the backbone iteration scheme for solving the uSARA problem.

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$ representative of a Gaussian graphical model that adequately explains the data. However, most maximum likelihood-based estimators usually require storing the $d^{2}$ values of the empirical covariance matrix, which can become prohibitive in a high-dimensional setting. In this work, we adopt a compressive viewpoint and aim to estimate a sparse $\Theta$ from a \emph{sketch} of the data, i.e. a low-dimensional vector of size $m \ll d^{2}$ carefully designed from $X$ using non-linear random features. Under certain assumptions on the spectrum of $\Theta$ (or its condition number), we show that it is possible to estimate it from a sketch of size $m=\Omega\left((d+2k)\log(d)\right)$ where $k$ is the maximal number of edges of the underlying graph. These information-theoretic guarantees are inspired by compressed sensing theory and involve restricted isometry properties and instance optimal decoders. We investigate the possibility of achieving practical recovery with an iterative algorithm based on the graphical lasso, viewed as a specific denoiser. We compare our approach and graphical lasso on synthetic datasets, demonstrating its favorable performance even when the dataset is compressed.

We provide a framework and algorithm for tuning the hyperparameters of the Graphical Lasso via a bilevel optimization problem solved with a first-order method. In particular, we derive the Jacobian of the Graphical Lasso solution with respect to its regularization hyperparameters.

This paper presents a multilevel fast iterative soft thresholding algorithm (FISTA), based on the use of the Moreau envelope to incorporate correction from coarse models, which is easy to compute when the explicit form of the proximal operator for the considered functions is known. This approach is supported by strong theoretical guarantees: we prove both the rate of convergence and the convergence of the iterates to a minimum in the convex case, an important result for ill-posed problems. We evaluate our approach on image restoration problems and we show that it outperforms classical FISTA for large-scale images.

Diffusing a graph signal at multiple scales requires to compute the action of the exponential of as many versions of the Laplacian matrix. Considering the truncated Chebyshev polynomial approximation of the exponential, we derive a tightened bound on the approximation error, allowing thus for a better estimate of the polynomial degree that reaches a prescribed error. We leverage the properties of these approximations to factorize the computation of the action of the diffusion operator over multiple scales, thus drastically reducing its computational cost.

In streaming environments, concept drift is a common problem and identifying whether it is occurring is of utmost importance. Most of the published drift detection methods work based on the results of a base classifier, for example, by using the classification error or the distance between two consecutive errors. But if a change occurs only in the attributes space without changing the boundaries inferred by the learner, drift detection methods may not able to correctly work. This paper proposes VDDM, a drift detection method specially able to identify virtual concept drifts. It works by using a multivariate nonparametric statistical test to identify changes in a window of the most recent instances. Experimental results indicate that the usage of a multivariate nonparametric statistical test presents competitive results specially in the number of detected changes, distances to the drift point, sensitivity and specificity scores, as well as the Matthews Correlation Coefficient and the F1 score.

The use of the heat kernel on graphs has recently given rise to a family of so-called Diffusion-Wasserstein distances which resort to Optimal Transport theory for comparing attributed graphs. In this paper, we address the open problem of optimizing the diffusion time used in these distances. Inspired from the notion of triplet-based constraints, we design a loss function that aims at bringing two graphs closer together while keeping an impostor away. After a thorough analysis of the properties of this function, we show on synthetic data that the resulting Diffusion-Wasserstein distances outperforms the Gromov and Fused-Gromov Wasserstein distances on unsupervised graph domain adaptation tasks.

Optimal Transport (OT) for structured data has received much attention in the machine learning community, especially for addressing graph classification or graph transfer learning tasks. In this paper, we present the Diffusion Wasserstein (\(\mathtt {DW}\)) distance, as a generalization of the standard Wasserstein distance to undirected and connected graphs where nodes are described by feature vectors. \(\mathtt {DW}\) is based on the Laplacian exponential kernel and benefits from the heat diffusion to catch both structural and feature information from the graphs. We further derive lower/upper bounds on \(\mathtt {DW}\) and show that it can be directly plugged into the Fused Gromov Wasserstein (\(\mathtt {FGW}\)) distance that has been recently proposed, leading - for free - to a DifFused Gromov Wasserstein distance (\(\mathtt {DFGW}\)) that allows a significant performance boost when solving graph domain adaptation tasks.

We study the inference of conditional independence graph from the partial Phase Locking Value (PLV) index of multivariate time series. A typical application is the inference of temporal functional connectivity from brain data. We extend the recently proposed time-varying graphical lasso to the measurement of partial locking values, yielding a sparse and temporally coherent dynamical graph that characterizes the evolution of the phase synchrony between each pair of signals. Cast as an optimization problem, we solve it using the alternating direction method of multipliers. The approach is validated on simulated Gaussian multivariate signals and Roessler oscillators. The potential of this regularized partial PLV is then illustrated on actual iEEG data during an epileptic seizure.

Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to study the dynamic behaviour of brain activity. However, these analyses rapidly become complex and time-consuming, since the number of connectivity components to be studied is quadratic with the number of electrodes. In this work, we address the problem of clustering FC into relevant ensembles of simultaneously activated components, yielding a multiplex network that reveals characteristic patterns of the epileptic seizures of a given patient. While $k-$means is certainly the most popular method for data clustering, it is known to perform poorly on large dimensional data sets, and to be highly sensitive to noise. To overcome the so-called curse of dimensionality, we propose a new tensor decomposition to reduce the size of the data set formed by FC time-series recorded for several seizures, prior to apply $k$-means. We propose an adapted procedure to infer a multiplex network from several FC time series, and we emphasise one particular variant that imposes sparsity constraint. Then, we conduct a real case study, applying the proposed sparse tensor decomposition to iEEG data to infer a multiplex network corresponding to the different stages of an epileptic seizure.

Intracranial electroencephalography (EEG) studies using stereotactic EEG (SEEG) have shown that during seizures, epileptic activity spreads across several anatomical regions from the seizure onset zone toward remote brain areas. A full and objective characterization of this patient-specific time-varying network is crucial for optimal surgical treatment. Functional connectivity (FC) analysis of SEEG signals recorded during seizures enables to describe the statistical relations between all pairs of recorded signals. However, extracting meaningful information from those large datasets is time consuming and requires high expertise. In the present study, we first propose a novel method named Brain-wide Time-varying Network Decomposition (BTND) to characterize the dynamic epileptogenic networks activated during seizures in individual patients recorded with SEEG electrodes. The method provides a number of pathological FC subgraphs with their temporal course of activation. The method can be applied to several seizures of the patient to extract reproducible subgraphs. Second, we compare the activated subgraphs obtained by the BTND method with visual interpretation of SEEG signals recorded in 27 seizures from nine different patients. As a whole, we found that activated subgraphs corresponded to brain regions involved during the course of the seizures and their time course was highly consistent with classical visual interpretation. We believe that the proposed method can complement the visual analysis of SEEG signals recorded during seizures by highlighting and characterizing the most significant parts of epileptic networks with their activation dynamics.

Functional connectivity is a graph-like data structure commonly used by neuroscientists to study the dynamic behaviour of brain activity. We address the problem of decomposing multi-trial functional connectivity data, with potential duration heterogeneity, into a set of common patterns contributing to each trial and their associated trial specific temporal activations. We apply our method on iEEG recording from different epileptic seizures of the same patient.

Le Transport Optimal entre donnees structurees pour l'apprentissage a fait l'objet de nombreusesetudes, notamment pour traiter des tâches de classification ou d'apprentissage par transfert entre graphes. Dans cet article, nous introduisons la distance de Wasserstein de diffusion (DW) qui generalise la distance classique de Wasserstein aux graphes attribues non-orientes connexes. DW exploite la diffusion de la chaleur sur le laplacien du graphe pour capturer de l'information non seulement au niveau des attributs des noeuds maisegalement sur la structure du graphe. Nouś etudions le comportement asymptotique de DW et montrons que cette distance peutetre directement exploitee dans la distance Fused Gro-mov Wasserstein, recemment proposee dans la litterature, donnant ainsi naissancea une nouvelle famille de distances entre graphes, appelee DifFused Gromov Wasserstein. Nous montrons que ces dernieres permettent de significativement ameliorer l'etat de l'art sur des tâches d'adaptation de domaine sur graphes par transport optimal.