Material

Abstracts and Presentations

If you would like a copy of any of the technical program presentations, please contact guillaume.ginolhac@univ-smb.fr.

Below are summaries of some of the presentations.

Lectures

## 1

Title: Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning

Speaker: Aapo Hyvärinen, University of Helsinki, Finland

Abstract: A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear representation learning, independent component analysis (ICA) has been successful in many applications areas, and it is  principled, i.e., based on a well-defined probabilistic model. However, extension of ICA to the nonlinear case has been problematic due to the lack of identifiability, i.e., uniqueness of the representation. Recently, nonlinear extensions that utilize temporal structure or some auxiliary information have been proposed. Such models are in fact identifiable, and consequently, an increasing number of algorithms have been developed.  This talk reviews the state-of-the-art of nonlinear ICA theory and algorithms, based on a review paper available at https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fpdf%2F2303.16535&data=05%7C02%7Cesa.ollila%40aalto.fi%7C8c3b019041834f37351108dd8922ae2a%7Cae1a772440414462a6dc538cb199707e%7C1%7C0%7C638817504235641585%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=nUt6tYqjKgMivl%2Fm9Skp9qXpNz%2FnB%2BB3UVEEe1YTBHg%3D&reserved=0 .

## 2

Title: Topological Convolutional Learning

Speaker: Elvin Isufi Delft University of Technology, Netherlands

Abstract: Processing signals on irregular domains, such as graphs, has led to remarkable advances in graph signal processing and graph neural networks by extending the convolutional operation from Euclidean spaces to more complex data structures. However, graphs are a simple example of a topological space, incorporating only pairwise interactions and leading to node-centric solutions. The goal of this talk is to generalize convolutional-based learning to more general topological spaces that incorporate multiway relationships of any order and process signals defined on any tuple. Such a setup is particularly relevant for processing vector fields and network flow signals, among others. I will introduce convolutional filtering on simplicial complexes in a principled manner, build simplicial convolutional neural networks, and use the Hodge theory to investigate these operations in the topological spectral domain. A few applications will be presented to highlight the potential of the proposed methods.

## 3

Title: Robust and Resistant Cross-Validation for Regularized and Penalized M-estimators of Covariance

Speaker: David E. Tyler, Rutgers University, USA

Abstract: Regularized estimates of the covariance matriix has been a topic of interest within multivariate statistics for over 50 years and has gained considerable attention in many areas within the past 20. This can be seen from the popular and well cited Ledoit-Wolf estimator. These regularized estimators are of particular importance in the sparse data setting, i.e. when the sample size n is of the same order as the dimension of the data q or even smaller. Earlier proposals for regularized estimates of the covariance matrix were developed under the multivariate Gaussian model and hence tend not to be robust. Within the past 10-15 years, various robust regularized estimators of covariance have been proposed, mainly regularized M-estimators of covariance. Although these estimators are robust in the sense of good relative efficiency over a range of distributions, there is little understanding of their resistance properties, i.e. their sensitivity to contaminated data. The robustness and resistance of a regularized M-estimator of covariance partially depends on the method used to choose its tuning parameter, with the oracle method being perhaps the most popular approach. In this talk, a cross validation (CV) approach is proposed for choosing the tuning parameter. The standard CV approach helps ensure the resulting estimate of covariance is a good fit to the data but may not give a resistant fit. Consequently, a median based CV criterion for selecting the tuning parameter is proposed which not only helps assure the resulting tuned scatter estimator is a good fit to the data but is also highly resistant to contamination in the data. A motivation for this new median based criterion is that when it is optimized over all possible covariance matrices, it results in a new high breakdown point affine equivariant estimator of the covariance matrix. * This talk is partially based on joint work with Mengxi Yi and Klaus Nordhausen

Short Talks

• Tensorized Neural Networks in Array Signal Processing, Sergiy Vorobyov, Aalto University

Abstract: Neural networks have demonstrated significant potential for array signal processing applications, particularly in challenging electromagnetic environments. However, conventional matrix-based neural network architectures require an excessive number of trainable parameters, leading to substantial computational demands during training. To address this limitation, we have investigated resource-efficient neural network architectures that incorporate algebraic tensor models into their layer formulations. The talk will be based on two tensorized neural network architectures for DOA estimation. First is a tensorized deep neural network (DNN) for 2D DOA estimation with a uniform rectangular array. The architecture formulates feedforward propagation across fully connected (FC) layers as an inverse Tucker decomposition, compressing FC parameters into inverse Tucker factors. Second is a tensorized convolutional neural network (CNN) for DOA estimation with a sparse planar array. In the tensorized CNN, convolutional kernels are decomposed via canonical polyadic (CP) decomposition, reducing kernel parameters into CP factors. Both architectures demonstrate superior resource efficiency while maintaining high accuracy and robustness for DOA estimation.

• DANSE – Data-driven Nonlinear State Estimation for Model-free Process in Unsupervised Learning Setup, Saikat Chatterhee, KTH, Sweden

Abstract: tbc

• On the endmembers detection for hyperspectral imaging in the high-dimensional regime. Hugo Jeannin, IMS, Univ. de Bordeaux

Abstract: This talk addresses the estimation of the number of endmembers in a hyperspectral image composed of $p$ spectral bands. Each pixel is modelled as a Dirichlet linear mixture of $k$ endmembers corrupted by an additive Gaussian noise correlated across the spectral bands and having a Toeplitz covariance matrix. Assuming than $n$ i.i.d. pixels are observed, we leverage on the spiked model techniques in random matrix theory to study the behaviour of the largest eigenvalues of the non-centered sample covariance matrice in the high-dimensional asymptotic regime in which $p,n$ converge to infinity at the same rate while $k$ is kept fixed. The results are further specified in the case where the noise covariance follows a first-order autoregressive model, and an estimate of $k$ is developed. Numerical experiments on real world datasets show promising results compared to alternative approaches of the literature. 

• Riemannian Flow Matching for InSAR phase denoising, Arnaud Breloy, CEDRIC, CNAM, France

Abstract: We will present a brief introduction to diffusion models and conditional flow matching, then an extension of the latter to Riemanian geometries from (Chen & Lipman 2024). Finally, an application to InSAR phase denoising will illustrut the interest of the approach.

• Toeplitz Unlabeled Sensing Manolis C. Taskiris, Chinese Academy of Sciences, Beijing, China

Abstract : tbc

• A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation, Hugo Lebeau, INRIA, ENS Lyon

Abstract : This work presents a comprehensive understanding of the estimation of a planted low-rank signal from a general spiked tensor model near the computational threshold. Relying on standard tools from the theory of large random matrices, we characterize the large-dimensional spectral behavior of the unfoldings of the data tensor and exhibit relevant signal-to-noise ratios governing the detectability of the principal directions of the signal. These results allow to accurately predict the reconstruction performance of truncated multilinear SVD (MLSVD) in the non-trivial regime. This is particularly important since it serves as an initialization of the higher-order orthogonal iteration (HOOI) scheme, whose convergence to the best low-multilinear-rank approximation depends entirely on its initialization. We give a sufficient condition for the convergence of HOOI and show that the number of iterations before convergence tends to 1 in the large-dimensional limit.

• Extending the oracle approximating shrinkage covariance matrix estimation method to complex distributions and robust M-estimators of the scatter matrix, Elias Raninen, Nokia Bell Labs

Abstract : Shrinkage covariance matrix estimation is an effective approach for reducing estimation error in scenarios, where the number of samples is low compared to the dimension of the data. Shrinkage is commonly applied to the sample covariance matrix (SCM) by combining it linearly with a structured target matrix. The goal is then to find an estimator for the optimal (oracle) shrinkage intensity that minimizes the mean squared error (MSE). In this talk, we focus on the popular oracle approximating shrinkage (OAS) estimation method by Chen et al. (IEEE Trans. Signal Process. 2010) and extend it to complex elliptically symmetric distributions (including the complex Gaussian case). We show that the OAS method essentially produces a shrinkage estimator of a sphericity parameter that measures how close the distribution is to an isotropic distribution. In case the sampling distribution is heavy-tailed or contains outliers, robust estimators such as M-estimators of scatter matrix are more preferable. Hence, we also discuss how the OAS method can be applied for reducing estimation error of M-estimators of the scatter matrix.

• Recent Advances in False Discovery Rate Control for Sparse Graphical Models, Taulant Koka,TU Darmstadt, Germany

Abstract: This talk presents recent advances in false discovery rate (FDR) control for Gaussian graphical model estimation, beginning with a method based on the T-Rex selector framework. Limitations of the underlying model are then discussed, especially the breakdown of assumptions when comparing null variables to dummies in more complex graph structures. The talk concludes with a brief overview of ongoing work addressing these challenges through more refined modeling approaches.

• Boundary-Informed Sound Field Reconstruction, David Sundström, Lund University

Abstract: We consider the problem of reconstructing the sound field in a room using microphone measurements and prior information of the boundary geometry, represented as a point cloud. In general, when no boundary information is available, an accurate sound field reconstruction over a large spatial region and at high frequencies requires numerous microphone measurements. On the other hand, if all geometrical and acoustical aspects of the boundaries are known, the sound field could, in theory, be simulated without any measurements. In this work, we address the intermediate case, where only partial or uncertain boundary information is available. The problem is formulated within a Bayesian framework, incorporating a boundary-informed prior derived from Robin boundary conditions. The formulation allows for joint optimization of the unknown hyperparameters, including the noise and signal variances and the impedance boundary conditions. Finally, a novel dataset is recorded to both assess the properties of the method and stimulate further research on this topic.

• Interferometric phase linking with Riemannian distances on covariance matrices, Elena Grosso, CEDRIC, CNAM & ONERA

Abstract: Multi-temporal interferometric SAR allows one to monitor Earth surface displacement from SAR image time series. In this context, Interferometric Phase Linking (IPL) is a technique used to denoise the phase of SAR images by leveraging all possible pairs of interferogram within the time series. The task can be reformulated as a covariance matrix fitting problem, where the aim is to recover the expected InSAR phase structure from a noisy estimate of the covariance matrix of a pixel patch. Such framework leaves open a choice regarding the matrix distance that will define the notion of “optimal fitting”. Existing methods from the state of the art have mostly focused on maximum-likelihood and least-squares fitting formulations. In this paper, we explore the use of several Riemannian distances on the space of covariance matrices (affine invariant, log-euclidean, and Bures-Wasserstein) for IPL. We derive an optimization algorithm to solve the corresponding fitting problems, and simulations illustrate the interest of these distances in terms of estimation accuracy and computational complexity.

• Deep-TRex: Deep Learning Driven Power Enhancement for the TRex Selector, Daniel Palomar, HKUST

Abstract: The Terminating-Random Experiments (TRex) selector effectively controls the False Discovery Rate (FDR) in high-dimensional variable selection. However, its conservative nature, particularly in low-SNR settings, can lead to an achieved FDR substantially below the target, limiting the True Positive Rate (TPR). We introduce Deep-TRex, which enhances TRex by incorporating a deep learning model to directly estimate the False Discovery Proportion (FDP) using the relative frequencies of candidate variables that result from the forward variable selection process. This learned FDP allows for a less conservative calibration of TRex’s parameters, pushing the achieved FDR closer to the target to improve TPR and discovery power, all while empirically controlling the FDR. We will outline the approach and present preliminary findings.

• Quantitative Acoustic Microscopy Imaging: A Brief Introduction, Lorena Leon, CREATIS, Univ. Lyon 1

Abstract: Quantitative Acoustic Microscopy (QAM) is an advanced imaging technique that uses high-frequency ultrasound to assess the acoustic and mechanical properties of biological tissues at microscopic scales. In this talk, I will present an overview of the main signal processing and computational imaging challenges in QAM, highlight recent advances in the field, and discuss perspectives for future developments.

• Random matrix theory improved Frechet mean of symmetric positive definite matrices, Florent Bouchard, L2S, CentraleSupelec, France

Abstract: In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.

• Resource-efficient active sensing via joint design of sparse array geometry and transmitted waveforms, Robin Rajamäki, Aalto University

Abstract:  This talk presents new insights into the combined role of transmit waveforms and (sparse) sensor array geometries in active sensing. Specifically, we consider the following fundamental question of identifiability: for which low-rank waveforms and redundant array geometries can the maximum number of unknown targets be uniquely recovered? Launching fewer linearly independent (i.e., low-rank) waveforms than transmitters has the benefit of lowering hardware costs and transmission time, whereas redundant arrays can increase noise resilience and robustify against sensor failures. We show that given any sufficiently redundant array geometry, there is a minimum waveform rank, strictly smaller than the number of transmit sensors, for which maximal identifiability may still be attained. Our main result is that achieving this lower bound is highly nontrivial and requires a new idea of tailoring the transmitted waveform to the array geometry, which we call redundancy-waveform matching. We rigorously establish that judicious array design is necessary for this matching. In particular, we show the existence of infinitely many array geometries for which matching is, respectively, is not possible. This further highlights the role of the redundancy pattern arising from repeated virtual sensors that correspond to different physical transmit-receive sensor pairs. This new “array-informed” approach to waveform design provides a novel perspective on MIMO active sensing systems, impacting emerging applications with stringent resource-efficiency requirements, such as automotive radar and integrated sensing & communications.

• False Discovery Rate Control for Complex-Valued High Dimensional Data with Applications in Array Signal Processing, Fabian Scheidt,TU Darmstadt, Germany

Abstract: Recent advances in false discovery rate (FDR) control focused on high-dimensional real-valued problems. This talk introduces the first framework for FDR control in high-dimensional settings within the complex number domain - a common scenario in modern signal processing problems but underexplored at depth. At its core we extend the established T-Rex theory to the complex number domain and propose the Complex-Valued Terminating Random Experiment Selector (CT-Rex), supporting single and group-variable selection with FDR control. Additionally, we demonstrate its application in direction-of-arrival (DOA) estimation and source localization problems, leveraging results from compressed sensing theory. Finally, we present initial insights into CT-Rex’s real-world impact in emergency and rescue scenarios - specifically, for vital sign detection using radar-equipped mobile robots in disaster aftermaths.

• Elliptical Wishart distributions: a new approach to classify covariance matrices, Frederic Pascal, CentraleSupelec, France

Abstract: Although the Elliptical Wishart distributions [Anderson , 1958], which generalize the Wishart distribution, have been defined a long time ago, they were not previously exploited in practice. In [Ayadi et al. , 2023a, 2024], two algorithms are proposed to compute the maximum likelihood estimator (MLE): a fixed-point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated, such as consistency, asymptotic normality, and an intrinsic version of Fisher’s efficiency. On the statistical learning side, novel classification and clustering methods are designed in [Ayadi et al. , 2023b, 2024]. For the t-Wishart distribution, the performance of the MLE and statistical learning algorithms is evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.