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In this paper, we introduce a new Bayesian approach for analyzing task fMRI data that simultaneously detects activation signatures and background connectivity. Our modeling involves a new hybrid tensor spatial-temporal basis strategy that enables scalable computing yet captures nearby and distant intervoxel correlation and long-memory temporal correlation. The spatial basis involves a composite hybrid transform with two levels: the first accounts for within-ROI correlation, and second between-ROI distant correlation. We demonstrate in simulations how our basis space regression modeling strategy increases sensitivity for identifying activation signatures, partly driven by the induced background connectivity that itself can be summarized to reveal biological insights. This strategy leads to computationally scalable fully Bayesian inference at the voxel or ROI level that adjusts for multiple testing. We apply this model to Human Connectome Project data to reveal insights into brain activation patterns and background connectivity related to working memory tasks.

We consider the application of the generalized Convolution Quadrature (gCQ) to approximate the solution of an important class of sectorial problems. The gCQ is a generalization of Lubich's Convolution Quadrature (CQ) that allows for variable steps. The available stability and convergence theory for the gCQ requires non realistic regularity assumptions on the data, which do not hold in many applications of interest, such as the approximation of subdiffusion equations. It is well known that for non smooth enough data the original CQ, with uniform steps, presents an order reduction close to the singularity. We generalize the analysis of the gCQ to data satisfying realistic regularity assumptions and provide sufficient conditions for stability and convergence on arbitrary sequences of time points. We consider the particular case of graded meshes and show how to choose them optimally, according to the behaviour of the data. An important advantage of the gCQ method is that it allows for a fast and memory reduced implementation. We describe how the fast and oblivious gCQ can be implemented and illustrate our theoretical results with several numerical experiments.

Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from the crack closure emerge. We address this issue by proposing a new strategy to cope with the entire process of failure, from the very inception in the form of diffuse damage to the final stage, i.e. the emergence of sharp cracks. To this end, we introduce a new strain field, termed discontinuity strain, to the conventional additive strain decomposition to account for discontinuities in a continuous sense so that the standard principle of virtual work applies. We treat this strain field similar to a strong discontinuity, yet without introducing new kinematic variables and nonlinear boundary conditions. In this paper, we demonstrate the effectiveness of this new strategy at a simple ductile damage constitutive model. The model uses a scalar damage index to control the degradation process. The discontinuity strain field is injected into the strain decomposition if this damage index exceeds a certain threshold. The threshold corresponds to the limit at which the induced imperfections merge and form a discrete crack. With three-point bending tests under pure mode I and mixed-mode conditions, we demonstrate that this augmentation does not show the early crack closure artifact which is wrongly predicted by plastic damage formulations at load reversal. We also use the concrete damaged plasticity model provided in Abaqus commercial finite element program for our comparison. Lastly, a high-intensity low-cycle fatigue test demonstrates the unilateral effects resulting from the complete closure of the induced crack.

We propose an innovative and generic methodology to analyse individual and collective behaviour through individual trajectory data. The work is motivated by the analysis of GPS trajectories of fishing vessels collected from regulatory tracking data in the context of marine biodiversity conservation and ecosystem-based fisheries management. We build a low-dimensional latent representation of trajectories using convolutional neural networks as non-linear mapping. This is done by training a conditional variational auto-encoder taking into account covariates. The posterior distributions of the latent representations can be linked to the characteristics of the actual trajectories. The latent distributions of the trajectories are compared with the Bhattacharyya coefficient, which is well-suited for comparing distributions. Using this coefficient, we analyse the variation of the individual behaviour of each vessel during time. For collective behaviour analysis, we build proximity graphs and use an extension of the stochastic block model for multiple networks. This model results in a clustering of the individuals based on their set of trajectories. The application to French fishing vessels enables us to obtain groups of vessels whose individual and collective behaviours exhibit spatio-temporal patterns over the period 2014-2018.

We present ParrotTTS, a modularized text-to-speech synthesis model leveraging disentangled self-supervised speech representations. It can train a multi-speaker variant effectively using transcripts from a single speaker. ParrotTTS adapts to a new language in low resource setup and generalizes to languages not seen while training the self-supervised backbone. Moreover, without training on bilingual or parallel examples, ParrotTTS can transfer voices across languages while preserving the speaker specific characteristics, e.g., synthesizing fluent Hindi speech using a French speaker's voice and accent. We present extensive results in monolingual and multi-lingual scenarios. ParrotTTS outperforms state-of-the-art multi-lingual TTS models using only a fraction of paired data as latter.

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and have been successfully applied to a variety of problems. The dynamical low- \rank approximation is a recent technique for solving high-dimensional differential equations by means of low-rank approximations. However, the domain is lacking numerical methods for stiff equations since existing methods are either not robust-to-stiffness or have unreasonably large hidden constants. In this paper, we focus on solving large-scale stiff matrix differential equations with a Sylvester-like structure, that admit good low-rank approximations. We propose two new methods that have good convergence properties, small memory footprint and that are fast to compute. The theoretical analysis shows that the new methods have order one and two, respectively. We also propose a practical implementation based on Krylov techniques. The approximation error is analyzed, leading to a priori error bounds and, therefore, a mean for choosing the size of the Krylov space. Numerical experiments are performed on several examples, confirming the theory and showing good speedup in comparison to existing techniques.

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decomposition or factorization, are natural potent instruments to study a collection of tensor-variate objects that may be dependent or independent. However, it is still in the early stage of developing statistical inferential theories for estimation of various low-rank structures, which are customary to play the role of signals of tensor factor models. In this paper, starting from tensor matricization, we aim to ``decode" estimation of a higher-order tensor factor model in the sense that, we recast it into mode-wise traditional high-dimensional vector/fiber factor models so as to deploy the conventional estimation of principle components analysis (PCA). Demonstrated by the Tucker tensor factor model (TuTFaM), which is induced from most popular Tucker decomposition, we summarize that estimations on signal components are essentially mode-wise PCA techniques, and the involvement of projection and iteration will enhance the signal-to-noise ratio to various extend. We establish the inferential theory of the proposed estimations and conduct rich simulation experiments under TuTFaM, and illustrate how the proposed estimations can work in tensor reconstruction, clustering for video and economic datasets, respectively.

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization of the latent MAP. In this work, we propose to use compressive autoencoders for latent estimation. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. We then introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs this estimation within the framework of variational inference. This allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.

In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. This paper challenges this notion, demonstrating its inaccuracy in high dimensions. Initially focusing on a dense scenario, we introduce robust semi-supervised estimators for the regression coefficient without relying on sparse structures in the population slope. Even when the true underlying model is linear, we show that leveraging information from large-scale unlabeled data improves both estimation accuracy and inference robustness. Moreover, we propose semi-supervised methods with further enhanced efficiency in scenarios with a sparse linear slope. Diverging from the standard semi-supervised literature, we also allow for covariate shift. The performance of the proposed methods is illustrated through extensive numerical studies, including simulations and a real-data application to the AIDS Clinical Trials Group Protocol 175 (ACTG175).

Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings directly depends on how much the geometry of the continuous space matches the graph structure. Manifolds are mathematical structure that can enable to incorporate in their topological spaces the graph characteristics, and in particular nodes distances. State-of-the-art of manifold-based graph embedding algorithms take advantage of the assumption that the projection on a tangential space of each point in the manifold (corresponding to a node in the graph) would locally resemble a Euclidean space. Although this condition helps in achieving efficient analytical solutions to the embedding problem, it does not represent an adequate set-up to work with modern real life graphs, that are characterized by weighted connections across nodes often computed over sparse datasets with missing records. In this work, we introduce a new class of manifold, named soft manifold, that can solve this situation. In particular, soft manifolds are mathematical structures with spherical symmetry where the tangent spaces to each point are hypocycloids whose shape is defined according to the velocity of information propagation across the data points. Using soft manifolds for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets. Experimental results on reconstruction tasks on synthetic and real datasets show how the proposed approach enable more accurate and reliable characterization of graphs in continuous spaces with respect to the state-of-the-art.