Related papers: A structured matrix factorization framework for la…
We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…
The hierarchical matrix framework partitions matrices into subblocks that are either small or of low numerical rank, enabling linear storage complexity and efficient matrix-vector multiplication. This work focuses on the $H^2$-matrix format…
Neurons are spatially extended cells; different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially…
Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…
This paper presents a general method for applying hierarchical matrix skeletonization factorizations to the numerical solution of boundary integral equations with possibly rank-deficient integral operators. Rank-deficient operators arise in…
We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the…
Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorised structure with a rank growing proportionally to its dimension remains a challenge, except when it is…
Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization…
The activity of an isolated and auto-connected neuron is studied using Hodgkin--Huxley and Integrate-and-Fire frameworks. Main ingredients of the modeling are the auto-stimulating autaptic current observed in experiments, with a spontaneous…
Denoising is a fundamental imaging problem. Versatile but fast filtering has been demanded for mobile camera systems. We present an approach to multiscale filtering which allows real-time applications on low-powered devices. The key idea is…
We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence…
In biomedical research and other fields, it is now common to generate high content data that are both multi-source and multi-way. Multi-source data are collected from different high-throughput technologies while multi-way data are collected…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
Long-time series of neuronal recordings are resulting from the activity of connected neuronal networks. Yet how neuronal properties can be extracted remains empirical. We review here the data analysis based on network models to recover…
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…
Matrix Factorization (MF) on large scale data takes substantial time on a Central Processing Unit (CPU). While Graphical Processing Unit (GPU)s could expedite the computation of MF, the available memory on a GPU is finite. Leveraging GPUs…
This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the precision and the observations, we show that the sample…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
Resting-state functional magnetic resonance imaging (rs-fMRI) is a noninvasive technique pivotal for understanding human neural mechanisms of intricate cognitive processes. Most rs-fMRI studies compute a single static functional…
We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…