相关论文: Noise-cleaning the precision matrix of fMRI time s…

This paper studies the multi-task high-dimensional linear regression models where the noise among different tasks is correlated, in the moderately high dimensional regime where sample size $n$ and dimension $p$ are of the same order. Our…

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Neuroradiologists and neurosurgeons increasingly opt to use functional magnetic resonance imaging (fMRI) to map functionally relevant brain regions for noninvasive presurgical planning and intraoperative neuronavigation. This application…

One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results…

Most of the existing wavelet image processing techniques are carried out in the form of single-scale reconstruction and multiple iterations. However, processing high-quality fMRI data presents problems such as mixed noise and excessive…

We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…

In computational neuroscience, it is important to estimate well the proportion of signal variance in the total variance of neural activity measurements. This explainable variance measure helps neuroscientists assess the adequacy of…

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including…

This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…

We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific…

The problem of noise covariance matrix identification of stochastic linear time-varying state-space models is addressed. The measurement difference method (MDM) is generalized to time-varying dimensions of the measurement and control. Three…

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance…

Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multi-probe) analyses of the large scale structure of the universe. Analytically computed covariances are noise-free and…

Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…

Brain decoding algorithms form an important part of the arsenal of analysis tools available to neuroscientists, allowing for a more detailed study of the kind of information represented in patterns of cortical activity. While most current…

We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…