Related papers: Structural Variability from Noisy Tomographic Proj…
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 address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for…
We introduce a noise-aware extension to the parametric maximum-likelihood framework for component separation by modeling correlated $1/f^\alpha$ noise as a harmonic-space power law. This approach addresses a key limitation of existing…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
Cryo-electron tomography (cryo-ET) has emerged as a powerful tool for studying the structural heterogeneity of proteins and their complexes, offering insights into macromolecular dynamics directly within cells. Driven by recent…
In this work, we study the positive definiteness (PDness) problem in covariance matrix estimation. For high dimensional data, many regularized estimators are proposed under structural assumptions on the true covariance matrix including…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…
The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the…
Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including cell-fate decision in developmental processes as well as genesis and progression of cancers. While various attempts have…
The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations over a time window, and…
The observable universe contains density perturbations on scales larger than any finite volume survey. Perturbations on scales larger than a survey can measure degrade its power to constrain cosmological parameters. The dependence of survey…
Recent studies inspired by results from random matrix theory [1,2,3] found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be…
As Deep Learning continues to yield successful applications in Computer Vision, the ability to quantify all forms of uncertainty is a paramount requirement for its safe and reliable deployment in the real-world. In this work, we leverage…
Cosmological parameter inference from galaxy clustering relies critically on accurate estimates of the covariance and precision matrices. These are often obtained from a limited number of mock catalogs, introducing noise and bias in the…
Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise…
The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns…
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…
Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we…