Related papers: Rectangular Rotational Invariant Estimator for Hig…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
The RHESSI experiment uses rotational modulation for x- and gamma ray imaging of solar eruptions. In order to disentangle rotational modulation from intrinsic time variation, an unbiased linear estimator for the spatially integrated photon…
In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very…
In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual…
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
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…
Estimating the true rank of a noisy data matrix is a fundamental problem underlying techniques such as principal component analysis, matrix completion, etc. Existing rank estimation criteria, including information-based and cross-validation…
Accurate measurement of spatially variant noise in dynamic magnetic resonance (MR) images acquired using parallel imaging methods is problematic. We propose a new method based on the random matrix theory to accurately assess the noise…
The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and…
It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…
We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or,…
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among…
Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
We consider the problem of estimating a low-rank signal matrix from noisy measurements under the assumption that the distribution of the data matrix belongs to an exponential family. In this setting, we derive generalized Stein's unbiased…
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…