Related papers: Estimation of matrix trace using machine learning
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
We consider the model {eqnarray*}y=X\theta^*+\xi, Z=X+\Xi,{eqnarray*} where the random vector $y\in\mathbb{R}^n$ and the random $n\times p$ matrix $Z$ are observed, the $n\times p$ matrix $X$ is unknown, $\Xi$ is an $n\times p$ random noise…
Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible…
We consider the task of estimating the trace of a matrix function, ${\rm tr}(f({\bf A}))$, of a large symmetric positive semi-definite matrix ${\bf A}$. This problem arises in multiple applications, including kernel methods and inverse…
Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem…
Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we…
Estimation of the prediction error of a linear estimation rule is difficult if the data analyst also use data to select a set of variables and construct the estimation rule using only the selected variables. In this work, we propose an…
Human motion prediction is a stochastic process: Given an observed sequence of poses, multiple future motions are plausible. Existing approaches to modeling this stochasticity typically combine a random noise vector with information about…
In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…
We present the analysis of two recently proposed noise reduction techniques, Hutch++ and XTrace, both based on inexact deflation. These methods were proven to have a better asymptotic convergence to the solution than the classical…
In this paper, we propose new randomized algorithms for estimating the two-to-infinity and one-to-two norms in a matrix-free setting, using only matrix-vector multiplications. Our methods are based on appropriate modifications of…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function.…
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
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,…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models…