相关论文: Unbiased Estimation of a Sparse Vector in White Ga…
We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…
We consider distributed estimation of a Gaussian vector with a linear observation model in an inhomogeneous wireless sensor network, where a fusion center (FC) reconstructs the unknown vector, using a linear estimator. Sensors employ…
We consider the problem of estimating an input signal from noisy measurements in both parallel scalar Gaussian channels and linear mixing systems. The performance of the estimation process is quantified by the $\ell_\infty$ norm error…
We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…
This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor…
This paper studies the minimum mean squared error (MMSE) of estimating $\mathbf{X} \in \mathbb{R}^d$ from the noisy observation $\mathbf{Y} \in \mathbb{R}^k$, under the assumption that the noise (i.e., $\mathbf{Y}|\mathbf{X}$) is a member…
Graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs. In the Gaussian case, these models are directly related to the sparsity of the inverse covariance…
We consider the problem of sequentially learning to estimate, in the mean squared error (MSE) sense, a Gaussian $K$-vector of unknown covariance by observing only $m < K$ of its entries in each round. We propose two MSE estimators, and…
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…
Non-Gaussian statistics of the projected weak lensing field are powerful estimators that can outperform the constraining power of the two-point functions in inferring cosmological parameters. This is because these estimators extract the…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to…
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…
Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…
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…
For the single index model $y=f(\beta^{\tau}x,\epsilon)$ with Gaussian design, %satisfying that rank $var(\mathbb{E}[x\mid y])=1$ where $f$ is unknown and $\beta$ is a sparse $p$-dimensional unit vector with at most $s$ nonzero entries, we…
Support Vector Machines (SVM) with $\ell_1$ penalty became a standard tool in analysis of highdimensional classification problems with sparsity constraints in many applications including bioinformatics and signal processing. Although SVM…