相关论文: Signal-to-noise ratio aware minimaxity and higher-…

We consider parameter estimation under sparse linear regression -- an extensively studied problem in high-dimensional statistics and compressed sensing. While the minimax framework has been one of the most fundamental approaches for…

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…

In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…

Reduced-rank approach has been used for decades in robust linear estimation of both deterministic and random vector of parameters in linear model y=Hx+\sqrt{epsilon}n. In practical settings, estimation is frequently performed under…

We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…

The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a…

We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…

We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…

Signal-to-noise ratios (SNR) play a crucial role in various statistical models, with important applications in tasks such as estimating heritability in genomics. The method-of-moments estimator is a widely used approach for estimating SNR,…

We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of the signal, we consider the general problem of…

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…

In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only…

Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation…

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…

Sparse linear regression is one of the classical and extensively studied problems in high-dimensional statistics and compressed sensing. Despite the substantial body of literature dedicated to this problem, the precise determination of its…

We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection…

This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…