Related papers: Near Minimax Line Spectral Estimation
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…
In some applications of frequency estimation, it is challenging to sample at as high as the Nyquist rate due to hardware limitations. An effective solution is to use multiple sub-Nyquist channels with coprime undersampling ratios to jointly…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
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…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations…
The area of spectral analysis has a traditional dichotomy between continuous spectra (spectral densities) which correspond to purely nondeterministic processes, and line spectra (Dirac impulses) which represent sinusoids. While the former…
Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
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…
In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
Real-world measurements often comprise a dominant signal contaminated by a noisy background. Robustly estimating the dominant signal in practice has been a fundamental statistical problem. Classically, mixture models have been used to…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…
The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…