Related papers: Sparse Estimation From Noisy Observations of an Ov…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement…
In the theory of compressed sensing (CS), the sparsity $\|x\|_0$ of the unknown signal $\mathbf{x} \in \mathcal{R}^n$ is of prime importance and the focus of reconstruction algorithms has mainly been either $\|x\|_0$ or its convex…
We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
This paper investigates system identification problems with Gaussian inputs and quantized observations under fixed thresholds. By reinterpreting the nonlinear effects induced by quantization as the product of the unknown parameter and an…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
A distributed adaptive algorithm for estimation of sparse unknown parameters in the presence of nonGaussian noise is proposed in this paper based on normalized least mean fourth (NLMF) criterion. At the first step, local adaptive NLMF…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…
This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and…