Related papers: Sparse High-Dimensional Isotonic Regression
The theory of compressive sensing (CS) asserts that an unknown signal $\mathbf{x} \in \mathbb{C}^N$ can be accurately recovered from $m$ measurements with $m\ll N$ provided that $\mathbf{x}$ is sparse. Most of the recovery algorithms need…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…
In this paper, we study the problem of sparse mixed linear regression on an unlabeled dataset that is generated from linear measurements from two different regression parameter vectors. Since the data is unlabeled, our task is not only to…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…
We consider the problem of parameter estimation, based on noisy chaotic signals, from the viewpoint of twisted modulation for waveform communication. In particular, we study communication systems where the parameter to be estimated is…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…
Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
We consider the problem of estimating a deterministic sparse vector x from underdetermined measurements Ax+w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse…