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We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
Residual variance and the signal-to-noise ratio are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics, in determining the performance limits in estimation and…
Sinusoidal parameter estimation is a computationally-intensive task, which can pose problems for real-time implementations. In this paper, we propose a low-complexity iterative method for estimating sinusoidal parameters that is based on…
Model selection aims to identify a sufficiently well performing model that is possibly simpler than the most complex model among a pool of candidates. However, the decision-making process itself can inadvertently introduce non-negligible…
We propose a learning-based approach for estimating the spectrum of a multisinusoidal signal from a finite number of samples. A neural-network is trained to approximate the spectra of such signals on simulated data. The proposed methodology…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
We consider ordinary least squares estimation and variations on least squares estimation such as penalized (regularized) least squares and spectral shrinkage estimates for problems with p > n and associated problems with prediction of new…
In this paper, we address the problem of parameter estimation of a 2-D chirp model under the assumption that the errors are stationary. We extend the 2-D periodogram method for the sinusoidal model, to find initial values to use in any…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…
The method of location and spectral estimation of weak signals on a noise background is being considered. The method is based on the optimized on order and noise dispersion autoregressive model of a sought signal. A new approach of model…
This paper considers least-square based estimation of the amplitude and square amplitude of a quantized sine wave, done by considering random initial record phase. Using amplitude- and frequency-domain modeling techniques, it is shown that…
A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…
This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…
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…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
A generalized multisensor sequential change detection problem is considered, in which a number of (possibly correlated) sensors monitor an environment in real time, the joint distribution of their observations is determined by a global…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…
Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…