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We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression…
In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_\lambda(\alpha, \beta) = \|Y - \alpha\mathbf{1} - X\beta\|_2^2 + p_{\lambda}(\beta)\] where $\alpha$ is the intercept which can be omitted…
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.…
We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
The nonlinear Schr\"odinger equation (NLSE) is a fundamental model for wave dynamics in nonlinear media ranging from optical fibers to Bose-Einstein condensates. Accurately estimating its parameters, which are often strongly correlated,…
In high-dimensional data settings where $p\gg n$, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable…
We study in detail the two main algorithms which have been considered for fitting constrained marginal models to discrete data, one based on Lagrange multipliers and the other on a regression model. We show that the updates produced by the…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
We use location model methodology to guide the least squares analysis of the Lasso problem of variable selection and inference. The nuisance parameter is taken to be an indicator for the selection of explanatory variables and the interest…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean square error (MSE) that decreases at best as…
We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
Recently, a Levenberg-Marquardt method with Singular Scaling matrix, called LMMSS, was proposed and successfully applied in parameter estimation in heat conduction problems, where the choice of suitable singular scaling matrix resulted in…
Quantization of signals is an integral part of modern signal processing applications, such as sensing, communication, and inference. While signal quantization provides many physical advantages, it usually degrades the subsequent estimation…
We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…
A rich literature exists on constructing non-parametric estimators with optimal asymptotic properties. In addition to asymptotic guarantees, it is often of interest to design estimators with desirable finite-sample properties; such as…