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For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally…

The class of Lq-regularized least squares (LQLS) are considered for estimating a p-dimensional vector \b{eta} from its n noisy linear observations y = X\b{eta}+w. The performance of these schemes are studied under the high-dimensional…

Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph…

This paper studies regularized least square recovery of signals whose samples' prior distributions are nonidentical, e.g., signals with time-variant sparsity. For this model, Bayesian framework suggests to regularize the least squares term…

In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…

This paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of…

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…

We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…

We introduce system norms which assess transient behavior of stable Linear Time-Invariant (LTI) systems. This allows us to address undesired responses to initial conditions, finite resource consumption signals, or persistent perturbations.…

In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…

In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

We propose a novel algorithm for greedy forward feature selection for regularized least-squares (RLS) regression and classification, also known as the least-squares support vector machine or ridge regression. The algorithm, which we call…

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…