Related papers: Performance Analysis of Parameter Estimation Using…

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…

The lasso procedure is ubiquitous in the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso…

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…

We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…

Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…

Surrogate Optimization (SO) algorithms have shown promise for optimizing expensive black-box functions. However, their performance is heavily influenced by hyperparameters related to sampling and surrogate fitting, which poses a challenge…

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,…

The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…

Selective Inference (SI) has been actively studied in the past few years for conducting inference on the features of linear models that are adaptively selected by feature selection methods such as Lasso. The basic idea of SI is to make…

Limited by fixed step-size and sparsity penalty factor, the conventional sparsity-aware normalized subband adaptive filtering (NSAF) type algorithms suffer from trade-off requirements of high filtering accurateness and quicker convergence…

Direction of arrival (DOA) estimation is a fundamental problem in array signal processing with applications spanning radar, sonar, wireless communications, and acoustic signal processing. This tutorial survey provides a comprehensive…

This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…

Convex estimators such as the Lasso, the matrix Lasso and the group Lasso have been studied extensively in the last two decades, demonstrating great success in both theory and practice. Two quantities are introduced, the noise barrier and…

The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that…

The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…

We consider a dynamical system with small noise for which the drift is parametrized by a finite dimensional parameter. For this model we consider minimum distance estimation from continuous time observations under $l^p$-penalty imposed on…

For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…

Regularization techniques are crucial to improving the generalization performance and training efficiency of deep neural networks. Many deep learning algorithms rely on weight decay, dropout, batch/layer normalization to converge faster and…