相关论文: Empirical Bayes Estimation for Lasso-Type Regulari…

We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization…

This paper studies the sensitivity to the observations of the block/group Lasso solution to an overdetermined linear regression model. Such a regularization is known to promote sparsity patterns structured as nonoverlapping groups of…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…

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 propose a new algorithm for estimating NARMAX models with $L_1$ regularization for models represented as a linear combination of basis functions. Due to the $L_1$-norm penalty the Lasso estimation tends to produce some coefficients that…

Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors $X_1,\ldots, X_p$ (for example: $Y = 1$ if the outcome occurred and $Y = 0$…

Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

Regularized regression has become very popular nowadays, particularly on high-dimensional problems where the addition of a penalty term to the log-likelihood allows inference where traditional methods fail. A number of penalties have been…

The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…

Regression adjustments are often considered by investigators to improve the estimation efficiency of causal effect in randomized experiments when there exists many pre-experiment covariates. In this paper, we provide conditions that…