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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.…
Choosing between classical and Bayesian sparse regression methods involves a real trade-off: penalized estimators like Lasso run in milliseconds but give no uncertainty estimates,while Horseshoe and Spike-and-Slab priors produce full…
This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
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…
We describe a simple, efficient, permutation based procedure for selecting the penalty parameter in the LASSO. The procedure, which is intended for applications where variable selection is the primary focus, can be applied in a variety of…
In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…
The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double…
Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
Regularized regression techniques for linear regression have been created the last few ten years to reduce the flaws of ordinary least squares regression with regard to prediction accuracy. In this paper, new methods for using regularized…
The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify…
Least Absolute Shrinkage and Selection Operator or the Lasso, introduced by Tibshirani (1996), is a popular estimation procedure in multiple linear regression when underlying design has a sparse structure, because of its property that it…
Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…
We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…
We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic…
Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the…