相关论文: A note relating ridge regression and OLS p-values …
There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…
A well-know drawback of l_1-penalized estimators is the systematic shrinkage of the large coefficients towards zero. A simple remedy is to treat Lasso as a model-selection procedure and to perform a second refitting step on the selected…
Lasso regression is a widely employed approach within the $\ell_1$ regularization framework used to promote sparsity and recover piecewise smooth signals $f:[a,b) \rightarrow \mathbb{R}$ when the given observations are obtained from noisy,…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…
Orthogonal Matching Pursuit and Basis Pursuit are popular reconstruction algorithms for recovery of sparse signals. The exact recovery property of both the methods has a relation with the coherence of the underlying redundant dictionary,…
In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. We aim to bridge the gap between these two…
In linear regression, SLOPE is a new convex analysis method that generalizes the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized more heavily. This magnitude-dependent regularization requires an input of penalty…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
We propose a novel quasi-Newton method for solving the sparse inverse covariance estimation problem also known as the graphical least absolute shrinkage and selection operator (GLASSO). This problem is often solved using a second-order…
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yielding a "pre-conditioned" response…
Pathwise coordinate descent algorithms have been used to compute entire solution paths for lasso and other penalized regression problems quickly with great success. They improve upon cold start algorithms by solving the problems that make…
For finite samples with binary outcomes penalized logistic regression such as ridge logistic regression (RR) has the potential of achieving smaller mean squared errors (MSE) of coefficients and predictions than maximum likelihood…
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…
We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic…
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)…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…
Orthogonal least square (OLS) is an important sparse signal recovery algorithm for compressive sensing, which enjoys superior probability of success over other well-known recovery algorithms under conditions of correlated measurement…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse…