Applications of the lasso and grouped lasso to the estimation of sparse graphical models
نویسندگان
چکیده
We propose several methods for estimating edge-sparse and nodesparse graphical models based on lasso and grouped lasso penalties. We develop efficient algorithms for fitting these models when the numbers of nodes and potential edges are large. We compare them to competing methods including the graphical lasso and SPACE (Peng, Wang, Zhou & Zhu 2008). Surprisingly, we find that for edge selection, a simple method based on univariate screening of the elements of the empirical correlation matrix usually performs as well or better than all of the more complex methods proposed here and elsewhere. Running title: Applications of the lasso and grouped lasso
منابع مشابه
Bayesian Quantile Regression with Adaptive Lasso Penalty for Dynamic Panel Data
Dynamic panel data models include the important part of medicine, social and economic studies. Existence of the lagged dependent variable as an explanatory variable is a sensible trait of these models. The estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbance. Recently, quantile regression to analyze dynamic pa...
متن کاملRobust Gaussian Graphical Modeling with the Trimmed Graphical Lasso
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust estimation of sparse GGMs. Our method guards ...
متن کاملDifferenced-Based Double Shrinking in Partial Linear Models
Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...
متن کاملMammalian Eye Gene Expression Using Support Vector Regression to Evaluate a Strategy for Detecting Human Eye Disease
Background and purpose: Machine learning is a class of modern and strong tools that can solve many important problems that nowadays humans may be faced with. Support vector regression (SVR) is a way to build a regression model which is an incredible member of the machine learning family. SVR has been proven to be an effective tool in real-value function estimation. As a supervised-learning appr...
متن کاملar X iv : 0 90 3 . 25 15 v 1 [ m at h . ST ] 1 3 M ar 2 00 9 Adaptive Lasso for High Dimensional Regression and Gaussian Graphical Modeling
We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al., 2008) are also sufficient for sparse structure estimation.
متن کامل