DeepAI AI Chat
Log In Sign Up

On Model Selection Consistency of Lasso for High-Dimensional Ising Models on Tree-like Graphs

by   Xiangming Meng, et al.
The University of Tokyo

We consider the problem of high-dimensional Ising model selection using neighborhood-based least absolute shrinkage and selection operator (Lasso). It is rigorously proved that under some mild coherence conditions on the population covariance matrix of the Ising model, consistent model selection can be achieved with sample sizes n=Ω(d^3logp) for any tree-like graph in the paramagnetic phase, where p is the number of variables and d is the maximum node degree. When the same conditions are imposed directly on the sample covariance matrices, it is shown that a reduced sample size n=Ω(d^2logp) suffices. The obtained sufficient conditions for consistent model selection with Lasso are the same in the scaling of the sample complexity as that of ℓ_1-regularized logistic regression. Given the popularity and efficiency of Lasso, our rigorous analysis provides a theoretical backing for its practical use in Ising model selection.


page 1

page 2

page 3

page 4


Model selection consistency from the perspective of generalization ability and VC theory with an application to Lasso

Model selection is difficult to analyse yet theoretically and empiricall...

High-dimensional structure estimation in Ising models: Local separation criterion

We consider the problem of high-dimensional Ising (graphical) model sele...

On an improvement of LASSO by scaling

A sparse modeling is a major topic in machine learning and statistics. L...

On model selection consistency of regularized M-estimators

Regularized M-estimators are used in diverse areas of science and engine...

Average case analysis of Lasso under ultra-sparse conditions

We analyze the performance of the least absolute shrinkage and selection...

Meta Learning for High-dimensional Ising Model Selection Using ℓ_1-regularized Logistic Regression

In this paper, we consider the meta learning problem for estimating the ...

Improving Lasso for model selection and prediction

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrins...