# Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery

@inproceedings{Laszkiewicz2021ThresholdedAV, title={Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery}, author={Mike Laszkiewicz and Asja Fischer and Johannes Lederer}, booktitle={AISTATS}, year={2021} }

The graphical lasso is the most popular estimator in Gaussian graphical models, but its performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a novel calibration scheme for this parameter. The scheme is equipped with theoretical guarantees and motivates a thresholding pipeline that can improve graph recovery. Moreover, requiring at most one line search over the regularization path of the graphical lasso, the…

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## References

SHOWING 1-10 OF 64 REFERENCES

TIGER: A Tuning-Insensitive Approach for Optimally Estimating Gaussian Graphical Models

- Computer Science
- 2012

This work proposes a new procedure for estimating high dimensional Gaussian graphical models that is asymptotically tuning-free and non-asymptotic tuning-insensitive, and theoretically, the obtained estimator is simultaneously minimax optimal for precision matrix estimation under different norms.

A Practical Scheme and Fast Algorithm to Tune the Lasso With Optimality Guarantees

- Computer ScienceJ. Mach. Learn. Res.
- 2016

We introduce a novel scheme for choosing the regularization parameter in high-dimensional linear regression with Lasso. This scheme, inspired by Lepski's method for bandwidth selection in…

New Insights and Faster Computations for the Graphical Lasso

- Computer Science, Mathematics
- 2011

A very simple necessary and sufficient condition can be employed to determine whether the estimated inverse covariance matrix will be block diagonal, and if so, then to identify the blocks in the graphical lasso solution.

NETWORK EXPLORATION VIA THE ADAPTIVE LASSO AND SCAD PENALTIES.

- Computer ScienceThe annals of applied statistics
- 2009

Non-concave penalties and the adaptive LASSO penalty are introduced to attenuate the bias problem in the network estimation to solve the problem of precision matrix estimation.

Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models

- Computer ScienceNIPS
- 2010

The method has a clear interpretation: the authors use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling, which requires essentially no conditions.

Sparse inverse covariance estimation with the graphical lasso.

- Computer ScienceBiostatistics
- 2008

Using a coordinate descent procedure for the lasso, a simple algorithm is developed that solves a 1000-node problem in at most a minute and is 30-4000 times faster than competing methods.

Selection of the Regularization Parameter in Graphical Models Using Network Characteristics

- Computer Science
- 2015

This article proposes several procedures to select the regularization parameter in the estimation of graphical models that focus on recovering reliably the appropriate network structure of the graph and conducts an extensive simulation study to show that the proposed methods produce useful results for different network topologies.

Model selection and estimation in the Gaussian graphical model

- Computer Science
- 2007

The implementation of the penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model is nontrivial, but it is shown that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization.

Inference in High-Dimensional Graphical Models

- Computer ScienceHandbook of Graphical Models
- 2018

An overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models and proposed estimators lead to confidence intervals for edge weights and recovery of the edge structure are provided.

Learning Scale Free Networks by Reweighted L1 regularization

- Computer ScienceAISTATS
- 2011

This work replaces the ‘1 regularization with a power law regularization and optimize the objective function by a sequence of iteratively reweighted ‘ 1 regularization problems, where the regularization coecients of nodes with high degree are reduced, encouraging the appearance of hubs with high degrees.