arXiv 29 Jan 2021 · Statistics — Methodology · 4 citations (OpenAlex)
arXiv:2101.12503 · PDF · DOI · OpenAlex · Extracted main text
High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical model. We develop a new convex regularized method, called the tree-aggregated graphical lasso or tag-lasso, that estimates graphical models that are both edge-sparse and node-aggregated. The aggregation is performed in a data-driven fashion by leveraging side information in the form of a tree that encodes node similarity and facilitates the interpretation of the resulting aggregated nodes. We provide an efficient implementation of the tag-lasso by using the locally adaptive alternating direction method of multipliers and illustrate our proposal's practical advantages in simulation and in applications in finance and biology.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Yan, X. and Bien, J (2020) Rare feature selection in high dimensions self | 0.843 | 3 | 3 | 100% |
| 2 | Pircalabelu, E. and Claeskens, G (2020) Community-Based Group Graphical Lasso | 0.811 | 4 | 2 | 100% |
| 3 | Banerjee, O.; Ghaoui, L. E. and d’Aspremont, A (2008) Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data | 0.737 | 3 | 2 | 100% |
| 4 | Eisenach, C.; Bunea, F.; Ning, Y. and Dinicu, C (2020) High-Dimensional Inference for Cluster-Based Graphical Models | 0.737 | 3 | 2 | 100% |
| 5 | Friedman, J.; Hastie, T. and Tibshirani, R (2008) Sparse inverse covariance estimation with the graphical lasso | 0.737 | 3 | 2 | 100% |
| 6 | Rothman, A. J.; Bickel, P. J.; Levina, E. and Zhu, J (2008) Sparse permutation invariant covariance estimation | 0.737 | 3 | 2 | 100% |
| 7 | Tan, K. M.; Witten, D. and Shojaie, A (2015) The cluster graphical lasso for improved estimation of Gaussian graphical models | 0.737 | 3 | 2 | 100% |
| 8 | Yuan, M. and Lin, Y (2007) Model selection and estimation in the Gaussian graphical model | 0.737 | 3 | 2 | 100% |
| 9 | Kurtz, Z. D.; Bonneau, R. and Müller, C. L (2019) Disentangling microbial associations from hidden environmental and technical factors via latent graphical models | 0.585 | 3 | 1 | 100% |
| 10 | Boyd, S.; Parikh, N.; Chu, E.; Peleato, B. and Eckstein, J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 34 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Sparse Tree-Based Aggregation for Time Series Regressions | 0.405 | 1 | 1 |