Block-enhanced precision matrix estimation for large-scale datasets

Eftekhari, Aryan; Pasadakis, Dimosthenis; Bollhöfer, Matthias; Scheidegger, Simon; Schenk, Olaf

doi:10.1016/j.jocs.2021.101389

Cited by 4 publications

(1 citation statement)

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“…LGMD+ alleviates this problem in some sense but is relatively more time-consuming. Fortunately, there has been some recent work dedicated to addressing this problem by introducing the novel block coordinate descent update on the precision matrix estimation [3,11,33]. In the future, we will try to use these newly developed techniques and adapt our method to large-scale data.…”

Section: Discussionmentioning

confidence: 99%

Learnable Graph-Regularization for Matrix Decomposition

Zhai

Zhang

2023

ACM Trans. Knowl. Discov. Data

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Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional data into low-dimensional spaces, which mitigates the effects of noise and uncovers latent relations. In order to make the learned representations inherit the structures in the original data, graph-regularization terms are often added to the loss function. However, the prior graph construction often fails to reflect the true network connectivity and the intrinsic relationships. In addition, many graph-regularized methods fail to take the dual spaces into account. Probabilistic models are often used to model the distribution of the representations, but most of previous methods often assume that the hidden variables are independent and identically distributed for simplicity. To this end, we propose a learnable graph-regularization model for matrix decomposition (LGMD), which builds a bridge between graph-regularized methods and probabilistic matrix decomposition models for the first time. LGMD incorporates two graphical structures (i.e., two precision matrices) learned in an iterative manner via sparse precision matrix estimation and is more robust to noise and missing entries. Extensive numerical results and comparison with competing methods demonstrate its effectiveness.

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Section: Discussionmentioning

confidence: 99%

Learnable Graph-Regularization for Matrix Decomposition

Zhai

Zhang

2023

ACM Trans. Knowl. Discov. Data

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Sparse Quadratic Approximation for Graph Learning

Pasadakis

Bollhöfer

Schenk

2023

IEEE Trans. Pattern Anal. Mach. Intell.

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Algorithm 1042: Sparse Precision Matrix Estimation with `SQUIC`

Eftekhari,

Gaedke-Merzhäuser,

Pasadakis

et al. 2024

ACM Trans. Math. Softw.

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We present SQUIC , a fast and scalable package for sparse precision matrix estimation. The algorithm employs a second-order method to solve the \(\ell_{1}\) -regularized maximum likelihood problem, utilizing highly optimized linear algebra subroutines. In comparative tests using synthetic datasets, we demonstrate that SQUIC not only scales to datasets of up to a million random variables but also consistently delivers run times that are significantly faster than other well-established sparse precision matrix estimation packages. Furthermore, we showcase the application of the introduced package in classifying microarray gene expressions. We demonstrate that by utilizing a matrix form of the tuning parameter (also known as the regularization parameter), SQUIC can effectively incorporate prior information into the estimation procedure, resulting in improved application results with minimal computational overhead.

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Block-enhanced precision matrix estimation for large-scale datasets

Cited by 4 publications

References 20 publications

Learnable Graph-Regularization for Matrix Decomposition

Learnable Graph-Regularization for Matrix Decomposition

Sparse Quadratic Approximation for Graph Learning

Algorithm 1042: Sparse Precision Matrix Estimation with `SQUIC`

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Block-enhanced precision matrix estimation for large-scale datasets

Cited by 4 publications

References 20 publications

Learnable Graph-Regularization for Matrix Decomposition

Learnable Graph-Regularization for Matrix Decomposition

Sparse Quadratic Approximation for Graph Learning

Algorithm 1042: Sparse Precision Matrix Estimation with SQUIC

Contact Info

Product

Resources

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Algorithm 1042: Sparse Precision Matrix Estimation with `SQUIC`