# On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series

@article{Tugnait2022OnSH,
title={On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series},
author={Jitendra Tugnait},
journal={Signal Process.},
year={2022},
volume={197},
pages={108539}
}

## References

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• Jitendra Tugnait
• Computer Science, Mathematics
2018 52nd Asilomar Conference on Signals, Systems, and Computers
• 2018
A novel formulation of joint graphical lasso in frequency domain, suitable for dependent time series, generalizing current time-domain approaches to i.i.d. time series is presented.

### Consistency of Sparse-Group Lasso Graphical Model Selection for Time Series

• Jitendra Tugnait
• Computer Science, Mathematics
2020 54th Asilomar Conference on Signals, Systems, and Computers
• 2020
Enough conditions are established for consistency of the inverse PSD estimator resulting from the sparse-group graphical lasso-based approach to inferring the conditional independence graph of a high-dimensional stationary multivariate Gaussian time series.

### Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach

• A. Jung
• Computer Science
IEEE Transactions on Signal Processing
• 2015
The proposed inference scheme works even for sample sizes much smaller than the number of scalar process components if the true underlying CIG is sufficiently sparse and a theoretical performance analysis provides sufficient conditions on the sample size such that the new method is consistent asymptotically.

### Compressive nonparametric graphical model selection for time series

• Computer Science, Mathematics
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 2014
This work provides analytical conditions for the method to correctly identify the CIG of a high-dimensional discrete-time Gaussian vector random process from finite-length observations and assumes certain spectral smoothness properties.

### On Sparse Complex Gaussian Graphical Model Selection

• Jitendra Tugnait
• Computer Science, Mathematics
2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)
• 2019
The focus of this paper is on theoretical analysis of a recently proposed graphical lasso approach based on an $\ell_{1} -$penalized log-likelihood objective function to estimate the sparse inverse covariance matrix.

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• Computer Science, Mathematics
• 2008
A method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings using a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty is proposed.

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• Computer Science, Mathematics
UAI
• 2015
This work takes a Bayesian approach to structure learning, placing priors on (i) the graph structure and (ii) spectral matrices given the graph, and uses a Whittle likelihood approximation and a conjugate prior to define a hyper complex inverse Wishart on the complex-valued and graph-constrained spectralMatrices.

### Learning graphical models for stationary time series

• Computer Science
IEEE Transactions on Signal Processing
• 2004
This paper describes an algorithm for efficient forecasting for stationary Gaussian time series whose spectral densities factorize in a graphical model and shows how to make use of Mercer kernels in this setting, allowing the ideas to be extended to nonlinear models.

### An Efficient Approach to Graphical Modeling of Time Series

• Computer Science
IEEE Transactions on Signal Processing
• 2015
It is shown that reformulation in terms of a multiple hypothesis test reduces computation time by O(p2) and simulations support the assertion that power levels are attained at least as good as those achieved by Matsuda's much slower approach.

### On the Sample Complexity of Graphical Model Selection From Non-Stationary Samples

• Computer Science, Mathematics
IEEE Transactions on Signal Processing
• 2020
A sufficient condition on the required sample size for accurate graphical model selection based on non-stationary data is derived by analyzing a conceptually simple model selection method.