Summary of Learning Sparse High-dimensional Matrix-valued Graphical Models From Dependent Data, by Jitendra K Tugnait
Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data
by Jitendra K Tugnait
First submitted to arxiv on: 29 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Signal Processing (eess.SP)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A novel approach is proposed to infer the conditional independence graph (CIG) of high-dimensional, sparse, and stationary matrix-variate Gaussian time series with dependent observations. Unlike previous work in high-dimensional matrix graphical models, which assumes independent and identically distributed (i.i.d.) observations, this method allows for dependent observations. A frequency-domain formulation is developed using a sparse-group lasso-based approach, solved via an alternating direction method of multipliers (ADMM) algorithm. The problem is bi-convex, requiring flip-flop optimization to converge. Sufficient conditions are provided for local convergence in the Frobenius norm of inverse PSD estimators to their true values, along with a rate of convergence. Numerical examples demonstrate the effectiveness of this approach using both synthetic and real data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Inferring the conditional independence graph (CIG) of high-dimensional data is an important problem. Usually, we assume that each observation is independent and identical, but what if they’re not? A new way to solve this problem has been discovered, allowing dependent observations. This method uses a special type of math called sparse-group lasso and solves it using a clever algorithm called ADMM. The result shows that the method works well for both fake and real data. |
Keywords
» Artificial intelligence » Optimization » Time series
