The Goodness of Covariance Selection Problem from AUC Bounds
| Autor: | Anthony Kuh, Navid Tafaghodi Khajavi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Kullback–Leibler divergence Markov chain Covariance matrix Gaussian Model selection Information Theory (cs.IT) Computer Science - Information Theory 02 engineering and technology Covariance 01 natural sciences Toeplitz matrix 010104 statistics & probability symbols.namesake 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics 020201 artificial intelligence & image processing Graphical model 0101 mathematics Mathematics |
| Zdroj: | Allerton |
| Popis: | We conduct a study of graphical models and discuss the quality of model selection approximation by formulating the problem as a detection problem and examining the area under the curve (AUC). We are specifically looking at the model selection problem for jointly Gaussian random vectors. For Gaussian random vectors, this problem simplifies to the covariance selection problem which is widely discussed in literature by Dempster [1]. In this paper, we give the definition for the correlation approximation matrix (CAM) which contains all information about the model selection problem and discuss the pth order Markov chain model and the $p$th order star network model for the a Gaussian distribution with Toeplitz covariance matrix. For each model, we compute the model covariance matrix as well as the KL divergence between the Gaussian distribution and its model. We also show that if the model order, p, is proportional to the number of nodes, n, then the model selection is asymptotically good as the number of nodes, n, goes to infinity since the AUC in this case is bounded away from one. We conduct some simulations which confirm the theoretical analysis and also show that the selected model quality increases as the model order, p, increases. arXiv admin note: substantial text overlap with arXiv:1605.05776 |
| Databáze: | OpenAIRE |
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