The covariance selection quality for graphs with junction trees through AUC bounds
| Autor: | Anthony Kuh, Navid Tafaghodi Khajavi |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematical optimization
Kullback–Leibler divergence Markov chain Covariance function Covariance matrix Model selection Approximation algorithm 02 engineering and technology Covariance 01 natural sciences 010104 statistics & probability 0202 electrical engineering electronic engineering information engineering Applied mathematics 020201 artificial intelligence & image processing Graphical model 0101 mathematics Mathematics |
| Zdroj: | APSIPA |
| DOI: | 10.1109/apsipa.2016.7820837 |
| 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 examine the area under the curve (AUC). We are specifically looking at the model selection problem for jointly Gaussian random vectors. For Gaussian distributions, this problem simplifies to the covariance selection problem which is widely discussed in literature by Dempster [1]. In this paper, we discuss graphical models such as the pth order Markov chain and the pth order star network interpretation which also have junction tree graphical representations and give the definition for the correlation approximation matrix (CAM) which contains all information about the model selection problem. We compute the model covariance matrix as well as the KL divergence between the original distribution and the approximated model distribution. We conduct some simulations which show that the quality of the selected model increases as the model order, p, increases. |
| Databáze: | OpenAIRE |
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