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Say you have a set of $n$ $p$-dimensional iid samples $\{ \textbf x_i \}_{i=1}^n$ drawn from some unknown continuous distribution that you want to estimate with an undirected graphical model. You can sometimes get away with assuming the $\textbf x_i$’s are drawn from a multivariate normal (MVN), and from there you can use a host of methods for estimating the covariance matrix $\Sigma$, and thus the graph structure $\Omega = \Sigma^{-1}$ (perhaps imposing sparsity constraints for inferring structure in high dimensional data, $n<<p$).

In other cases the Gaussian assumption is too restrictive (e.g. when marginals exhibit multimodal behavior).

One way to augment the expressivity of the MVN while maintaining some of the desirable properties is to assume that some function of the data is MVN. Continue reading “Nonparanormal Activity”