Reviews: Algebraic tests of general Gaussian latent tree models

Paper Summary: The paper presents a technique for testing whether a given set of samples are drawn from a postulated Gaussian latent tree model or a saturated Gaussian graphical model. The paper first characterizes a set of necessary and sufficient constraints that any covariance matrix of a Gaussian latent tree model should satisfy. It then uses these constraints to come up with a test statistic. The paper extends past work on testing for Gaussian latent tree models to settings where the observed variables are allowed to have degree up to 2. The test statistic presented in the paper is based on gaussian approximation for maxima of high dimensional sums. Simulations suggest that the test statistic can potentially work in high dimensional settings.