For correctly specified latent tree graphical models, we show that a global optimum of the optimization problem can be obtained via a recursive decomposition algorithm. This algorithm recovers previous spectral algorithms for hidden Markov models (Hsu et al., 2009; Foster et al., 2012) and latent tree graphical models (Parikh et al., 2011; Song et al., 2011) as special cases, elucidating the global objective these algorithms are optimizing. For misspecified latent tree graphical models, we derive a novel decomposition based on our framework, and provide approximation guarantee and computational complexity analysis. In both synthetic and real world data, this new estimator significantly improves over the state-of-the-art.
