Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: <lb>This work considers the problem of learning the structure of multivariate linear tree models, which<lb>include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables<lb>such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolu-<lb>tionary trees. The setting is one where we only have samples from certain observed variables in the tree,<lb>and our goal is to estimate the tree structure (i.e., the graph of how the underlying hidden variables are<lb>connected to each other and to the observed variables). We propose the Spectral Recursive Grouping al-<lb>gorithm, an efficient and simple bottom-up procedure for recovering the tree structure from independent<lb>samples of the observed variables. Our finite sample size bounds for exact recovery of the tree structure<lb>reveal certain natural dependencies on underlying statistical and structural properties of the underlying<lb>joint distribution. Furthermore, our sample complexity guarantees have no explicit dependence on the<lb>dimensionality of the observed variables, making the algorithm applicable to many high-dimensional set-<lb>tings. At the heart of our algorithm is a spectral quartet test for determining the relative topology of a<lb>quartet of variables from second-order statistics.
Output:
Spectral Methods for Learning Multivariate Latent Tree Structure