Teacher: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.
Teacher: Now, understand the problem? Solve this instance: We develop a latent variable model and an efficient spectral algorithm motivated<lb>by the recent emergence of very large data sets of chromatin marks from multiple<lb>human cell types. A natural model for chromatin data in one cell type is a Hidden<lb>Markov Model (HMM); we model the relationship between multiple cell types by<lb>connecting their hidden states by a fixed tree of known structure.<lb>The main challenge with learning parameters of such models is that iterative meth-<lb>ods such as EM are very slow, while naive spectral methods result in time and<lb>space complexity exponential in the number of cell types. We exploit properties<lb>of the tree structure of the hidden states to provide spectral algorithms that are<lb>more computationally efficient for current biological datasets. We provide sample<lb>complexity bounds for our algorithm and evaluate it experimentally on biological<lb>data from nine human cell types. Finally, we show that beyond our specific model,<lb>some of our algorithmic ideas can be applied to other graphical models.
Student:
Spectral Learning of Large Structured HMMs for Comparative Epigenomics