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.

<lb>We consider a situation in which we see samples Xn ∈ R drawn i.i.d. from some<lb>distribution with mean zero and unknown covariance A. We wish to compute the<lb>top eigenvector of A in an incremental fashion with an algorithm that maintains<lb>an estimate of the top eigenvector in O(d) space, and incrementally adjusts the<lb>estimate with each new data point that arrives. Two classical such schemes are<lb>due to Krasulina (1969) and Oja (1983). We give finite-sample convergence rates<lb>for both.
The Fast Convergence of Incremental PCA

We develop a probabilistic latent-variable model to discover semantic frames—types of events and their participants—from corpora. We present a Dirichlet-multinomial model in which frames are latent categories that explain the linking of verb-subject-object triples, given document-level sparsity. We analyze what the model learns, and compare it to FrameNet, noting it learns some novel and interesting frames. This document also contains a discussion of inference issues, including concentration parameter learning; and a small-scale error analysis of syntactic parsing accuracy. Note: this work was originally posted online October 2012 as part of CMU MLD’s Data Analysis Project requirement. This version has no new experiments or results, but has added some discussion of new related work.
Learning Frames from Text with an Unsupervised Latent Variable Model

This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture models, FAB for HMMs is derived as an iterative lower bound maximization algorithm of a factorized information criterion (FIC). It inherits, from FAB for mixture models, several desirable properties for learning HMMs, such as asymptotic consistency of FIC with marginal log-likelihood, a shrinkage effect for hidden state selection, monotonic increase of the lower FIC bound through the iterative optimization. Further, it does not have a tunable hyper-parameter, and thus its model selection process can be fully automated. Experimental results shows that FAB outperforms states-of-the-art variational Bayesian HMM and non-parametric Bayesian HMM in terms of model selection accuracy and computational efficiency.

Factorized Asymptotic Bayesian Hidden Markov Models