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.
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Question: <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.

Answer: The Fast Convergence of Incremental PCA

Question: A pseudo independent (PI) model is a proba bilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a single link search. Earlier work on learning PI models has sug gested a straightforward multi-link search al gorithm. However, when a domain contains recursively embedded PI submodels, it may escape the detection of such an algorithm. In this paper, we propose an improved al gorithm that ensures the learning of all em bedded PI submodels whose sizes are upper bounded by a predetermined parameter. We show that this improved learning capability only increases the complexity slightly beyond that of the previous algorithm. The perfor mance of the new algorithm is demonstrated through experiment.

Answer: Learning Belief Networks in Domains with Recursively Embedded Pseudo Independent Submodels

Question: We extend the theory of boosting for regression problems to the online learning setting. Generalizing from the batch setting for boosting, the notion of a weak learning algorithm is modeled as an online learning algorithm with linear loss functions that competes with a base class of regression functions, while a strong learning algorithm is an online learning algorithm with smooth convex loss functions that competes with a larger class of regression functions. Our main result is an online gradient boosting algorithm that converts a weak online learning algorithm into a strong one where the larger class of functions is the linear span of the base class. We also give a simpler boosting algorithm that converts a weak online learning algorithm into a strong one where the larger class of functions is the convex hull of the base class, and prove its optimality.

Answer:
Online Gradient Boosting