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: Common statistical practice has shown that the full power of Bayesian methods is not realized until hierarchical priors are used, as these allow for greater “robustness” and the ability to “share statistical strength.” Yet it is an ongoing challenge to provide a learning-theoretically sound formalism of such notions that: offers practical guidance concerning when and how best to utilize hierarchical models; provides insights into what makes for a good hierarchical prior; and, when the form of the prior has been chosen, can guide the choice of hyperparameter settings. We present a set of analytical tools for understanding hierarchical priors in both the online and batch learning settings. We provide regret bounds under log-loss, which show how certain hierarchical models compare, in retrospect, to the best single model in the model class. We also show how to convert a Bayesian log-loss regret bound into a Bayesian risk bound for any bounded loss, a result which may be of independent interest. Risk and regret bounds for Student’s t and hierarchical Gaussian priors allow us to formalize the concepts of “robustness” and “sharing statistical strength.” Priors for feature selection are investigated as well. Our results suggest that the learning-theoretic benefits of using hierarchical priors can often come at little cost on practical problems.

Answer: Risk and Regret of Hierarchical Bayesian Learners


Question: The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it avoids projections the computational bottleneck in many applications replacing it by a linear optimization step. Despite this advantage, the known convergence rates of the FW method fall behind standard first order methods for most settings of interest. It is an active line of research to derive faster linear optimization-based algorithms for various settings of convex optimization. In this paper we consider the special case of optimization over strongly convex sets, for which we prove that the vanila FW method converges at a rate of 1 t2 . This gives a quadratic improvement in convergence rate compared to the general case, in which convergence is of the order 1t , and known to be tight. We show that various balls induced by `p norms, Schatten norms and group norms are strongly convex on one hand and on the other hand, linear optimization over these sets is straightforward and admits a closed-form solution. We further show how several previous fastrate results for the FW method follow easily from our analysis.

Answer: Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets


Question: We present a factorized compositional distributional semantics model for the representation of transitive verb constructions. Our model first produces (subject, verb) and (verb, object) vector representations based on the similarity of the nouns in the construction to each of the nouns in the vocabulary and the tendency of these nouns to take the subject and object roles of the verb. These vectors are then combined into a final (subject,verb,object) representation through simple vector operations. On two established tasks for the transitive verb construction our model outperforms recent previous work.

Answer:
A Factorized Model for Transitive Verbs in Compositional Distributional Semantics