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.

Q: Marginal MAP inference involves making MAP predictions in systems defined<lb>with latent variables or missing information. It is significantly more difficult than<lb>pure marginalization and MAP tasks, for which a large class of efficient and con-<lb>vergent variational algorithms, such as dual decomposition, exist. In this work, we<lb>generalize dual decomposition to a generic power sum inference task, which in-<lb>cludes marginal MAP, along with pure marginalization and MAP, as special cases.<lb>Our method is based on a block coordinate descent algorithm on a new convex<lb>decomposition bound, that is guaranteed to converge monotonically, and can be<lb>parallelized efficiently. We demonstrate our approach on marginal MAP queries<lb>defined on real-world problems from the UAI approximate inference challenge,<lb>showing that our framework is faster and more reliable than previous methods.

A: Decomposition Bounds for Marginal MAP
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Q: We develop a new semantics for defeasible infer­ ence based on extended probability measures al­ lowed to take infinitesimal values, on the inter­ pretation of defaults as generalized conditional probability constraints and on a preferred-model implementation of entropy-maximization.

A: Defaults and lnfinitesimals Defeasible Inference by Nonarchimedean Entropy Maximization
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Q: The Support Vector Machine using Privileged Information (SVM+) has been proposed to train a classifier to utilize the additional privileged information that is only available in the training phase but not available in the test phase. In this work, we propose an efficient solution for SVM+ by simply utilizing the squared hinge loss instead of the hinge loss as in the existing SVM+ formulation, which interestingly leads to a dual form with less variables and in the same form with the dual of the standard SVM. The proposed algorithm is utilized to leverage the additional web knowledge that is only available during training for the image categorization tasks. The extensive experimental results on both Caltech101 and WebQueries datasets show that our proposed method can achieve a factor of up to hundred times speedup with the comparable accuracy when compared with the existing SVM+ method.

A:
Simple and Efficient Learning using Privileged Information
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