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.

Ex Input:
We introduce a new spatial data structure for high dimensional data called the approximate principal direction tree (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy similar to that of computationally-expensive PCA trees with similar time-complexity to that of loweraccuracy RP trees. APD trees use a small number of powermethod iterations to find splitting planes for recursively partitioning the data. As such they provide a natural trade-off between the running-time and accuracy achieved by RP and PCA trees. Our theoretical results establish a) strong performance guarantees regardless of the convergence rate of the powermethod and b) that O(log d) iterations suffice to establish the guarantee of PCA trees when the intrinsic dimension is d. We demonstrate this trade-off and the efficacy of our data structure on both the CPU and GPU.

Ex Output:
Approximate Principal Direction Trees


Ex Input:
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.

Ex Output:
Decomposition Bounds for Marginal MAP


Ex Input:
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in sparsityrelated techniques. We cast the problem, resembling group or collaborative sparsity formulations, as a non-smooth convex optimization problem that can be efficiently solved using augmented Lagrangian techniques. The method can deal with weighted or unweighted graphs, as well as multimodal data, where different graphs represent different types of data. The proposed approach is also naturally integrated with collaborative graph inference techniques, solving general network inference problems where the observed variables, possibly coming from different modalities, are not in correspondence. The algorithm is tested and compared with state-of-the-art graph matching techniques in both synthetic and real graphs. We also present results on multimodal graphs and applications to collaborative inference of brain connectivity from alignment-free functional magnetic resonance imaging (fMRI) data. The code is publicly available.

Ex Output:

Robust Multimodal Graph Matching: Sparse Coding Meets Graph Matching