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: Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

Answer: Robust Spectral Detection of Global Structures in the Data by Learning a Regularization


Question: We study multi-turn response generation in chatbots where a response is generated according to a conversation context. Existing work has modeled the hierarchy of the context, but does not pay enough attention to the fact that words and utterances in the context are differentially important. As a result, they may lose important information in context and generate irrelevant responses. We propose a hierarchical recurrent attention network (HRAN) to model both aspects in a unified framework. In HRAN, a hierarchical attention mechanism attends to important parts within and among utterances with word level attention and utterance level attention respectively. With the word level attention, hidden vectors of a word level encoder are synthesized as utterance vectors and fed to an utterance level encoder to construct hidden representations of the context. The hidden vectors of the context are then processed by the utterance level attention and formed as context vectors for decoding the response. Empirical studies on both automatic evaluation and human judgment show that HRAN can significantly outperform state-of-the-art models for multi-turn response generation.

Answer: Hierarchical Recurrent Attention Network for Response Generation


Question: The fastest known exact algorithms for scorebased structure discovery in Bayesian networks on n nodes run in time and space 2n. The usage of these algorithms is limited to networks on at most around 25 nodes mainly due to the space requirement. Here, we study space–time tradeoffs for finding an optimal network structure. When little space is available, we apply the Gurevich– Shelah recurrence—originally proposed for the Hamiltonian path problem—and obtain time 2n in space 2n for any s = n/2, n/4, n/8, . . .; we assume the indegree of each node is bounded by a constant. For the more practical setting with moderate amounts of space, we present a novel scheme. It yields running time 2(3/2)n in space 2(3/4)n for any p = 0, 1, . . . , n/2; these bounds hold as long as the indegrees are at most 0.238n. Furthermore, the latter scheme allows easy and efficient parallelization beyond previous algorithms. We also explore empirically the potential of the presented techniques.

Answer:
Exact Structure Discovery in Bayesian Networks with Less Space