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 Q]: 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.
[EX A]: Robust Spectral Detection of Global Structures in the Data by Learning a Regularization

[EX Q]: In this paper, we introduce a new deep convolutional neural network (ConvNet) module that promotes competition among a set of multi-scale convolutional filters. This new module is inspired by the inception module, where we replace the original collaborative pooling stage (consisting of a concatenation of the multi-scale filter outputs) by a competitive pooling represented by a maxout activation unit. This extension has the following two objectives: 1) the selection of the maximum response among the multi-scale filters prevents filter co-adaptation and allows the formation of multiple sub-networks within the same model, which has been shown to facilitate the training of complex learning problems; and 2) the maxout unit reduces the dimensionality of the outputs from the multi-scale filters. We show that the use of our proposed module in typical deep ConvNets produces classification results that are either better than or comparable to the state of the art on the following benchmark datasets: MNIST, CIFAR-10, CIFAR-100 and SVHN.
[EX A]: Competitive Multi-scale Convolution

[EX Q]: Conditional independence and Markov prop erties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As mul tidimensional possibilistic models have been studied for several years, the demand for analogous tools in possibility theory seems to be quite natural. This paper is intended to be a promotion of de Cooman's measure theoretic approach to possibility theory, as this approach allows us to find analogies to many important results obtained in prob abilistic framework. First we recall semi graphoid properties of conditional possibilis tic independence, parameterized by a contin uous t-norm, and find sufficient conditions for a class of Archimedean t-norms to have the graphoid property. Then we introduce Markov properties and factorization of possi bility distributions (again parameterized by a continuous t-norm) and find the relation ships between them. These results are ac companied by a number of counterexamples, which show that the assumptions of specific theorems are substantial.
[EX A]:
Conditional Independence and Markov Properties in Possibility Theory