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


Ex Input:
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.

Ex Output:
Risk and Regret of Hierarchical Bayesian Learners


Ex Input:
The Internet of Things is arriving to our homes or cities through fields already known like Smart Homes, Smart Cities, or Smart Towns. The monitoring of environmental conditions of cities can help to adapt the indoor locations of the cities in order to be more comfortable for people who stay there. A way to improve the indoor conditions is an efficient temperature control, however, it depends on many factors like the different combinations of outdoor temperature and humidity. Therefore, adjusting the indoor temperature is not setting a value according to other value. There are many more factors to take into consideration, hence the traditional logic based in binary states cannot be used. Many problems cannot be solved with a set of binary solutions and we need a new way of development. Fuzzy logic is able to interpret many states, more than two states, giving to computers the capacity to react in a similar way to people. In this paper we will propose a new approach to control the temperature using the Internet of Things together its platforms and fuzzy logic regarding not only the indoor temperature but also the outdoor temperature and humidity in order to save energy and to set a more comfortable environment for their users. Finally, ∗Corresponding author Email addresses: danielmeanallorian@gmail.com (Daniel Meana-Llorián), gonzalezgarciacristian@hotmail.com (Cristian González Garćıa), crispelayo@uniovi.es (B. Cristina Pelayo G-Bustelo), cueva@uniovi.es (Juan Manuel Cueva Lovelle), nestor@uniovi.es (Nestor Garcia-Fernandez)

Ex Output:

IoFClime: The fuzzy logic and the Internet of Things to control indoor temperature regarding the outdoor ambient conditions