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.

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

We introduce an abductive method for a coherent integration of independent datasources. The idea is to compute a list of data-facts that should be inserted to the amalgamated database or retracted from it in order to restore its consistency. This method is implemented by an abductive solver, called Asystem, that applies SLDNFA-resolution on a meta-theory that relates different, possibly contradicting, input databases. We also give a pure model-theoretic analysis of the possible ways to ‘recover’ consistent data from an inconsistent database in terms of those models of the database that exhibit as minimal inconsistent information as reasonably possible. This allows us to characterize the ‘recovered databases’ in terms of the ‘preferred’ (i.e., most consistent) models of the theory. The outcome is an abductive-based application that is sound and complete with respect to a corresponding model-based, preferential semantics, and – to the best of our knowledge – is more expressive (thus more general) than any other implementation of coherent integration of databases.
Coherent Integration of Databases by Abductive Logic Programming

Decision making in uncertain and risky environments is a prominent area of research. Standard economic theories fail to fully explain human behaviour, while a potentially promising alternative may lie in the direction of Reinforcement Learning (RL) theory. We analyse data for 46 players extracted from a financial market online game and test whether Reinforcement Learning (Q-Learning) could capture these players behaviour using a risk measure based on financial modeling. Moreover we test an earlier hypothesis that players are “naı̈ve” (short-sighted). Our results indicate that a simple Reinforcement Learning model which considers only the selling component of the task captures the decision-making process for a subset of players but this is not sufficient to draw any conclusion on the population. We also find that there is not a significant improvement of fitting of the players when using a full RL model against a myopic version, where only immediate reward is valued by the players. This indicates that players, if using a Reinforcement Learning approach, do so naı̈vely.

Modelling Stock-market Investors as Reinforcement Learning Agents [Correction]