Robust and sparse estimation of large precision matrices

The thesis considers the estimation of sparse precision matrices in the highdimensional setting. First, we introduce an integrated approach to estimate undirected graphs and to perform model selection in high-dimensional Gaussian Graphical Models (GGMs). The approach is based on a parametrization of the inverse covariance matrix in terms of the prediction errors of the best linear predictor of each node in the graph. We exploit the relationship between partial correlation coefficients and the distribution of the prediction errors to propose a novel forward-backward algorithm for detecting pairs of variables having nonzero partial correlations among a large number of random variables based on i.i.d. samples. Then, we are able to establish asymptotic properties under mild conditions. Finally, numerical studies through simulation and real data examples provide evidence of the practical advantage of the procedure, where the proposed approach outperforms state-of-the-art methods such as the Graphical lasso and CLIME under different settings. Furthermore, we study the problem of robust estimation of GGMs in the highdimensional setting when the data may contain outlying observations. We propose a robust precision matrix estimator under the cellwise contamination mechanism that is robust against structural bivariate outliers. This framework exploits robust pairwise weighted correlation coefficient estimates, where the weights are computed by the Mahalanobis distance with respect to an affine equivariant robust correlation coefficient estimator. We show that the convergence rate of the proposed estimator is the same as the correlation coefficient used to compute the Mahalanobis distance. We conduct numerical simulation under different contamination settings to compare the graph recovery performance of different robust estimators. The proposed method is then applied to the classiffication of tumors using gene expression data. We show that our procedure can effectively recover the true graph under cellwise data contamination.Programa Oficial de Doctorado en Economía de la Empresa y Métodos CuantitativosPresidente: José Manuel Mira Mcwilliams; Secretario: Andrés Modesto Alonso Fernández; Vocal: José Ramón Berrendero Día

Robust and sparse estimation of high-dimensional precision matrices via bivariate outlier detection

Robust estimation of Gaussian Graphical models in the high-dimensional setting is becoming increasingly important since large and real data may contain outlying observations. These outliers can lead to drastically wrong inference on the intrinsic graph structure. Several procedures apply univariate transformations to make the data Gaussian distributed. However, these transformations do not work well under the presence of structural bivariate outliers. We propose a robust precision matrix estimator under the cellwise contamination mechanism that is robust against structural bivariate outliers. This estimator exploits robust pairwise weighted correlation coefficient estimates, where the weights are computed by the Mahalanobis distance with respect to an affine equivariant robust correlation coefficient estimator. We show that the convergence rate of the proposed estimator is the same as the correlation coefficient used to compute the Mahalanobis distance. We conduct numerical simulation under different contamination settings to compare the graph recovery performance of different robust estimators. Finally, the proposed method is then applied to the classification of tumors using gene expression data. We show that our procedure can effectively recover the true graph under cellwise data contamination.Acknowledgements: the authors acknowledge financial support from the Spanish Ministry of Education and Science, research project MTM2013-44902-P

Ranking Edges and Model Selection in High-Dimensional Graphs

In this article we present an approach to rank edges in a network modeled through a Gaussian Graphical Model. We obtain a path of precision matrices such that, in each step of the procedure, an edge is added. We also guarantee that the matrices along the path are symmetric and positive definite. To select the edges, we estimate the covariates that have the largest absolute correlation with a node conditional to the set of edges estimated in previous iterations. Simulation studies show that the procedure is able to detect true edges until the sparsity level of the population network is recovered. Moreover, it can add efficiently true edges in the first iterations avoiding to enter false ones. We show that the top-rank edges are associated with the largest partial correlated variables. Finally, we compare the graph recovery performance with that of Glasso under different settings.The research of Ginette Lafit and Francisco J. Nogales is supported by the Spanish Government through project MTM2013-44902-

An investigation into the factor structure of the Attitudes to Suicide Prevention Scale

Aim: The aim of this study was to investigate the factor structure of the Attitudes to Suicide Prevention Scale (ASPS). Method: The ASPS was distributed to all staff in a UK National Health Service Trust (N = 957). We conducted an exploratory factor analysis followed by a confirmatory factor analysis by splitting the data 60/40 into training and testing subsets. A multiple regression analysis was carried out to investigate whether the overall scale score varied as a function of professional role, age, and gender and whether respondents had completed suicide prevention training or not. Results: Two items displaying poor item-scale correlation were excluded from the factor analysis and a further item was excluded as it was based on different anchor points. For the remaining 11 items, no adequate factor structure emerged. The scale total demonstrated statistically significant differences in attitudes between staff groups (defined by attendance at suicide awareness or prevention training, by gender, and by level of patient contact), but not between groups defined by age range. Generally, however, there were positive attitudes across all Trust staff. Limitations: This study had a low response rate (24%) and was cross-sectional which limits the conclusions that could be drawn. Furthermore, other areas such as convergent validity and test–retest reliability were not examined. Conclusion: Our findings found no satisfactory factor structure for the ASPS. Further scale development would be beneficial

Investigating real-time social interaction in pairs of adolescents with the Perceptual Crossing Experiment

The study of real-time social interaction provides ecologically valid insight into social behavior. The objective of the current research is to experimentally assess real-time social contingency detection in an adolescent population, using a shortened version of the Perceptual Crossing Experiment (PCE). Pairs of 148 adolescents aged between 12 and 19 were instructed to find each other in a virtual environment interspersed with other objects by interacting with each other using tactile feedback only. Across six rounds, participants demonstrated increasing accuracy in social contingency detection, which was associated with increasing subjective experience of the mutual interaction. Subjective experience was highest in rounds when both participants were simultaneously accurate in detecting each other\u27s presence. The six-round version yielded comparable social contingency detection outcome measures to a ten-round version of the task. The shortened six-round version of the PCE has therefore enabled us to extend the previous findings on social contingency detection in adults to an adolescent population, enabling implementation in prospective research designs to assess the development of social contingency detection over time

Emotion regulation in response to daily negative and positive events in youth:The role of event intensity and psychopathology

Environmental and individual contextual factors profoundly influence how people regulate their emotions. The current article addresses the role of event intensity and psychopathology (an admixture of depression, anxiety, and psychoticism) on emotion regulation in response to naturally occurring events. For six days each evening, a youth sample (aged 15-25, N = 713) recorded the intensity of the most positive and most negative event of the day and their subsequent emotion regulation. The intensity of negative events was positively associated with summed total emotion regulation effort, strategy diversity, engaging in rumination, situation modification, emotion expression, and sharing and negatively associated with reappraisal and acceptance. The intensity of positive events was positively associated with strategy diversity, savoring, emotion expression, and sharing. Higher psychopathology symptoms were only related to ruminating more about negative events. We interpret these findings as support for the role of context in the degree of effort and type of emotion regulation that young people engage in

Capacity for social contingency detection continues to develop across adolescence

The capacity for dynamically coordinating behaviour is assumed to have largely matured in infancy. In adolescence—another sensitive period for social development—the primary focus on individual social cognition as the main driver of interaction has prevented the study of actual social interaction as behavioural coordination within dyads. From a dynamic perspective, however, capturing real-time social dynamics is essential for the assessment of social interactive processes. In order to improve the understanding of social development during adolescence, we investigated the potential developmental course of social contingency detection in dynamic interactions. Pairs of 205 Belgian adolescents (83 male, 122 female), aged 11–19, engaged in real-time social interaction via the Perceptual Crossing Experiment (PCE). Comparing early, middle and late adolescents, we found a generally higher performance of late adolescents on behavioural and cognitive measures of social contingency detection, while the reported awareness of the implicitly established social interaction was lower in this group overall. Additionally, late adolescents demonstrated faster improvement of behavioural social coordination throughout the experiment, compared with the other groups. Our results indicate that social interactive processes continue to develop throughout adolescence, which manifests as faster social coordination at the behavioural level. This finding underscores dynamic social interaction within dyads as a new opportunity for identifying altered social development during adolescence

El impacto de las crisis financieras internacionales en las economías emergentes y el desempeño de las políticas fiscales discrecionales: El caso de Argentina

Although international crises partially accounted for the recent weakArgentine economic performance, main causes have to be sought in domesticeconomic policies adding uncertainty to the decision process of economicsectors and amplifying crises’ effects. Government revenues exhibiteda positive, though decreasing, evolution explained by a contraction oftax revenues despite transfers from the eliminated Private Pension Systemand IMF`s special draw rights. However, public spending was in the rootof the government’s fi scal strain as their growth rate outweighed that ofrevenues and caused an erosion of the primary surplus, whose present levelartifi cially stemmed from exceptional revenue fl ows and the discretionaryseizing of pension funds. Finally, although the overall cyclical sensitivity of tax revenues increased, budget balance’s response to GDP did not suffi ce tocheck cycles and active fi scal policies had to strengthen stabilizing actions.Si bien las crisis internacionales explican parcialmente el débil desempeñoeconómico argentino reciente, las políticas económicas domésticas aumentaronla incertidumbre en los procesos de decisión económica y amplificaronlos efectos de las crisis. Los ingresos públicos exhibieron una evoluciónpositiva, aunque decreciente, por la contracción de los ingresos tributarios, apesar de la transferencia del eliminado Régimen Privado de Pensiones y laentrada de derechos especiales de giro. Sin embargo, las dificultades fiscalesse debieron en gran medida al gasto público, cuya tasa de crecimiento superóa la de los ingresos y erosionó el superávit primario, cuyo nivel actualartificial responde a ingresos excepcionales y a la transferencia de los fondosde pensión. Finalmente, aunque la sensibilidad cíclica total de los ingresosimpositivos creció, la respuesta del saldo presupuestario al producto noalcanzó a compensar los ciclos, y debieron usarse políticas fiscales activaspara fortalecer las acciones de estabilización