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

Facial regulation during dyadic interaction: interpersonal effects on cooperation

This study investigated interpersonal effects of regulating naturalistic facial signals on cooperation during an iterative Prisoner’s Dilemma (IPD) game. Fifty pairs of participants played ten IPD rounds across a video link then reported on their own and their partner’s expressed emotion and facial regulation in a video-cued recall (VCR) procedure. iMotions software allowed us to auto-code actors’ and partners’ facial activity following the outcome of each round. We used two-level mixed effects logistic regression to assess over-time actor and partner effects of auto-coded facial activity, self-reported facial regulation, and perceptions of the partner’s facial regulation on the actor’s subsequent cooperation. Actors were significantly less likely to cooperate when their partners had defected on the previous round. None of the lagged scores based on auto-coded facial activity were significant predictors of cooperation. However, VCR variables representing partner’s positive regulation of expressions and actor’s perception of partner’s positive regulation both significantly increased the probability of subsequent actor cooperation after controlling for prior defection. These results offer preliminary evidence about interpersonal effects of facial regulation in interactive contexts and illustrate how dynamic dyadic emotional processes can be systematically investigated in controlled settings

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-

Is daily-life stress reactivity a measure of stress recovery? An investigation of laboratory and daily-life stress

Typical measures of laboratory reactivity (i.e. difference between control and stress) and recovery (i.e. difference between stress and post-stress) were compared with a conventional measure of daily-life reactivity, best known as event-related stress. Fifty-three healthy individuals between 19 and 35 years of age took part in a laboratory session where stress was induced using the repeated Montreal Imaging Stress Task and 8 days of experience sampling method. Measures of negative affect, heart rate (HR), HR variability, and skin conductance level were collected. Findings show no strong associations between laboratory and daily life measures with the exception of laboratory affective recovery and daily life reactivity. Findings and their implications are discussed.</p

Oxytocin and state attachment responses to secure base support after stress in middle childhood

We tried to replicate the finding that receiving care increases children’s oxytocin and secure state attachment levels, and tested whether secure trait attachment moderates the oxytocin and state attachment response to care. 109 children (9-11 years old; M = 9.59; SD = 0.63; 34.9% boys) participated in a within-subject experiment. After stress induction (Trier Social Stress Test), children first remained alone and then received maternal secure base support. Salivary oxytocin was measured eight times. Secure trait and state attachment were measured with questionnaires, and Secure Base Script knowledge was assessed. Oxytocin levels increased after receiving secure base support from mother after having been alone. Secure state attachment changed less. Trait attachment and Secure Base Script knowledge did not moderate oxytocin or state attachment responses to support. This might mean that, regardless of the attachment history, in-the-moment positive attachment experiences might have a beneficial effect on trait attachment development in middle childhood.info:eu-repo/semantics/publishedVersio

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