Vicenç Gómez

Statistical analysis of the social network and discussion threads in slashdot

We analyze the social network emerging from the user comment activity on the website Slashdot. The network presents common features of traditional social networks such as a giant component, small average path length and high clustering, but differs from them showing moderate reciprocity and neutral assortativity by degree. Using Kolmogorov-Smirnov statistical tests, we show that the degree distributions are better explained by log-normal instead of power-law distributions. We also study the structure of discussion threads using an intuitive radial tree representation. Threads show strong heterogeneity and self-similarity throughout the different nesting levels of a conversation. We use these results to propose a simple measure to evaluate the degree of controversy provoked by a post.

Description and Prediction of Slashdot Activity

We perform a statistical analysis of users reaction time to a new discussion thread in online debates on the popular news site Slashdot. First, we show with Kolmogorov-Smirnov tests that a mixture of two log-normal distributions combined with the circadian rhythm of the community is able to explain with surprising accuracy the reaction time of comments within a discussion thread. Second, this characterization allows to predict intermediate and long-term user behavior with acceptable precision. The prediction method is based on activity-prototypes, which consist of a mixture of two log-normal distributions, and represent the average activity in a particular region of the circadian cycle.

Modeling the structure and evolution of discussion cascades

We analyze the structure and evolution of discussion cascades in four popular websites: Slashdot, Barrapunto, Meneame and Wikipedia. Despite the big heterogeneities between these sites, a preferential attachment (PA) model with bias to the root can capture the temporal evolution of the observed trees and many of their statistical properties, namely, probability distributions of the branching factors (degrees), subtree sizes and certain correlations. The parameters of the model are learned efficiently using a novel maximum likelihood estimation scheme for PA and provide a figurative interpretation about the communication habits and the resulting discussion cascades on the four different websites.

On the use of interaction error potentials for adaptive brain computer interfaces

We propose an adaptive classification method for the Brain Computer Interfaces (BCI) which uses Interaction Error Potentials (IErrPs) as a reinforcement signal and adapts the classifier parameters when an error is detected. We analyze the quality of the proposed approach in relation to the misclassification of the IErrPs. In addition we compare static versus adaptive classification performance using artificial and MEG data. We show that the proposed adaptive framework significantly improves the static classification methods.

Learning price-elasticity of smart consumers in power distribution systems

Demand Response is an emerging technology which will transform the power grid of tomorrow. It is revolutionary, not only because it will enable peak load shaving and will add resources to manage large distribution systems, but mainly because it will tap into an almost unexplored and extremely powerful pool of resources comprised of many small individual consumers on distribution grids. However, to utilize these resources effectively, the methods used to engage these resources must yield accurate and reliable control. A diversity of methods have been proposed to engage these new resources. As opposed to direct load control, many methods rely on consumers and/or loads responding to exogenous signals, typically in the form of energy pricing, originating from the utility or system operator. Here, we propose an open loop communication-lite method for estimating the price elasticity of many customers comprising a distribution system. We utilize a sparse linear regression method that relies on operator-controlled, inhomogeneous minor price variations, which will be fair to all the consumers. Our numerical experiments show that reliable estimation of individual and thus aggregated instantaneous elasticities is possible. We describe the limits of the reliable reconstruction as functions of the three key parameters of the system: (i) ratio of the number of communication slots (time units) per number of engaged consumers; (ii) level of sparsity (in consumer response); and (iii) signal-to-noise ratio.

Adaptive classification on brain-computer interfaces using reinforcement signals

We introduce a probabilistic model that combines a classifier with an extra reinforcement signal (RS) encoding the probability of an erroneous feedback being delivered by the classifier. This representation computes the class probabilities given the task related features and the reinforcement signal. Using expectation maximization (EM) to estimate the parameter values under such a model shows that some existing adaptive classifiers are particular cases of such an EM algorithm. Further, we present a new algorithm for adaptive classification, which we call constrained means adaptive classifier, and show using EEG data and simulated RS that this classifier is able to significantly outperform state-of-the-art adaptive classifiers.

Adaptive multiclass classification for brain computer interfaces

We consider the problem of multiclass adaptive classification for brain-computer interfaces and propose the use of multiclass pooled mean linear discriminant analysis (MPMLDA), a multiclass generalization of the adaptation rule introduced by Vidaurre, Kawanabe, von Bünau, Blankertz, and Müller (2010) for the binary class setting. Using publicly available EEG data sets and tangent space mapping (Barachant, Bonnet, Congedo, & Jutten, 2012) as a feature extractor, we demonstrate that MPMLDA can significantly outperform state-of-the-art multiclass static and adaptive methods. Furthermore, efficient learning rates can be achieved using data from different subjects.

Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons

An ensemble of stochastic nonleaky integrate-and-fire neurons with global, delayed, and excitatory coupling and a small refractory period is analyzed. Simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength. Below the critical coupling production of spikes in the ensemble is governed by the stochastic dynamics, whereas for coupling greater than the critical value, the stochastic dynamics loses its influence and the units organize into several clusters with self-sustained activity. All units within one cluster spike in unison, and the clusters themselves are phase-locked. Theoretical analysis leads to upper and lower bounds for the average interspike interval of the ensemble valid for all possible coupling strengths. The bounds allow calculating the limit behavior for large ensembles and characterize the phase transition analytically. These results may be extensible to pulse-coupled oscillators.

Action selection in growing state spaces: control of network structure growth

The dynamical processes taking place on a network depend on its topology. Influencing the growth process of a network therefore has important implications on such dynamical processes. We formulate the problem of influencing the growth of a network as a stochastic optimal control problem in which a structural cost function penalizes undesired topologies. We approximate this control problem with a restricted class of control problems that can be solved using probabilistic inference methods. To deal with the increasing problem dimensionality, we introduce an adaptive importance sampling method for approximating the optimal control. We illustrate this methodology in the context of formation of information cascades, considering the task of influencing the structure of a growing conversation thread, as in Internet forums. Using a realistic model of growing trees, we show that our approach can yield conversation threads with better structural properties than the ones observed without control.

Generative models of online discussion threads: state of the art and research challenges

Online discussion in form of written comments is a core component of many social media platforms. It has attracted increasing attention from academia, mainly because theories from social sciences can be explored at an unprecedented scale. This interest has led to the development of statistical models which are able to characterize the dynamics of threaded online conversations.In this paper, we review research on statistical modeling of online discussions, in particular, we describe current generative models of the structure and growth of discussion threads. These are parametrized network formation models that are able to generate synthetic discussion threads that reproduce certain features of the real discussions present in different online platforms. We aim to provide a clear overview of the state of the art and to motivate future work in this relevant research field.