Section: New Results

Trace and Statistical Analysis

Although we often use Markovian approaches to model large scale distributed system, these probabilistic tools can also be used to lay the foundation of statistical analysis of traces of real systems.

• In [36] , we explain how we apply statistical statistical modelling and statistical inference of the ANR GEOMEDIA corpus, that is a collection of international RSS news feeds. Central to this project, RSS news feeds are viewed as a representation of the information in geopolitical space. As such they allow us to study media events of global extent and how they affect international relations. Here we propose hidden Markov models (HMM) as an adequate modelling framework to study the evolution of media events in time. This set of models respect the characteristic properties of the data, such as temporal dependencies and correlations between feeds. Its specific structure corresponds well to our conceptualisation of media attention and media events. We specify the general model structure that we use for modelling an ensemble of RSS news feeds. Finally, we apply the proposed models to a case study dedicated to the analysis of the media attention for the Ebola epidemic which spread through West Africa in 2014.

• The use of stochastic formalisms, such as Stochastic Automata Networks (SAN), can be very useful for statistical prediction and behavior analysis. Once well fitted, such formalisms can generate probabilities about a target reality. These probabilities can be seen as a statistical approach of knowledge discovery. However, the building process of models for real world problems is time consuming even for experienced modelers. Furthermore, it is often necessary to be a domain specialist to create a model. In  [34] , we present a new method to automatically learn simple SAN models directly from a data source. This method is encapsulated in a tool called SAN GEnerator (SANGE). Through examples we show how this new model fitting method is powerful and relatively easy to use, which can grant access to a much broader community to such powerful modeling formalisms.

• In [32] , we have presented our recent results on macroscopic analysis of huge traces of parallel/distributed applications. To identify a macroscopic phenomenon over large traces, one needs to change the representation scale and to aggregate data both in time, space and application structure through meaningful operators to propose multi-scale visualizations. The question is then to know the quantity of information lost by such scaling to be able to correctly interpret them. The principles underlying this approach are based on information theory since the conditional entropy of an aggregation indicates the quantity of information loss when data are aggregated. This approach has been integrated in the Framesoc framework [35] .

• In [27] , We study the problem of making forecasts about the future availability of bicycles in stations of a bike-sharing system (BSS). This is relevant in order to make recommendations guaranteeing that the probability that a user will be able to make a journey is sufficiently high. To this end, we use probabilistic predictions obtained from a queuing theoretical time-inhomogeneous model of a BSS. The model is parametrized and successfully validated using historical data from the Vélib ' BSS of the City of Paris. We develop a critique of the standard root-mean-square-error (RMSE), commonly adopted in the bike-sharing research as an index of the prediction accuracy, because it does not account for the stochasticity inherent in the real system. Instead we introduce a new metric based on scoring rules. We evaluate the average score of our model against classical predictors used in the literature. We show that these are outperformed by our model for prediction horizons of up to a few hours. We also discuss that, in general, measuring the current number of available bikes is only relevant for prediction horizons of up to few hours.