Giang T. Nguyen

Nigel Bean, Giang T. Nguyen, Federico Poloni

Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the literature as the matrix $Ψ$. Here, we present a probabilistic interpretation of the family of algorithms known as \emph{doubling}, which are currently the most effective algorithms for computing the return probability matrix $Ψ$. To this end, we first revisit the links described in \cite{ram99, soares02} between fluid queues and Quasi-Birth-Death processes; in particular, we give new probabilistic interpretations for these connections. We generalize this framework to give a probabilistic meaning for the initial step of doubling algorithms, and include also an interpretation for the iterative step of these algorithms. Our work is the first probabilistic interpretation available for doubling algorithms.

Peter Mathews, Caitlin Gray, Lewis Mitchell et al.

Tweet clustering for event detection is a powerful modern method to automate the real-time detection of events. In this work we present a new tweet clustering approach, using a probabilistic approach to incorporate temporal information. By analysing the distribution of time gaps between tweets we show that the gaps between pairs of related tweets exhibit exponential decay, whereas the gaps between unrelated tweets are approximately uniform. Guided by this insight, we use probabilistic arguments to estimate the likelihood that a pair of tweets are related, and build an improved clustering method. Our method Social Media Event Response Clustering (SMERC) creates clusters of tweets based on their tendency to be related to a single event. We evaluate our method at three levels: through traditional event prediction from tweet clustering, by measuring the improvement in quality of clusters created, and also comparing the clustering precision and recall with other methods. By applying SMERC to tweets collected during a number of sporting events, we demonstrate that incorporating temporal information leads to state of the art clustering performance.