Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings

We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent signals while simultaneously achieving state-of-the-art performance. We highlight the latent covariances with an EEG classification dataset where latent brain processes and their couplings simultaneously emerge from the model.Comment: 17 pages, 6 figures; accepted to ACML 201

Modeling, Predicting and Capturing Human Mobility

Realistic models of human mobility are critical for modern day applications, specifically for recommendation systems, resource planning and process optimization domains. Given the rapid proliferation of mobile devices equipped with Internet connectivity and GPS functionality today, aggregating large sums of individual geolocation data is feasible. The thesis focuses on methodologies to facilitate data-driven mobility modeling by drawing parallels between the inherent nature of mobility trajectories, statistical physics and information theory. On the applied side, the thesis contributions lie in leveraging the formulated mobility models to construct prediction workflows by adopting a privacy-by-design perspective. This enables end users to derive utility from location-based services while preserving their location privacy. Finally, the thesis presents several approaches to generate large-scale synthetic mobility datasets by applying machine learning approaches to facilitate experimental reproducibility

Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures

Tweet-SCAN: an event discovery technique for geo-located tweets

Twitter has become one of the most popular Location-based Social Networks (LBSNs) that bridges physical and virtual worlds. Tweets, 140-character-long messages, are aimed to give answer to the What’s happening? question. Occurrences and events in the real life (such as political protests, music concerts, natural disasters or terrorist acts) are usually reported through geo-located tweets by users on site. Uncovering event-related tweets from the rest is a challenging problem that necessarily requires exploiting different tweet features. With that in mind, we propose Tweet-SCAN, a novel event discovery technique based on the popular density-based clustering algorithm called DBSCAN. Tweet-SCAN takes into account four main features from a tweet, namely content, time, location and user to group together event-related tweets. The proposed technique models textual content through a probabilistic topic model called Hierarchical Dirichlet Process and introduces Jensen–Shannon distance for the task of neighborhood identification in the textual dimension. As a matter of fact, we show Tweet-SCAN performance in two real data sets of geo-located tweets posted during Barcelona local festivities in 2014 and 2015, for which some of the events were identified by domain experts beforehand. Through these tagged data sets, we are able to assess Tweet-SCAN capabilities to discover events, justify using a textual component and highlight the effects of several parameters.Peer ReviewedPostprint (author's final draft