Modeling and Estimation for Self-Exciting Spatio-Temporal Models of Terrorist Activity

Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal diffusion is placed, as a matter of convenience, in the process model allowing for straightforward estimation of the diffusion parameters through Bayesian techniques. However, this method of modeling does not allow for the existence of self-excitation, or a temporal data model dependency, that has been shown to exist in criminal and terrorism data. In this manuscript we will use existing theories on how violence spreads to create models that allow for both spatio-temporal diffusion in the process model as well as temporal diffusion, or self-excitation, in the data model. We will further demonstrate how Laplace approximations similar to their use in Integrated Nested Laplace Approximation can be used to quickly and accurately conduct inference of self-exciting spatio-temporal models allowing practitioners a new way of fitting and comparing multiple process models. We will illustrate this approach by fitting a self-exciting spatio-temporal model to terrorism data in Iraq and demonstrate how choice of process model leads to differing conclusions on the existence of self-excitation in the data and differing conclusions on how violence is spreading spatio-temporally

A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

Temporal Cross-Media Retrieval with Soft-Smoothing

Multimedia information have strong temporal correlations that shape the way modalities co-occur over time. In this paper we study the dynamic nature of multimedia and social-media information, where the temporal dimension emerges as a strong source of evidence for learning the temporal correlations across visual and textual modalities. So far, cross-media retrieval models, explored the correlations between different modalities (e.g. text and image) to learn a common subspace, in which semantically similar instances lie in the same neighbourhood. Building on such knowledge, we propose a novel temporal cross-media neural architecture, that departs from standard cross-media methods, by explicitly accounting for the temporal dimension through temporal subspace learning. The model is softly-constrained with temporal and inter-modality constraints that guide the new subspace learning task by favouring temporal correlations between semantically similar and temporally close instances. Experiments on three distinct datasets show that accounting for time turns out to be important for cross-media retrieval. Namely, the proposed method outperforms a set of baselines on the task of temporal cross-media retrieval, demonstrating its effectiveness for performing temporal subspace learning.Comment: To appear in ACM MM 201

Logics of Temporal-Epistemic Actions

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in Dynamic Epistemic Logic

Cascaded Boundary Regression for Temporal Action Detection

Temporal action detection in long videos is an important problem. State-of-the-art methods address this problem by applying action classifiers on sliding windows. Although sliding windows may contain an identifiable portion of the actions, they may not necessarily cover the entire action instance, which would lead to inferior performance. We adapt a two-stage temporal action detection pipeline with Cascaded Boundary Regression (CBR) model. Class-agnostic proposals and specific actions are detected respectively in the first and the second stage. CBR uses temporal coordinate regression to refine the temporal boundaries of the sliding windows. The salient aspect of the refinement process is that, inside each stage, the temporal boundaries are adjusted in a cascaded way by feeding the refined windows back to the system for further boundary refinement. We test CBR on THUMOS-14 and TVSeries, and achieve state-of-the-art performance on both datasets. The performance gain is especially remarkable under high IoU thresholds, e.g. map@tIoU=0.5 on THUMOS-14 is improved from 19.0% to 31.0%

Higher-Order Aggregate Networks in the Analysis of Temporal Networks: Path structures and centralities

Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in which links occur in real-world temporal networks affects causality structures and thus the evolution of dynamical processes, and ii) higher-order aggregate representations of temporal networks can be used to analytically study the effect of these order correlations on dynamical processes. In this article we analyze the effect of order correlations on path-based centrality measures in real-world temporal networks. Analyzing temporal equivalents of betweenness, closeness and reach centrality in six empirical temporal networks, we first show that an analysis of the commonly used static, time-aggregated representation can give misleading results about the actual importance of nodes. We further study higher-order time-aggregated networks, a recently proposed generalization of the commonly applied static, time-aggregated representation of temporal networks. Here, we particularly define path-based centrality measures based on second-order aggregate networks, empirically validating that node centralities calculated in this way better capture the true temporal centralities of nodes than node centralities calculated based on the commonly used static (first-order) representation. Apart from providing a simple and practical method for the approximation of path-based centralities in temporal networks, our results highlight interesting perspectives for the use of higher-order aggregate networks in the analysis of time-stamped network data.Comment: 27 pages, 13 figures, 3 table