A variety of real-world processes (over networks) produce sequences of data whose complex temporal dynamics need to be studied. More especially, the event timestamps can carry important information about the underlying network dynamics, which otherwise are not available from the time-series evenly sampled from continuous signals. Moreover, in most complex processes, event sequences and evenly-sampled times series data can interact with each other, which renders joint modeling of those two sources of data necessary. To tackle the above problems, in this paper, we utilize the rich framework of (temporal) point processes to model event data and timely update its intensity function by the synergic twin Recurrent Neural Networks (RNNs). In the proposed architecture, the intensity function is synergistically modulated by one RNN with asynchronous events as input and another RNN with time series as input. Furthermore, to enhance the interpretability of the model, the attention mechanism for the neural point process is introduced. The whole model with event type and timestamp prediction output layers can be trained end-to-end and allows a black-box treatment for modeling the intensity. We substantiate the superiority of our model in synthetic data and three real-world benchmark datasets.
3) @cite_50 : Recently, Hawkes process has received a wide attention in network cascades modeling @cite_38 @cite_49 , community structure @cite_47 , viral diffusion and activity shaping @cite_25 , criminology @cite_18 , optimization and intervention in social networks @cite_31 , recommendation systems @cite_3 , and verification of crowd generated data @cite_37 . As an illustration example intensively used in this paper, we particularly write out its intensity function is: where @math is the infectivity matrix, indicating the directional influence strength from dimension @math to @math . It explicitly uses a triggering term to model the excitation effect from history events where the parameter @math denotes the decaying bandwidth. The model is originally motivated to analyze the earthquake and its aftershocks @cite_8 .
@cite_38 @cite_18 @cite_31 @cite_37 @cite_8 @cite_3 @cite_49 @cite_50 @cite_47 @cite_25
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How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities in a quantitative way? Such critical and valuable knowledge is unfortunately not readily accessible and we tend to only observe its manifestation in the form of recurrent and time-stamped events occurring at the individuals involved in the social network. It is an important yet challenging problem to infer the underlying network of social inference based on the temporal patterns of those historical events that we can observe. In this paper, we propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multidimensional Hawkes processes, emphasizing the mutual-excitation nature of the dynamics of event occurrence. Furthermore, our estimation procedure, using nuclear and l1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination in the social network. To efficiently solve the resulting optimization problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model than several baselines. We consider the problem of how to optimize multi-stage campaigning over social networks. The dynamic programming framework is employed to balance the high present reward and large penalty on low future outcome in the presence of extensive uncertainties. In particular, we establish theoretical foundations of optimal campaigning over social networks where the user activities are modeled as a multivariate Hawkes process, and we derive a time dependent linear relation between the intensity of exogenous events and several commonly used objective functions of campaigning. We further develop a convex dynamic programming framework for determining the optimal intervention policy that prescribes the required level of external drive at each stage for the desired campaigning result. Experiments on both synthetic data and the real-world MemeTracker dataset show that our algorithm can steer the user activities for optimal campaigning much more accurately than baselines. Online knowledge repositories typically rely on their users or dedicated editors to evaluate the reliability of their contents. These explicit feedback mechanisms can be viewed as noisy measurements of both information reliability and information source trustworthiness. Can we leverage these noisy measurements, often biased, to distill a robust, unbiased and interpretable measure of both notions? In this paper, we argue that the large volume of digital traces left by the users within knowledge repositories also reflect information reliability and source trustworthiness. In particular, we propose a temporal point process modeling framework which links the temporal behavior of the users to information reliability and source trustworthiness. Furthermore, we develop an efficient convex optimization procedure to learn the parameters of the model from historical traces of the evaluations provided by these users. Experiments on real-world data gathered from Wikipedia and Stack Overflow show that our modeling framework accurately predicts evaluation events, provides an interpretable measure of information reliability and source trustworthiness, and yields interesting insights about real-world events. Abstract This article discusses several classes of stochastic models for the origin times and magnitudes of earthquakes. The models are compared for a Japanese data set for the years 1885–1980 using likelihood methods. For the best model, a change of time scale is made to investigate the deviation of the data from the model. Conventional graphical methods associated with stationary Poisson processes can be used with the transformed time scale. For point processes, effective use of such residual analysis makes it possible to find features of the data set that are not captured in the model. Based on such analyses, the utility of seismic quiescence for the prediction of a major earthquake is investigated. Poisson factorization is a probabilistic model of users and items for recommendation systems, where the so-called implicit consumer data is modeled by a factorized Poisson distribution. There are many variants of Poisson factorization methods who show state-of-the-art performance on real-world recommendation tasks. However, most of them do not explicitly take into account the temporal behavior and the recurrent activities of users which is essential to recommend the right item to the right user at the right time. In this paper, we introduce Recurrent Poisson Factorization (RPF) framework that generalizes the classical PF methods by utilizing a Poisson process for modeling the implicit feedback. RPF treats time as a natural constituent of the model and brings to the table a rich family of time-sensitive factorization models. To elaborate, we instantiate several variants of RPF who are capable of handling dynamic user preferences and item specification (DRPF), modeling the social-aspect of product adoption (SRPF), and capturing the consumption heterogeneity among users and items (HRPF). We also develop a variational algorithm for approximate posterior inference that scales up to massive data sets. Furthermore, we demonstrate RPF's superior performance over many state-of-the-art methods on synthetic dataset, and large scale real-world datasets on music streaming logs, and user-item interactions in M-Commerce platforms. Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn these links are alternating the way information spreads. However, these two highly intertwined stochastic processes, information diffusion and network evolution, have been predominantly studied separately, ignoring their co-evolutionary dynamics. We propose a temporal point process model, COEVOLVE, for such joint dynamics, allowing the intensity of one process to be modulated by that of the other. This model allows us to efficiently simulate interleaved diffusion and network events, and generate traces obeying common diffusion and network patterns observed in real-world networks. Furthermore, we also develop a convex optimization framework to learn the parameters of the model from historical diffusion and network evolution traces. We experimented with both synthetic data and data gathered from Twitter, and show that our model provides a good fit to the data as well as more accurate predictions than alternatives. SUMMARY In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a,b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed. A particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process. These are not distinguishable by methods of data analysis based on these properties. The real social network and associated communities are often hidden under the declared friend or group lists in social networks. We usually observe the manifestation of these hidden networks and communities in the form of recurrent and time-stamped individuals’ activities in the social network. Inferring the underlying network and finding coherent communities are therefore two key challenges in social networks analysis. In this paper, we address the following question: Could we simultaneously detect community structure and network infectivity among individuals from their activities? Based on the fact that the two characteristics intertwine and that knowing one will help better revealing the other, we propose a multidimensional Hawkes process that can address them simultaneously. To this end, we parametrize the network infectivity in terms of individuals’ participation in communities and the popularity of each individual. We show that this modeling approach has many benefits, both conceptually and experimentally. We utilize Bayesian variational inference to design NetCodec, an efficient inference algorithm which is verified with both synthetic and real world data sets. The experiments show that NetCodec can discover the underlying network infectivity and community structure more accurately than baseline method.