Temporal point process is an expressive tool for modeling event sequences over time. In this paper, we take a reinforcement learning view whereby the observed sequences are assumed to be generated from a mixture of latent policies. The purpose is to cluster the sequences with different temporal patterns into the underlying policies while learning each of the policy model. The flexibility of our model lies in: i) all the components are networks including the policy network for modeling the intensity function of temporal point process; ii) to handle varying-length event sequences, we resort to inverse reinforcement learning by decomposing the observed sequence into states (RNN hidden embedding of history) and actions (time interval to next event) in order to learn the reward function, thus achieving better performance or increasing efficiency compared to existing methods using rewards over the entire sequence such as log-likelihood or Wasserstein distance. We adopt an expectation-maximization framework with the E-step estimating the cluster labels for each sequence, and the M-step aiming to learn the respective policy. Extensive experiments show the efficacy of our method against state-of-the-arts.
Traditional TPP models are mostly developed around the design of the intensity function @math which measures the instantaneous event occurrence rate at time @math , like Reinforced Poisson processes @cite_13 , Self-exciting process (Hawkes process) @cite_8 , Reactive point process @cite_16 , etc. An obvious limitation of these traditional models is that they all assume all the samples obey a single parametric form which is too idealistic for real-world data. This also suggests the need for learning clustered behaviors beyond single model based methods.
@cite_16 @cite_13 @cite_8
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Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in Hough(2006) , which generate the desired distribution point wise through rejection sampling. Unfortunately, the size of rejection could be very large. In this paper, we investigate the application of perfect simulation via coupling from the past (CFTP) on DPP. We give a general framework for perfect simulation on DPP model. It is shown that the limiting sequence of the time-to-coalescence of the coupling is bounded by @math An application is given to the stationary models in DPP. Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity function which limits model's expressiveness due to unrealistic assumptions on its parametric form used in practice. Furthermore, they are learned via maximum likelihood approach which is prone to failure in multi-modal distributions of sequences. In this paper, we propose an intensity-free approach for point processes modeling that transforms nuisance processes to a target one. Furthermore, we train the model using a likelihood-free leveraging Wasserstein distance between point processes. Experiments on various synthetic and real-world data substantiate the superiority of the proposed point process model over conventional ones. Large volumes of event data are becoming increasingly available in a wide variety of applications, such as healthcare analytics, smart cities and social network analysis. The precise time interval or the exact distance between two events carries a great deal of information about the dynamics of the underlying systems. These characteristics make such data fundamentally different from independently and identically distributed data and time-series data where time and space are treated as indexes rather than random variables. Marked temporal point processes are the mathematical framework for modeling event data with covariates. However, typical point process models often make strong assumptions about the generative processes of the event data, which may or may not reflect the reality, and the specifically fixed parametric assumptions also have restricted the expressive power of the respective processes. Can we obtain a more expressive model of marked temporal point processes? How can we learn such a model from massive data? In this paper, we propose the Recurrent Marked Temporal Point Process (RMTPP) to simultaneously model the event timings and the markers. The key idea of our approach is to view the intensity function of a temporal point process as a nonlinear function of the history, and use a recurrent neural network to automatically learn a representation of influences from the event history. We develop an efficient stochastic gradient algorithm for learning the model parameters which can readily scale up to millions of events. Using both synthetic and real world datasets, we show that, in the case where the true models have parametric specifications, RMTPP can learn the dynamics of such models without the need to know the actual parametric forms; and in the case where the true models are unknown, RMTPP can also learn the dynamics and achieve better predictive performance than other parametric alternatives based on particular prior assumptions. type="main" xml:id="rssb12096-abs-0001"> Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern data sets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted by using the likelihood or moment properties of DPP models, and we provide freely available software for simulation and statistical inference.