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.
There are alternative objectives for TPP learning for both parametric models and neural models. Traditional methods mostly follow the maximum likelihood estimation (MLE) procedure under the probabilistic framework @cite_17 . While the MLE objective may not be the only choice. This is because we are often given only a limited number of sequences which may further contain arbitrary noises. Recent efforts have been made for devising adversarial learning based objective inspired by generative adversarial networks (GAN) @cite_11 and especially Wasserstein GAN @cite_27 . In @cite_12 , adversarial objective is developed in addition with MLE loss by approximating the continuous domain predictions using a discrete time series. In @cite_32 , Wasserstein distance over temporal event sequences is explicitly defined to learn a deep generative point process model for temporal events generation. Another line of works consider the challenge for learning high-dimensional TPP models, whereby the so-called infectivity matrix to be learned can be of squared size of the dimensionality. One popular technique is imposing low-rank regularizer @cite_31 or factorization model @cite_29 on the infectivity matrix. However, they do not explicitly deal with the sequence clustering problem. In fact, the observed dimension marker does not correspond to the underlying cluster.
@cite_29 @cite_32 @cite_17 @cite_27 @cite_31 @cite_12 @cite_11
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This paper presents a factorial marked temporal point process model and presents efficient learning methods. In conventional (multi-dimensional) marked temporal point process models, an event is often encoded by a single discrete variable (marker). We describe the factorial marked point processes whereby time-stamped event is factored into multiple markers. Accordingly the size of the infectivity matrix modeling the effect between pairwise markers is in exponential order regarding the number of discrete markers. We propose a decoupled learning method with two learning procedures: i) directly solving the model based on two techniques: Alternating Direction Method of Multipliers and Fast Iterative Shrinkage-Thresholding Algorithm; ii) involving a reformulation that transforms the original problem into a Logistic Regression model for more efficient learning. Moreover, a sparse group regularizer is added to identify the key profile features and event labels. Empirical results on real world datasets demonstrate the efficiency of our decoupled and reformulated method. 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. A maximum likelihood estimation procedure of Hawkes' self-exciting point process model is proposed with explicit presentations of the log-likelihood of the model and its gradient and Hessian. A simulation method of the process is also presented. Some numerical results are given. 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 propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.