Learning Temporal Point Processes via Reinforcement Learning

Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their dynamics. Temporal point processes offer an elegant framework for modeling event data without discretizing the time. However, the existing maximum-likelihood-estimation (MLE) learning paradigm requires hand-crafting the intensity function beforehand and cannot directly monitor the goodness-of-fit of the estimated model in the process of training. To alleviate the risk of model-misspecification in MLE, we propose to generate samples from the generative model and monitor the quality of the samples in the process of training until the samples and the real data are indistinguishable. We take inspiration from reinforcement learning (RL) and treat the generation of each event as the action taken by a stochastic policy. We parameterize the policy as a flexible recurrent neural network and gradually improve the policy to mimic the observed event distribution. Since the reward function is unknown in this setting, we uncover an analytic and nonparametric form of the reward function using an inverse reinforcement learning formulation. This new RL framework allows us to derive an efficient policy gradient algorithm for learning flexible point process models, and we show that it performs well in both synthetic and real data

Fully Neural Network based Model for General Temporal Point Processes

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time course of the intensity function of a point process (e.g., exponentially decreasing or increasing with the time since the most recent event). However, such an assumption can restrict the expressive power of the model. We herein propose a novel RNN based model in which the time course of the intensity function is represented in a general manner. In our approach, we first model the integral of the intensity function using a feedforward neural network and then obtain the intensity function as its derivative. This approach enables us to both obtain a flexible model of the intensity function and exactly evaluate the log-likelihood function, which contains the integral of the intensity function, without any numerical approximations. Our model achieves competitive or superior performances compared to the previous state-of-the-art methods for both synthetic and real datasets

Reinforcement Learning with Policy Mixture Model for Temporal Point Processes Clustering

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.Comment: 8 pages, 3 figures, 4 table

Self-Attentive Hawkes Processes

Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events will happen next and when. A de facto standard mathematical framework to do this is the Hawkes process. In order to enhance expressivity of multivariate Hawkes processes, conventional statistical methods and deep recurrent networks have been employed to modify its intensity function. The former is highly interpretable and requires small size of training data but relies on correct model design while the latter has less dependency on prior knowledge and is more powerful in capturing complicated patterns. We leverage pros and cons of these models and propose a self-attentive Hawkes process(SAHP). The proposed method adapts self-attention to fit the intensity function of Hawkes processes. This design has two benefits:(1) compared with conventional statistical methods, the SAHP is more powerful to identify complicated dependency relationships between temporal events; (2)compared with deep recurrent networks, the self-attention mechanism is able to capture longer historical information, and is more interpretable because the learnt attention weight tensor shows contributions of each historical event. Experiments on four real-world datasets demonstrate the effectiveness of the proposed method

ABC Learning of Hawkes Processes with Missing or Noisy Event Times

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such distortion can severely bias the learning of the Hawkes process parameters. To circumvent this, we propose modeling the distortion function explicitly. This leads to a model with an intractable likelihood function which makes it difficult to deploy standard parameter estimation techniques. As such, we develop the ABC-Hawkes algorithm which is a novel approach to estimation based on Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo. This allows the parameters of the Hawkes process to be learned in settings where conventional methods induce substantial bias or are inapplicable. The proposed approach is shown to perform well on both real and simulated data.Comment: Added comparison to literatur

Insider Threat Detection via Hierarchical Neural Temporal Point Processes

Insiders usually cause significant losses to organizations and are hard to detect. Currently, various approaches have been proposed to achieve insider threat detection based on analyzing the audit data that record information of the employee's activity type and time. However, the existing approaches usually focus on modeling the users' activity types but do not consider the activity time information. In this paper, we propose a hierarchical neural temporal point process model by combining the temporal point processes and recurrent neural networks for insider threat detection. Our model is capable of capturing a general nonlinear dependency over the history of all activities by the two-level structure that effectively models activity times, activity types, session durations, and session intervals information. Experimental results on two datasets demonstrate that our model outperforms the models that only consider information of the activity types or time alone

Learning Latent Process from High-Dimensional Event Sequences via Efficient Sampling

We target modeling latent dynamics in high-dimension marked event sequences without any prior knowledge about marker relations. Such problem has been rarely studied by previous works which would have fundamental difficulty to handle the arisen challenges: 1) the high-dimensional markers and unknown relation network among them pose intractable obstacles for modeling the latent dynamic process; 2) one observed event sequence may concurrently contain several different chains of interdependent events; 3) it is hard to well define the distance between two high-dimension event sequences. To these ends, in this paper, we propose a seminal adversarial imitation learning framework for high-dimension event sequence generation which could be decomposed into: 1) a latent structural intensity model that estimates the adjacent nodes without explicit networks and learns to capture the temporal dynamics in the latent space of markers over observed sequence; 2) an efficient random walk based generation model that aims at imitating the generation process of high-dimension event sequences from a bottom-up view; 3) a discriminator specified as a seq2seq network optimizing the rewards to help the generator output event sequences as real as possible. Experimental results on both synthetic and real-world datasets demonstrate that the proposed method could effectively detect the hidden network among markers and make decent prediction for future marked events, even when the number of markers scales to million level

Understanding the Spread of COVID-19 Epidemic: A Spatio-Temporal Point Process View

Since the first coronavirus case was identified in the U.S. on Jan. 21, more than 1 million people in the U.S. have confirmed cases of COVID-19. This infectious respiratory disease has spread rapidly across more than 3000 counties and 50 states in the U.S. and have exhibited evolutionary clustering and complex triggering patterns. It is essential to understand the complex spacetime intertwined propagation of this disease so that accurate prediction or smart external intervention can be carried out. In this paper, we model the propagation of the COVID-19 as spatio-temporal point processes and propose a generative and intensity-free model to track the spread of the disease. We further adopt a generative adversarial imitation learning framework to learn the model parameters. In comparison with the traditional likelihood-based learning methods, this imitation learning framework does not need to prespecify an intensity function, which alleviates the model-misspecification. Moreover, the adversarial learning procedure bypasses the difficult-to-evaluate integral involved in the likelihood evaluation, which makes the model inference more scalable with the data and variables. We showcase the dynamic learning performance on the COVID-19 confirmed cases in the U.S. and evaluate the social distancing policy based on the learned generative model

Transformer Hawkes Process

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often exhibit complicated short-term and long-term temporal dependencies. However, most of the existing recurrent neural network based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorporate additional structural knowledge. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information

Thinking While Moving: Deep Reinforcement Learning with Concurrent Control

We study reinforcement learning in settings where sampling an action from the policy must be done concurrently with the time evolution of the controlled system, such as when a robot must decide on the next action while still performing the previous action. Much like a person or an animal, the robot must think and move at the same time, deciding on its next action before the previous one has completed. In order to develop an algorithmic framework for such concurrent control problems, we start with a continuous-time formulation of the Bellman equations, and then discretize them in a way that is aware of system delays. We instantiate this new class of approximate dynamic programming methods via a simple architectural extension to existing value-based deep reinforcement learning algorithms. We evaluate our methods on simulated benchmark tasks and a large-scale robotic grasping task where the robot must "think while moving".Comment: Published as a conference paper at ICLR 202