Self-Attentive hawkes process

Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs successes in processing sequential data such as languages. Recent evidence suggests that self-Attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-Attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-Attentive Hawkes process (SAHP). SAHP employs self-Attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional selfattention, when applied to event sequences, is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-Attention in Hawkes processes

Order flow and price formation

I present an overview of some recent advancements on the empirical analysis and theoretical modeling of the process of price formation in financial markets as the result of the arrival of orders in a limit order book exchange. After discussing critically the possible modeling approaches and the observed stylized facts of order flow, I consider in detail market impact and transaction cost of trades executed incrementally over an extended period of time, by comparing model predictions and recent extensive empirical results. I also discuss how the simultaneous presence of many algorithmic trading executions affects the quality and cost of trading

Modeling Events and Interactions through Temporal Processes -- A Survey

In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate probabilistic models for modeling event sequences through temporal processes. We revise the notion of event modeling and provide the mathematical foundations that characterize the literature on the topic. We define an ontology to categorize the existing approaches in terms of three families: simple, marked, and spatio-temporal point processes. For each family, we systematically review the existing approaches based based on deep learning. Finally, we analyze the scenarios where the proposed techniques can be used for addressing prediction and modeling aspects.Comment: Image replacement

Convex Parameter Recovery for Interacting Marked Processes

We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category to occur in a location may be influenced by past events at this and other locations. We do not restrict interactions to be positive or decaying over time as it is commonly adopted, allowing us to capture an arbitrary shape of influence from historical events, locations, and events of different categories. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters. We develop two parameter estimation procedures utilizing the constrained Least Squares (LS) and Maximum Likelihood (ML) estimation, which are solved using variational inequalities with monotone operators. We discuss different applications of our approach and illustrate the performance of proposed recovery routines on synthetic examples and a real-world police dataset

HAP-SAP: Semantic Annotation in LBSNs using Latent Spatio-Temporal Hawkes Process

The prevalence of location-based social networks (LBSNs) has eased the understanding of human mobility patterns. Knowledge of human dynamics can aid in various ways like urban planning, managing traffic congestion, personalized recommendation etc. These dynamics are influenced by factors like social impact, periodicity in mobility, spatial proximity, influence among users and semantic categories etc., which makes location modelling a critical task. However, categories which act as semantic characterization of the location, might be missing for some check-ins and can adversely affect modelling the mobility dynamics of users. At the same time, mobility patterns provide a cue on the missing semantic category. In this paper, we simultaneously address the problem of semantic annotation of locations and location adoption dynamics of users. We propose our model HAP-SAP, a latent spatio-temporal multivariate Hawkes process, which considers latent semantic category influences, and temporal and spatial mobility patterns of users. The model parameters and latent semantic categories are inferred using expectation-maximization algorithm, which uses Gibbs sampling to obtain posterior distribution over latent semantic categories. The inferred semantic categories can supplement our model on predicting the next check-in events by users. Our experiments on real datasets demonstrate the effectiveness of the proposed model for the semantic annotation and location adoption modelling tasks.Comment: 11 page

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure

EasyTPP: Towards Open Benchmarking Temporal Point Processes

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.Comment: ICLR 2024 camera read

Learning Neural Point Processes with Latent Graphs

Neural point processes (NPPs) employ neural networks to capture complicated dynamics of asynchronous event sequences. Existing NPPs feed all history events into neural networks, assuming that all event types contribute to the prediction of the target type. How- ever, this assumption can be problematic because in reality some event types do not contribute to the predictions of another type. To correct this defect, we learn to omit those types of events that do not contribute to the prediction of one target type during the formulation of NPPs. Towards this end, we simultaneously consider the tasks of (1) finding event types that contribute to predictions of the target types and (2) learning a NPP model from event se- quences. For the former, we formulate a latent graph, with event types being vertices and non-zero contributing relationships being directed edges; then we propose a probabilistic graph generator, from which we sample a latent graph. For the latter, the sampled graph can be readily used as a plug-in to modify an existing NPP model. Because these two tasks are nested, we propose to optimize the model parameters through bilevel programming, and develop an efficient solution based on truncated gradient back-propagation. Experimental results on both synthetic and real-world datasets show the improved performance against state-of-the-art baselines. This work removes disturbance of non-contributing event types with the aid of a validation procedure, similar to the practice to mitigate overfitting used when training machine learning models