Continuous-time convolutions model of event sequences

Event sequences often emerge in data mining. Modeling these sequences presents two main challenges: methodological and computational. Methodologically, event sequences are non-uniform and sparse, making traditional models unsuitable. Computationally, the vast amount of data and the significant length of each sequence necessitate complex and efficient models. Existing solutions, such as recurrent and transformer neural networks, rely on parametric intensity functions defined at each moment. These functions are either limited in their ability to represent complex event sequences or notably inefficient. We propose COTIC, a method based on an efficient convolution neural network designed to handle the non-uniform occurrence of events over time. Our paper introduces a continuous convolution layer, allowing a model to capture complex dependencies, including, e.g., the self-excitement effect, with little computational expense. COTIC outperforms existing models in predicting the next event time and type, achieving an average rank of 1.5 compared to 3.714 for the nearest competitor. Furthermore, COTIC`s ability to produce effective embeddings demonstrates its potential for various downstream tasks. Our code is open and available at: https://github.com/VladislavZh/COTIC.