Utilizing Functional-MLP for Point Process Encoding in a Variational Autoencoder

Point processes, characterized by intensity functions, are widely used to describe infrequent occurrences within continuous domains in real-world scenarios. An important challenge in studying point processes is encoding their observations, which is essential in learning representations of diverse point processes and designing Variational Autoencoders (VAEs) for point process data. Most existing works employs LSTM as the encoder in VAEs to map temporal point process observations into the latent space. However, such works fail to account for the relationship between observed data and background intensity, as well as ignoring key properties like exchangeability, making it challenging to model spatial point processes. In this study, we propose a novel encoding method that utilizes functional-MLP to encode intensity functions, tailored for analyzing point process observations. Importantly, we demonstrate that our proposed method is invariant to the order of input points, rendering it exceptionally suitable for spatial point processes. Finally, we evaluate the performance of our proposed structure against traditional VAE encoding methods, with a particular focus on representing learning tasks. Experiments confirm the superiority of our method in modeling point processes.