Predicting discrete events in time and space has many scientific applications, such as predicting hazardous earthquakes and outbreaks of infectious diseases. History-dependent spatio-temporal Hawkes processes are often used to mathematically model these point events. However, previous approaches have faced numerous challenges, particularly when attempting to forecast one or multiple future events. In this work, we propose a new neural architecture for simultaneous multi-event forecasting of spatio-temporal point processes, utilizing transformers, augmented with normalizing flows and probabilistic layers. Our network makes batched predictions of complex history-dependent spatio-temporal distributions of future discrete events, achieving state-of-the-art performance on a variety of benchmark datasets including the South California Earthquakes, Citibike, Covid-19, and Hawkes synthetic pinwheel datasets. More generally, we illustrate how our network can be applied to any dataset of discrete events with associated markers, even when no underlying physics is known.

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In particular, hybrid Bayesian neural networks utilize standard deterministic layers together with few probabilistic layers judicially positioned in the networks for uncertainty estimation. A major aspect and benefit of Bayesian inference is that priors, in principle, provide the means to encode prior knowledge for use in inference and prediction. However, it is difficult to specify priors on weights since the weights have no intuitive interpretation. Further, the relationships of priors on weights to the functions computed by networks are difficult to characterize. In contrast, functions are intuitive to interpret and are direct since they map inputs to outputs. Therefore, it is natural to specify priors on functions to encode prior knowledge, and to use them in inference and prediction based on functions. To support this, we propose hybrid Bayesian neural networks with functional probabilistic layers that encode function (and activation) uncertainty. We discuss their foundations in functional Bayesian inference, functional variational inference, sparse Gaussian processes, and sparse variational Gaussian processes. We further perform few proof-of-concept experiments using GPflus, a new library that provides Gaussian process layers and supports their use with deterministic Keras layers to form hybrid neural network and Gaussian process models.

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their deterministic counter parts, Bayesian neural networks provide a direct and natural way to extend conventional deep neural networks to support probabilistic deep learning. However, it is nontrivial to understand, design and train Bayesian neural networks due to their complexities. We discuss the essentials of Bayesian neural networks including duality (deep neural networks, probabilistic models), approximate Bayesian inference, Bayesian priors, Bayesian posteriors, and deep variational learning. We use TensorFlow Probability APIs and code examples for illustration. The main problem with Bayesian neural networks is that the architecture of deep neural networks makes it quite redundant, and costly, to account for uncertainty for a large number of successive layers. Hybrid Bayesian neural networks, which use few probabilistic layers judicially positioned in the networks, provide a practical solution.

Conventional deep learning models have limited capacity in learning multiple tasks sequentially. The issue of forgetting the previously learned tasks in continual learning is known as catastrophic forgetting or interference. When the input data or the goal of learning change, a continual model will learn and adapt to the new status. However, the model will not remember or recognise any revisits to the previous states. This causes performance reduction and re-training curves in dealing with periodic or irregularly reoccurring changes in the data or goals. The changes in goals or data are referred to as new tasks in a continual learning model. Most of the continual learning methods have a task-known setup in which the task identities are known in advance to the learning model. We propose Multi-view Task Conditional Neural Networks (Mv-TCNN) that does not require to known the reoccurring tasks in advance. We evaluate our model on standard datasets using MNIST, CIFAR10, CIFAR100, and also a real-world dataset that we have collected in a remote healthcare monitoring study (i.e. TIHM dataset). The proposed model outperforms the state-of-the-art solutions in continual learning and adapting to new tasks that are not defined in advance.