Deciding on an appropriate intervention requires a causal model of a treatment, the outcome, and potential mediators. Causal mediation analysis lets us distinguish between direct and indirect effects of the intervention, but has mostly been studied in a static setting. In healthcare, data come in the form of complex, irregularly sampled time-series, with dynamic interdependencies between a treatment, outcomes, and mediators across time. Existing approaches to dynamic causal mediation analysis are limited to regular measurement intervals, simple parametric models, and disregard long-range mediator--outcome interactions. To address these limitations, we propose a non-parametric mediator--outcome model where the mediator is assumed to be a temporal point process that interacts with the outcome process. With this model, we estimate the direct and indirect effects of an external intervention on the outcome, showing how each of these affects the whole future trajectory. We demonstrate on semi-synthetic data that our method can accurately estimate direct and indirect effects. On real-world healthcare data, our model infers clinically meaningful direct and indirect effect trajectories for blood glucose after a surgery.

Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatio-temporal modeling, Bayesian Optimization and continuous control, inherently contain equivariances – for example to translation – which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values.However, selecting an appropriate kernel can be challenging. Deep GPs avoid manual kernel engineering by successively parameterizing kernels with GP layers, allowing them to learn low-dimensional embeddings of the inputs that explain the output data. Following the architecture of deep neural networks, the most common deep GPs warp the input space layer-by-layer but lose all the interpretability of shallow GPs. An alternative construction is to successively parameterize the lengthscale of a kernel, improving the interpretability but ultimately giving away the notion of learning lower-dimensional embeddings. Unfortunately, both methods are susceptible to particular pathologies which may hinder fitting and limit their interpretability. This work proposes a novel synthesis of both previous approaches: {Thin and Deep GP} (TDGP). Each TDGP layer defines locally linear transformations of the original input data maintaining the concept of latent embeddings while also retaining the interpretation of lengthscales of a kernel. Moreover, unlike the prior solutions, TDGP induces non-pathological manifolds that admit learning lower-dimensional representations. We show with theoretical and experimental results that i) TDGP is, unlike previous models, tailored to specifically discover lower-dimensional manifolds in the input data, ii) TDGP behaves well when increasing the number of layers, and iii) TDGP performs well in standard benchmark datasets.