Identifying latent state transition in non-linear dynamical systems

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the realm of dynamical systems focused on the latent states, possibly with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior. Inspired by the advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present. We introduce a practical algorithm based on variational auto-encoders and empirically demonstrate in realistic synthetic settings that we can (i) recover latent state dynamics with high accuracy, (ii) correspondingly achieve high future prediction accuracy, and (iii) adapt fast to new environments.

Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventions

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.

Joint Non-parametric Point Process model for Treatments and Outcomes: Counterfactual Time-series Prediction Under Policy Interventions

Policy makers need to predict the progression of an outcome before adopting a new treatment policy, which defines when and how a sequence of treatments affecting the outcome occurs in continuous time. Commonly, algorithms that predict interventional future outcome trajectories take a fixed sequence of future treatments as input. This either neglects the dependence of future treatments on outcomes preceding them or implicitly assumes the treatment policy is known, and hence excludes scenarios where the policy is unknown or a counterfactual analysis is needed. To handle these limitations, we develop a joint model for treatments and outcomes, which allows for the estimation of treatment policies and effects from sequential treatment--outcome data. It can answer interventional and counterfactual queries about interventions on treatment policies, as we show with real-world data on blood glucose progression and a simulation study building on top of this.