  Sum-product networks (SPNs) have recently emerged as a novel deep learning
architecture enabling highly efficient probabilistic inference. Since their
introduction, SPNs have been applied to a wide range of data modalities and
extended to time-sequence data. In this paper, we propose a general framework
for modelling sequential treatment decision-making behaviour and treatment
response using recurrent sum-product networks (RSPNs). Models developed using
our framework benefit from the full range of RSPN capabilities, including the
abilities to model the full distribution of the data, to seamlessly handle
latent variables, missing values and categorical data, and to efficiently
perform marginal and conditional inference. Our methodology is complemented by
a novel variant of the expectation-maximization algorithm for RSPNs, enabling
efficient training of our models. We evaluate our approach on a synthetic
dataset as well as real-world data from the MIMIC-IV intensive care unit
medical database. Our evaluation demonstrates that our approach can closely
match the ground-truth data generation process on synthetic data and achieve
results close to neural and probabilistic baselines while using a tractable and
interpretable model.
