Topic Models with Survival Supervision: Archetypal Analysis and Neural Approaches

We introduce two approaches to topic modeling supervised by survival analysis. Both approaches predict time-to-event outcomes while simultaneously learning topics over features that help prediction. The high-level idea is to represent each data point as a distribution over topics using some underlying topic model. Then each data point's distribution over topics is fed as input to a survival model. The topic and survival models are jointly learned. The two approaches we propose differ in the generality of topic models they can learn. The first approach finds topics via archetypal analysis, a nonnegative matrix factorization method that optimizes over a wide class of topic models encompassing latent Dirichlet allocation (LDA), correlated topic models, and topic models based on the ``anchor word'' assumption; the resulting survival-supervised variant solves an alternating minimization problem. Our second approach builds on recent work that approximates LDA in a neural net framework. We add a survival loss layer to this neural net to form an approximation to survival-supervised LDA. Both of our approaches can be combined with a variety of survival models. We demonstrate our approach on two survival datasets, showing that survival-supervised topic models can achieve competitive time-to-event prediction accuracy while outputting clinically interpretable topics.