  Unsupervised learning is often used to uncover clusters in data. However,
different kinds of noise may impede the discovery of useful patterns from
real-world time-series data. In this work, we focus on mitigating the
interference of interval censoring in the task of clustering for disease
phenotyping. We develop a deep generative, continuous-time model of time-series
data that clusters time-series while correcting for censorship time. We provide
conditions under which clusters and the amount of delayed entry may be
identified from data under a noiseless model. On synthetic data, we demonstrate
accurate, stable, and interpretable results that outperform several benchmarks.
On real-world clinical datasets of heart failure and Parkinson's disease
patients, we study how interval censoring can adversely affect the task of
disease phenotyping. Our model corrects for this source of error and recovers
known clinical subtypes.
