Efficient Inference of Gaussian-Process-Modulated Renewal Processes with Application to Medical Event Data

The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables (or events) by modeling them as a renewal pro- cess and inferring a probability density over non- parametric longitudinal intensity functions that modulate the process. Several methods exist for inferring such a density over intensity func- tions, but either their constraints prevent their use with our potentially bursty event streams, or their time complexity renders their use in- tractable on our long-duration observations of high-resolution events, or both. In this paper we present a new efficient and flexible infer- ence method that uses direct numeric integra- tion and smooth interpolation over Gaussian pro- cesses. We demonstrate that our direct method is up to twice as accurate and two orders of magni- tude more efficient than the best existing method (thinning). Importantly, our direct method can infer intensity functions over the full range of bursty to memoryless to regular events, which thinning and many other methods cannot do. Fi- nally, we apply the method to clinical event data and demonstrate a simple example application facilitated by the abstraction.