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The episodic, irregular and asynchronous nature of medical data render themdifficult substrates for standard machine learning algorithms. We would like toabstract away this difficulty for the class of time-stamped categoricalvariables (or events) by modeling them as a renewal process and inferring aprobability density over continuous, longitudinal, nonparametric intensityfunctions modulating that process. Several methods exist for inferring such adensity over intensity functions, but either their constraints and assumptionsprevent their use with our potentially bursty event streams, or their timecomplexity renders their use intractable on our long-duration observations ofhigh-resolution events, or both. In this paper we present a new and efficientmethod for inferring a distribution over intensity functions that uses directnumeric integration and smooth interpolation over Gaussian processes. Wedemonstrate that our direct method is up to twice as accurate and two orders ofmagnitude more efficient than the best existing method (thinning). Importantly,the direct method can infer intensity functions over the full range of burstyto memoryless to regular events, which thinning and many other methods cannot.Finally, we apply the method to clinical event data and demonstrate theface-validity of the abstraction, which is now amenable to standard learningalgorithms.

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