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With the ability to create time varying basis functions, the Ensemble Empirical Mode Decomposition (EEMD) has quickly become the preferred way to decompose nonlinear and nonstationary signals. However, we find current EEMD signal cleaning techniques lacking, unable to deal with the nonlinearities that are common for the complex signals that the EEMD is used for. By combining change point detection and a new sparse basis function optimization problem, we are able to show that it is possible to create unique filters for each change point which emphasize the basis functions that are observing a change. This not only allows one to understand which frequency bands are observing a change, but cleaning the signal to emphasize changes can lead to improved signal classification accuracy. We show that this technique has implications for a variety of applications including acoustics and medicine. The technique is implemented in R via the LCDSC package.

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Many fundamental problems affecting the care of critically ill patients lead to similar analytical challenges: physicians cannot easily estimate the effects of at-risk medical conditions or treatments (which is problematic for treatment decisions) because the causal effects of medical conditions and drugs are entangled. They also cannot easily perform studies: there are not enough critically ill patients for high-dimensional observational causal inference analysis, and randomized controlled trials often cannot ethically be conducted. However, mechanistic knowledge is available, including how drugs are absorbed into the body, and the combination of this knowledge with the limited data could potentially suffice -if we knew how to combine them. In this work, we present a framework for interpretable estimation of causal effects for critically ill patients under exactly these complex conditions: interactions between drugs and observations over time, patient data sets that are not large, and mechanistic knowledge that can substitute for lack of data. Our framework incorporates pharmacokinetics and pharmacodynamics with interpretable matching methods to adjust for confounders such as patients' drug response, medical history, and demographic variables. We apply this framework to an extremely important problem affecting critically ill patients, namely the effect of seizures and other potentially harmful electrical events in the brain (called epileptiform activity -EA) on outcomes. EA is a key indicator of whether the patient will suffer long term severe