Physiological signals such as blood pressure might contain key information to predict a medical condition, but are challenging to mine. Wavelets possess the ability to unveil location-specific features within signals but there exists no principled method to choose the optimal scales and time shifts. We present a scalable, robust system to find the best wavelet parameters using Gaussian processes (GPs). We demonstrate our system by assessing wavelets as predictors for the occurrence of acute hypotensive episodes (AHEs) using over 1 billion blood pressure beats. We obtain an AUROC of 0.79 with wavelet features only, and the false positive rate when the true positive rate is fixed at 0.90 is reduced by 14% when the wavelet feature is used in conjunction with other statistical features. Furthermore, the use of GPs reduces the selection effort by a factor of 3 compared with a naive grid search.