Algorithm 1 Hard-gating Algorithm for In-Stage IDKCascade Input Ds: Training data containing Ns samples in stage-s Ms: Sorted list of the models trained for stage-s C: Dictionary of models' spatio-temporal costs cs: User-defined budget of spatio-temporal cost for stage-s q: Confidence function maxA: Value for the upper bound of the cutoffs to avoid over-fitting nBins: Number of bins for the grid search Output s: The optimal IDK cutoff vector for stage-s 1: procedure HARDGATING(Ds, Ms, cs, C, q, maxA, nBins) 2: s =[], ModelAssign = 1, cost = P We use the Sepsis-3 toolkit3 to obtain the suspected infection time in patients, and following the process in Seymour et al. (2016) to finally label the onset of sepsis. We result at a total number of 20,009 sepsis patients out of the 52,902 adult patients from MIMIC-III database. We exclude those patients who stay in ICUs less than 6 hours and also exclude those patients who developed sepsis within the first 6 hours after ICU admission. This reduces our cohort to a total of 34,475ICU patient, and only 2,370(6.8%) Then according to Singer et al. (2016), we identify the onset of septic shock as Algorithm 3 End-to-End Training algorithm for UnfoldML Input D: Full training data containing N instances M: Full model zoo C: Dictionary of models' spatio-temporal costs q: Confidence criterion Output: the optimal ICK1 gate parameters (or a,b): the optimal IDK gate parameters 1: procedure END-TO-ENDTRAINING (D, M) 2: Pre-allocate costs cs for each stage s. Figure 4: Transitions in model calls: both cascades always call the first model per each stage for an entrance and transition to next models (IDK) or next stage (ICK).