The Extreme Value Machine – Supplemental Material

For brevity, we adopt array notation. The function takes four arguments (cf. line 1): X and y correspond to all training data and labels respectively, τ is the tailsize, and ς is the coverage threshold. The training function then iterates through every class Cl ∈ C (line 2), fitting a vector of Ψ-models (Ψl) for that class (line 3). The fitting function is presented in Alg. 2 and takes four arguments: X , y, τ , and the class identifier Cl. At each fit, only the Ψ-models for the points and labels corresponding to class Cl, i.e., Xl and yl are considered. The function returns Ψl – a vector of Weibull parameters. Next, the model reduction routine is called (line 4), which takes as argumentsXl, Ψl, and coverage threshold ς . This routine can correspond to Algs. 3 or 4. A vector, I , of indices is returned by this routine, and is then used to select Weibull parameters Ψl, points Xl, and labels yl to keep (lines 5-7). Note that for conceptual clarity, we have presented Alg. 1 in an iterative fashion. However, it is possible to parallelize the loop in lines 2-8, fitting each class separately. The extent to which that is effective is an implementation-level consideration that depends on the hardware at hand, particularly since each Ψli in the fitting algorithm (Alg. 2) can also be parallelized as can pair-wise distance computations within all subroutines (Algs. 2-4).