A Proofs Proposition 1 The mapping f

See proof of Proposition 3 below for the form of the Jacobian. Theorem 4.7] and so is the product p Equation ( 50) is an element-wise division. The main preprocessing we did was to (i) remove the "label" attribute from each data set, and (ii) Descriptions for all data set are below. All data have been completely anonymized. The original task was to predict whether an applicant would be recommended for acceptance by hierarchical decision model, which has been removed during preprocessing.