A Proofs A.1 Proof of Proposition 1 We first show that for any T T

A.2 Proof of Relation (3) We can write D One class of transport maps we consider in our numerical experiments (i.e., to approximate Another underlying class of transports that we use in our numerical experiments are inverse auto-regressive flows (IAFs). IAFs are built as a composition of component-wise affine transformations, where the shift and scaling functions of each component only depend on earlier indexed variables. Flows are typically comprised of several IAF stages with the components either randomly permuted or, as we choose, reversed in between each stage. Here we discuss how generalized linear models may naturally admit lazy structure. Here we describe the numerical algorithms required by the lazy map framework.