Supplementary materials - NeuMiss networks: differentiable programming for supervised learning with missing values A Proofs

Proof of Lemma 2. Identifying the second and first order terms in X we get: The last equality allows to conclude the proof. Additionally, assume that either Assumption 2 or Assumption 3 holds. This concludes the proof according to Lemma 1. Here we establish an auxiliary result, controlling the convergence of Neumann iterates to the matrix inverse. Note that Proposition A.1 can easily be extended to the general case by working with M (61) i.e., a M nonlinearity is applied to the activations.