another subject’s 24-month image. To assess the performance of prediction models trained on these two types of paired data, we (1) perform the same type of registrations on the held-out 20 subjects and (2) compare the 2-norm of the deformation error computed from the output of the prediction models with respect to the result obtained by numerical optimization of LDDMM[^2] (which serves as the “ground-truth”). Table \[tab:1\] shows the results which confirm our hypothesis that training the prediction model with longitudinal registration cases is preferred for longitudinal registration over training with cross-sectional data. The deformation error is very small for longitudinal training / testing which provides strong evidence that the predictive method exhibits performance comparable to the (costly) optimization-based LDDMM. Another interpretation of these results is, that it is beneficial to train a prediction model with deformations that are to be *expected*, i.e., relatively small deformations for longitudinal registrations and larger deformations for cross-sectional registrations. As we are interested in longitudinal registrations for the `ADNI` data, we only train our 3D models using longitudinal registrations in the following.

1ex **Training for regression.** The `ADNI-1` dataset contains 228 normal controls, 257 subjects with mild cognitive impairment (MCI), 149 with late mild 