- Central parts of the paper are unclear eg. in line 80 \log P_M (X; \theta) should be the negative cross entropy. - The proposed objective Eq. 2 in line 128, requires the optimisation over both the parameters of the transformation \phi and the shared model \theta_S. The effect on the number of parameters vs. prior work eg. AlignFlow (Grover et. al. 2019) has not been discussed clearly. - The paper is sparse in quantitative results and does not compare to important prior work based on GANs [1]. The only quantitative results are on adaptation from USPS to MNIST in line 268. However, prior work [1] achieves 96.5% accuracy in comparison to the 55% accuracy achieved by the proposed method. - The empirical evaluation is restricted to small datasets eg. moons, MNIST and USPS. It would be desirable to evaluate the proposed approach on the more complex Facades/Maps/Cityscapes using the MSE metric to facilitate comparison with AlignFlow and [1]. - The shared model (\theta_s) is trained on two datasets simultaneously. It is unclear how the inductive bias from each of the datasets influence the shared space. [1] CyCADA: Cycle-Consistent Adversarial Domain Adaptation, ICML 2018.
- The proposed objective Eq. 2 in line 128, requires the optimisation over both the parameters of the transformation \phi and the shared model \theta_S. The effect on the number of parameters vs. prior work eg. AlignFlow (Grover et. al. 2019) has not been discussed clearly.