Weakly supervised causal representation learning: Supplementary material Johann Brehmer Qualcomm AI Research

In the following we provide additional results and details that did not fit into our main paper. In Appendix A we provide precise definitions and a complete proof of our identifiability theorem. We then discuss the assumptions underlying this result and their generalization in Appendix B. Appendix C covers implicit latent causal models (ILCMs) and their training, while Appendix D provides details for our experiments. We describe causal structure with SCMs. Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc. a probability measure We will need to reason about vectors being "equal up to permutation and elementwise reparameteri-zations".