(Algorithm 1). Then, we propose another strategy (Algorithm 2) to solve FSPCA for the general covariance by iteratively building a carefully designed proxy.

This concludes the proof that ˆ c is related to the true content c via a smooth invertible mapping.

Unlike prior work on disentanglement and independent component analysis, we allow for both nontrivial statistical and causal dependencies in the latent space.

Do the main claims made in the abstract and introduction accurately reflect the paper's Did you discuss any potential negative societal impacts of your work? Such methods could provide biased representations that could have negative downstream use cases as features for models, in search (for example). Did you include complete proofs of all theoretical results? Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Y es] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? Did you include the total amount of compute and the type of resources used (e.g., type Did you include any new assets either in the supplemental material or as a URL? [Y es] Did you discuss whether and how consent was obtained from people whose data you're using/curating?

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans.