Fréchet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables.

A.1 Proof of Proposition 1 We note that 1 is restated and was proved in [25, Appendix A.1] Proof of 2: Non-negativity directly follows by non-negativity of mutual information. Proof of 5: The proof relies on the independence of functions of independent random variables. This concludes the proof. 1 A.2 Proof of Proposition 2 By translation invariance of mutual information, we may assume w.l.o.g. that the means are Next, we show that we may equivalently optimize with the added unit variance constraint. Example 3.4]), we have I (A B) null, where the last equality uses the unit variance property and Schur's determinant formula. Armed with Lemma 1, we are in place to prove Proposition 2. Since the CCA solutions Theorem 2.2], which is restated next for completeness.

This work proposes a middle ground in the form of a scalable information-theoretic generalization of CCA, termed max-sliced mutual information (mSMI).

In recent years, machine learning has shown great promise in a variety of real-world applications.

For a subclass of models, a finite number of densities suffice.