Supplementary Material A Proof of Paper Results

We now consider the gradient of the log-variance loss. Using the definition from Eq. 5, we see that From [Reiss, 2012, Lemma A.3.5] we have the bound Combining these estimates we arrive at the claimed result. The claim follows by direct calculation. In fact, it is possible to take K = 15 . Lemma 3 shows that the kurtosis term in our bound Eq. 16 can be bounded for Gaussian families.