Over half of cancer patients experience long-term pain management challenges.

What is the minimum necessary information required by a neural netD() from an image x to accurately predict its class? Extracting such information in the input space fromx can allocate the areasD() mainly attending to and shed novel insights to the detection and defense of adversarial attacks. In this paper, we propose "class-disentanglement" that trains a variational autoencoder G() to extract this class-dependent information asx G(x) via a trade-off between reconstructingx by G(x) and classifying x by D(x G(x)), where the former competes with the latter in decomposingx so the latter retains only necessary information for classification inx G(x).

Here we provide proofs of the statements made in the main text as well as further figures of numerical experiments and a more detailed discussion of heteroskedasticity effects regarding causal discovery. Z. Testing whether the Pearson correlation between X and Y is zero is equivalent to testing whether the slope parameter β is equal to zero. Therefore, this is a homoskedastic problem. A.1.2 Discussion of Effect 2: We start by discussing the homoskedastic case to see where non-constant variance of noise leads to problems within the t-test. For homoskedastic noise the second factor is an estimator of the standard error of ˆβ, which we derive by using the mean of the squared residual as an estimator for the error variance.