This section illustrates that (7) holds.

The example shows the learned IT map with high w =2 0 approximating the ET map.

In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image.

P and Q, respectively, is tight in P (X Y). Hero, 2004; Ghourchian et al., 2017), we present the outline of our argument into three steps: K P (X) is tight iff the closure of K is sequentially compact in P ( X) with respect to the weak convergence. Remark 1. W e could proceed differently by imposing stronger assumptions using the following W e briefly discuss the outline of the proof for the sake of completeness. (Loeve, 2017). The argument here depends on two important facts: 1.

In many applications, the number of features could be very large.

A popular heuristic method for improving clustering results is to apply dimensionality reduction before running clustering algorithms.

Proof of Lemma 5. Suppose M is a matrix then we can write M = UV

A.1 Experiment 1 A.1.1 Participants Experiment 1 recruited 21 participants (11 females, aged 18-25). All participants had provided informed consent before the experiment. Cover story Participants were told that they were apprentice magicians in a magical world. In this world, dangerous magic lava rocks were emitted from an unknown number of invisible volcano(es). On each trial, they observed past landing locations of lava rocks in a specific area (on the screen), and their job was to predict the probability density of future landing locations. More specifically, they were asked to draw a probability density by reporting, using click-and-drag mouse gestures, three key properties of the volcano(es), corresponding to the mean, the weight, and the standard deviation of a Gaussian component. They were told that their bonus payment depended on the accuracy of the reported predictive density.