Another idea to represent the empirical distribution into a fixed-size two dimensional object would be to represent the pair given as input as a scatter plot; the algorithms would then try to visually identify causal patterns in the drawn scatter plot. This approach, exploited by Singh et al. through a deep convolutional neural network, aligns itself with the examples and the idea that non-invertible causal mechanisms (a visually noticeable feature) give away the causal direction.

Many different visual representations of the distributions are available to the practitioners, and little is known on their influence.Here are two of them:

• the “raw” scatter plot of the data, where a pixel is either 1 or 0 depending on whether a data point is present in the region represented by the pixel
• a Gaussian distribution centered on each point, with a relatively low variance