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Define a structural causal model

The structural causal model used in the publication is printed below.
The setup is easy:

  1. Define the background noise variables (i.e. variables not caused by any other variable)

  2. variable is the internal name

  3. label is a longer name; when these corerspond to measurements of the images (like here size and variance), they will be used to sample images
  4. type noise vs dependent
  5. distribution where to draw the variable from; for the dependent variables, this is the conditional distribution
  6. param_1 and param_2 are the canonical parameters for the distribution (e.g. location and scale for Normal)

  7. Define the relationships between the noise variables and the dependent variables, using b_... columns to define coefficients from the noise variable to ... in a linear model.

variable label type distribution variable_model param_1 param_2 b_x b_t b_y
u1 u1 noise Normal 0 0.7071 1 0 -2
u2 u2 noise Normal 0 0.7071 -1 1.828 0
z variance noise Normal 0 1 0 0 -1
n_x noise_x noise Normal 0 0.05 1 0 0
n_t noise_t noise Normal 0 0.05 0 1 0
n_y noise_y noise Normal 0 0.05 0 0 1
x size dependent Normal Linear 0 0 0 0
t treatment dependent Bernoulli Logistic -0.5 0 0 1
y survival dependent Normal Linear -0.5 0 0 0