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# Define a structural causal model |
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The structural causal model used in the publication is printed below. |
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The setup is easy: |
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1. Define the background noise variables (i.e. variables not caused by any other variable) |
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* **variable** is the internal name |
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* **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 |
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* **type** noise vs dependent |
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* **distribution** where to draw the variable from; for the dependent variables, this is the *conditional* distribution |
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* **param_1** and **param_2** are the canonical parameters for the distribution (e.g. location and scale for Normal) |
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2. 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. |
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| variable | label | type | distribution | variable_model | param_1 | param_2 | b_x | b_t | b_y | |
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|----------|-----------|-----------|--------------|----------------|---------|---------|-----|-------|-----| |
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| u1 | u1 | noise | Normal | | 0 | 0.7071 | 1 | 0 | -2 | |
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| u2 | u2 | noise | Normal | | 0 | 0.7071 | -1 | 1.828 | 0 | |
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| z | variance | noise | Normal | | 0 | 1 | 0 | 0 | -1 | |
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| n_x | noise_x | noise | Normal | | 0 | 0.05 | 1 | 0 | 0 | |
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| n_t | noise_t | noise | Normal | | 0 | 0.05 | 0 | 1 | 0 | |
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| n_y | noise_y | noise | Normal | | 0 | 0.05 | 0 | 0 | 1 | |
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| x | size | dependent | Normal | Linear | 0 | | 0 | 0 | 0 | |
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| t | treatment | dependent | Bernoulli | Logistic | -0.5 | | 0 | 0 | 1 | |
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| y | survival | dependent | Normal | Linear | -0.5 | | 0 | 0 | 0 | |