Correlation and causation

Correlation (r between −1 and 1) measures how much two variables co-vary linearly. Ice cream sales and drownings correlate strongly — but ice cream does not cause drowning. The summer causes both: a confounder.

Other traps: reverse causation (firefighters do not cause fires, even though more firefighters = a larger fire), selection (among admitted students the entrance test correlates negatively with school grades — because both were used in the admission), chance (with 1 000 variables you always find some that correlate).

An ML model finds correlations. It knows nothing about causation. It is you who has to know that before the model is used to change anything.

import numpy as np
rng = np.random.default_rng(0)

summer = rng.uniform(0, 1, 200)             # the hidden confounder
ice_cream = 100 * summer + rng.normal(0, 10, 200)
drowning = 5 * summer + rng.normal(0, 1, 200)
print(np.corrcoef(ice_cream, drowning)[0, 1])   # ≈ 0.8 — a strong correlation with no causation

# control for the summer: the residuals
res_i = ice_cream - np.polyval(np.polyfit(summer, ice_cream, 1), summer)
res_d = drowning - np.polyval(np.polyfit(summer, drowning, 1), summer)
print(np.corrcoef(res_i, res_d)[0, 1])      # ≈ 0 — the relationship disappears

To claim causation: a randomised experiment (an A/B test) or very careful control for every confounder — and even then with reservations.