Hi Adam. These articles are superb — thanks for putting them together!
Your approach to the “beta-problem” versus the “y-hat” problem is really interesting, but a little beyond me at present. If I’ve understood correctly, you randomly generate candidate causal graphs and perform regression using just the “parents” as explanatory variables, then compare the results to Lasso, is that correct?
How much can you say about the “likelihoods” of the different causal graphs at the end of this process? For example, can you get a probability distribution over the possible graph structures? Or do you just pick the graph(s) with the highest r-squared and say, “based on my data, these seem like reasonable causal model(s)”?
Really looking forward to reading the next installment! Best wishes.