Use of prior knowledge in NOTEARS

[maurovidal23]

It could be interesting to leverage the ability of optimization-based algorithms to incorporate prior knowledge as constraints. In the case of NOTEARS, which uses scipy.optimize, you can easily introduce bounds.

Using prior knowledge in this context means setting (i, j) = 0 if we want to forbid that edge, or (i, j) = 1 if we want to force its inclusion. I believe this is a fundamental feature for integrating both data and expert knowledge into the algorithm.

PS: This approach could potentially be extended to other optimization algorithms, but I haven't reviewed the code yet. For NOTEARS, it seems like it wouldn't require major changes.

[shaido987]

Hi @maurovidal23, sorry for the delayed answer. That sounds like a plausible approach to introducing prior knowledge into NOTEARS (and it aligns with our aim of introducing prior knowledge to more algorithms #79). Currently, we already do this for the matrix diagonal:

trustworthyAI/gcastle/castle/algorithms/gradient/notears/linear.py

Lines 190 to 191 in bd9cac2

	bnds = [(0, 0) if i == j else (0, None) for _ in range(2)
	for i in range(d) for j in range(d)]

Extending this to other prior knowledge should not be a large step but some tests would be needed to ensure that it works correctly. If you are interested we would welcome an PR for this.