A new causal discovery method can handle feedback loops and hidden variables that most prior techniques either ignore or assume away.
The approach, described in a new arXiv paper, works on linear Gaussian models - the standard setup for many causal-inference problems - but drops two assumptions almost every competing method relies on: that cause-and-effect relationships never loop back on themselves, and that every relevant variable is actually observed. The researchers allow for directed cycles and for an unknown number of hidden confounders, up to a set maximum, and introduce a concept called marginal quasi-equivalence to identify when two different causal structures are indistinguishable from the same data. Instead of searching through a combinatorial explosion of possible graphs, they use continuous Bernoulli gates to decide which edges and latent variables belong, letting gradient descent handle what used to require brute-force search. The paper also proves this smoothed, differentiable version of the problem lands on the same answer as the original discrete one.
That combination matters because real systems - biological networks, economic data, sensor arrays - routinely loop back on themselves and routinely have hidden common causes. Causal-discovery tools that assume otherwise can produce clean-looking graphs that are simply wrong about the system they claim to describe. Pairing a formal consistency proof with a practical, gradient-based optimizer is a step toward tools that handle both complications without throwing out mathematical guarantees.
The paper reports lower recovery error than previous methods in its own test settings - as these papers tend to - so the real test is whether the gains survive contact with data nobody picked for the benchmark.