Suppose we have a regression problem that many people want to solve, but information is distributed across agents --- different agents see different subsets of features. And the agents are embedded in a network (DAG). When one makes predictions, they are observed by its children.

This was also part of a fun exploration we did at the same time in how to incorporate modern AI tools in the process of doing theoretical and experimental science. We learned a lot about that too --- we'll write more at some point.

@LuJiuyao The globally optimal linear predictor need not be in the span of the locally optimal linear predictors (when the features are not independent), since the relative weighting of features differs in each case.

@LuJiuyao The red line btw plots what actually happens when you run this on samples from the generalization of this instance to 10 variables. The chain is A1->A2->...->A10->A1->A2->...->A10->... etc going round robin forever. You get an error drop after each pass but it never goes to 0