  We introduce tree linear cascades, a class of linear structural equation
models for which the error variables are uncorrelated but need not be Gaussian
nor independent. We show that, in spite of this weak assumption, the tree
structure of this class of models is identifiable. In a similar vein, we
introduce a constrained regression problem for fitting a tree-structured linear
structural equation model and solve the problem analytically. We connect these
results to the classical Chow-Liu approach for Gaussian graphical models. We
conclude by giving an empirical-risk form of the regression and illustrating
the computationally attractive implications of our theoretical results on a
basic example involving stock prices.
