  Structural equation models (SEMs) are widely used in sciences, ranging from
economics to psychology, to uncover causal relationships underlying a complex
system under consideration and estimate structural parameters of interest. We
study estimation in a class of generalized SEMs where the object of interest is
defined as the solution to a linear operator equation. We formulate the linear
operator equation as a min-max game, where both players are parameterized by
neural networks (NNs), and learn the parameters of these neural networks using
the stochastic gradient descent. We consider both 2-layer and multi-layer NNs
with ReLU activation functions and prove global convergence in an
overparametrized regime, where the number of neurons is diverging. The results
are established using techniques from online learning and local linearization
of NNs, and improve in several aspects the current state-of-the-art. For the
first time we provide a tractable estimation procedure for SEMs based on NNs
with provable convergence and without the need for sample splitting.
