Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach

Understand

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.