DeepAI AI Chat
Log In Sign Up

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

by   Luofeng Liao, et al.

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.


page 1

page 2

page 3

page 4


A global convergence theory for deep ReLU implicit networks via over-parameterization

Implicit deep learning has received increasing attention recently due to...

Global Convergence of Frank Wolfe on One Hidden Layer Networks

We derive global convergence bounds for the Frank Wolfe algorithm when t...

On Feature Learning in Neural Networks with Global Convergence Guarantees

We study the optimization of wide neural networks (NNs) via gradient flo...

Stochastic Gradient Descent Learns State Equations with Nonlinear Activations

We study discrete time dynamical systems governed by the state equation ...

Learning Causal Graphs in Manufacturing Domains using Structural Equation Models

Many production processes are characterized by numerous and complex caus...

Structural Equation Modeling using Computation Graphs

Structural equation modeling (SEM) is evolving as available data is beco...