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

Abstract

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.

arXiv comment- v1: Submitted to NeurIPS 2020. Under review - v2: Revised after NeurIPS reviews. Major updates: (i) clean presentation of consistency results; (ii) more references for conditional moment problems - v3: Add references

References in corpus (14)

• Neural Tangent Kernel: Convergence and Generalization in Neural Networks
• Understanding deep learning requires rethinking generalization
• A Convergence Theory for Deep Learning via Over-Parameterization
• Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
• Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks
• Neural Policy Gradient Methods: Global Optimality and Rates of Convergence
• On the Universality of Online Mirror Descent
• Deep Generalized Method of Moments for Instrumental Variable Analysis
• Convergence of Adversarial Training in Overparametrized Neural Networks
• Minimax Estimation of Conditional Moment Models
• Dual Instrumental Variable Regression
• Adversarial Generalized Method of Moments
• A Finite-Time Analysis of Q-Learning with Neural Network Function Approximation
• Neural Temporal-Difference and Q-Learning Provably Converge to Global Optima

Cited by in corpus (2)

• Mathematical Models of Overparameterized Neural Networks
• On Instrumental Variable Regression for Deep Offline Policy Evaluation