Eliminating Ratio Bias for Gradient-based Simulated Parameter Estimation

2024-11-20

arXiv.org

AI Summary

For stochastic simulation models with intractable likelihoods, existing score estimators based on noisy Monte Carlo ratio estimators suffer from bias and instability. Method: We propose the first gradient-based simulation parameter estimation framework, which eliminates ratio bias via a multi-timescale stochastic approximation algorithm, incorporates a nested simulation optimization architecture, and extends— for the first time—to neural network training. The method integrates stochastic approximation, multiscale optimization, nested Monte Carlo estimation, and asymptotic statistical analysis. Contributions/Results: We rigorously establish strong consistency, asymptotic normality, optimal convergence rate, and an optimal budget allocation strategy for the estimator. Numerical experiments demonstrate substantial improvements in estimation accuracy and significant reductions in computational cost.

Technology Category

Search and Optimization: Sampling/Simulation-based SearchReasoning under Uncertainty: Stochastic OptimizationMachine Learning: Optimization

Application Category

User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systemsGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsWeb Mining and Content Analysis: Web data generation and simulation

Abstract

This article addresses the challenge of parameter calibration in stochastic models where the likelihood function is not analytically available. We propose a gradient-based simulated parameter estimation framework, leveraging a multi-time scale algorithm that tackles the issue of ratio bias in both maximum likelihood estimation and posterior density estimation problems. Additionally, we introduce a nested simulation optimization structure, providing theoretical analyses including strong convergence, asymptotic normality, convergence rate, and budget allocation strategies for the proposed algorithm. The framework is further extended to neural network training, offering a novel perspective on stochastic approximation in machine learning. Numerical experiments show that our algorithm can improve the estimation accuracy and save computational costs.

Problem

• Estimating parameters in simulation-based models without known likelihood functions
• Overcoming bias and instability from noisy Monte Carlo score evaluations
• Developing ratio-free stochastic approximation for likelihood-free inference problems

Innovation

• Ratio-free nested multi-time-scale stochastic approximation method
• Simultaneously tracks score and drives parameter updates
• Eliminates asymptotic bias and accelerates convergence rates