提出新算法，高效精准估算无法直接求解的随机模型参数。
A New Stochastic Approximation Method for Gradient-based Simulated Parameter Estimation
- 用多时标随机逼近法优化梯度模拟参数估计
- 显著降低比率偏差，提升估计精度并节省计算成本
- 适合处理隐马尔可夫模型等复杂随机系统
本文针对难以获得解析形式似然函数的随机模型参数校准问题，提出一种基于梯度的模拟参数估计框架，采用多时标随机逼近算法。该方法有效缓解了最大似然估计与后验密度估计中常见的比率偏差问题。通过大量数值实验验证，新算法在提升估计精度的同时显著降低计算开销。研究将GSPE框架拓展至隐马尔可夫模型及基于变分推断的问题，为复杂随机环境下的参数估计提供稳健解决方案。
原文摘要 · Abstract (English)
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation framework, which employs a multi-time scale stochastic approximation algorithm. This approach effectively addresses the ratio bias that arises in both maximum likelihood estimation and posterior density estimation problems. The proposed algorithm enhances estimation accuracy and significantly reduces computational costs, as demonstrated through extensive numerical experiments. Our work extends the GSPE framework to handle complex models such as hidden Markov models and variational inference-based problems, offering a robust solution for parameter estimation in challenging stochastic environments.
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