无需显式似然函数，用模拟数据直接估计 Fisher 信息，加速模型训练。
Direct Fisher Score Estimation for Likelihood Maximization
- 基于局部模拟数据，直接建模 Fisher 评分，避免复杂似然计算。
- 采用线性参数化实现闭式解，计算高效且稳定。
- 适合似然不可计算但可模拟的复杂模型，如生成模型、统计推断。
当似然函数难以计算但模型模拟容易获取时，我们提出一种基于梯度的序列优化方法，直接通过局部评分匹配技术构建 Fisher 评分的近似模型。该方法利用每个参数迭代点附近的局部模拟数据，采用线性参数化，得到闭式最小二乘解，从而快速、灵活地逼近 Fisher 评分，有效平滑似然目标，缓解复杂似然曲面带来的优化挑战。我们提供了评分估计器的理论保证，包括平滑引入偏差的界。在多种合成与真实世界问题上的实验表明，该方法性能优于现有基准。
原文摘要 · Abstract (English)
We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based on a local score matching technique which uses simulations from a localized region around each parameter iterate. By employing a linear parameterization to the surrogate score model, our technique admits a closed-form, least-squares solution. This approach yields a fast, flexible, and efficient approximation to the Fisher score, effectively smoothing the likelihood objective and mitigating the challenges posed by complex likelihood landscapes. We provide theoretical guarantees for our score estimator, including bounds on the bias introduced by the smoothing. Empirical results on a range of synthetic and real-world problems demonstrate the superior performance of our method compared to existing benchmarks.
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