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.

翻译：我们研究了似然函数难以计算但模型模拟易于获得时的似然最大化问题。我们提出了一种基于梯度的序列优化方法，该方法通过局部分数匹配技术直接建模Fisher分数，该技术利用了每个参数迭代周围局部区域的模拟数据。通过采用对替代分数模型的线性参数化，我们的方法获得了闭式的最小二乘解。该方法为Fisher分数提供了一种快速、灵活且高效的近似，有效平滑了似然目标函数，并缓解了复杂似然景观带来的挑战。我们为分数估计器提供了理论保证，包括平滑引入偏差的界限。在一系列合成与真实世界问题上的实验结果表明，与现有基准方法相比，我们的方法具有优越性能。