Title: Direct Fisher Score Estimation for Likelihood Maximization Show Chinese title

Title: 直接Fisher分数估计用于最大化似然性

Abstract: 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. Show Chinese abstract

Abstract: 我们研究了当似然函数无法解析但模型模拟易于获得时的似然最大化问题。 我们提出了一种顺序梯度优化方法，该方法基于局部分数匹配技术直接对Fisher得分建模，该技术使用在每个参数迭代点周围的局部区域内进行的模拟。 通过采用线性参数化来替代分数模型，我们的技术得到了一个闭式最小二乘解。 这种方法对Fisher得分提供了一个快速、灵活且高效的近似值，有效地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，包括由平滑引入的偏差的界限。 在一系列合成和真实世界的问题上的实证结果显示，与现有基准相比，我们的方法表现更优。