Direct Fisher Score Estimation for Likelihood Maximization
It provides a fast, flexible, and efficient approximation to the Fisher score for likelihood-free inference, addressing a known bottleneck in simulation-based inference.
The paper proposes a gradient-based optimization method for likelihood maximization when the likelihood is intractable but simulations are available, using a local score matching technique to estimate the Fisher score. The method achieves superior performance on synthetic and real-world problems compared to existing benchmarks.
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.