Direct Fisher Score Estimation for Likelihood Maximization

• URL: http://arxiv.org/abs/2506.06542v1
• Date: Fri, 06 Jun 2025 21:19:14 GMT
• Title: Direct Fisher Score Estimation for Likelihood Maximization
• Abstract summary: We study the problem of sequential likelihood when the likelihood function is intractable.<n>We propose a gradient-based optimization method that directly models the Fisher score based on a local score matching technique.<n>We provide theoretical guarantees for our score estimator, including bounds on the bias introduced by smoothing.
• Score: 5.327217542835735
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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