Kernel Recursive ABC: Point Estimation with Intractable Likelihood

2018/02/23 by Takafumi Kajihara, Motonobu Kanagawa, Kajihara, Takafumi +5
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #stat.ML

paper · pdf · doi:10.48550/arxiv.1802.08404

to appear in ICML 2018. 18 pages

openalex publication_date 2018/02/23 · arxiv created 2018/06/12 · arxiv updated 2018/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.

Citations

• A Method for Simulating Stable Random Variables
• Statistical inference for noisy nonlinear ecological dynamic systems
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

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