Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models
This work addresses efficient Bayesian inference for researchers in computational statistics and machine learning, offering incremental improvements in simulation cost reduction.
The authors tackled Bayesian inference in simulator-based models by introducing Sequential Neural Posterior Score Estimation (SNPSE), a score-based method that generates posterior samples using conditional diffusion models, achieving comparable or superior performance to state-of-the-art methods like SNPE in numerical examples.
We introduce Sequential Neural Posterior Score Estimation (SNPSE), a score-based method for Bayesian inference in simulator-based models. Our method, inspired by the remarkable success of score-based methods in generative modelling, leverages conditional score-based diffusion models to generate samples from the posterior distribution of interest. The model is trained using an objective function which directly estimates the score of the posterior. We embed the model into a sequential training procedure, which guides simulations using the current approximation of the posterior at the observation of interest, thereby reducing the simulation cost. We also introduce several alternative sequential approaches, and discuss their relative merits. We then validate our method, as well as its amortised, non-sequential, variant on several numerical examples, demonstrating comparable or superior performance to existing state-of-the-art methods such as Sequential Neural Posterior Estimation (SNPE).