sbi-dev
Multifidelity Simulation-based Inference for Computationally Expensive Simulators
🚀 Feature Request
Problem: Computationally expensive simulators
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high accuracy) to the phenomena under study being often preferable. However, inferring parameters of high-fidelity models via simulation-based inference is challenging, especially when the simulator is computationally expensive.
Multifidelity simulation-based inference
We introduce MF-NPE, a multifidelity approach to neural posterior estimation that leverages inexpensive low-fidelity simulations to infer parameters of high-fidelity simulators within a limited simulation budget. MF-NPE performs neural posterior estimation with limited high-fidelity resources by virtue of transfer learning, with the ability to prioritize individual observations using active learning.
Alternative solutions
We can also use transformers or integrate this approach with neural likelihood estimation.
📌 Additional Context
On one statistical task with analytical ground truth and two real-world tasks, MF-NPE shows comparable performance to current approaches while requiring up to two orders of magnitude fewer high-fidelity simulations. Overall, MF-NPE opens new opportunities to perform efficient Bayesian inference on computationally expensive simulators.
For instance:
(A) Posterior density estimates for a single observation from the OU process with two free parameters (OU2). The orange contour lines contain 68% of the probability mass of the true posterior distribution. (B) C2ST averaged over 10 network initializations: means and 95% confidence intervals. MF-NPE3 is pre-trained on a low-fidelity dataset of size 103, while MF-NPE4 and MF-NPE5 use datasets of 104 and 105 low-fidelity simulations, respectively. MF-NPE improves its performance with a larger number of low-fidelity samples, and all variants of our method perform better than NPE.
