Acquisition of simulations

[Justinezgh]

(from https://arxiv.org/pdf/2101.04653.pdf and https://arxiv.org/pdf/1903.00007.pdf)

Different strategies:

• Sequential:

  • New simulations are drawn from a proposal density based on the current posterior approximation. BUT when the posterior is targeted directly, using a proposal distribution p ̃(θ) different from the prior requires a correction step without it, the posterior under the proposal distribution would be inferred. The so-called proposal posterior:
    • https://arxiv.org/pdf/1605.06376.pdf, target the proposal posterior p ̃(θ|x) by minimizing the log likelihood loss −sum log qψ(θn|xn), and then post-hoc solves for p(θ|x).
    • https://arxiv.org/abs/1711.01861, directly recover p(θ|x) with the weighted loss - sum p(θn)/p ̃(θn) log qψ(θn|xn). However, the importance weights can have high variance during training, leading to inaccurate inference for some tasks.
    • https://arxiv.org/pdf/1905.07488.pdf
  • Use the geometric mean of the prior and the current posterior approximation as the proposal density: https://arxiv.org/pdf/1808.06040.pdf.

• Bayesian optimization. It requires two ingredients:

  • some way of quantifying uncertainty in the current learned posterior surface
  • acquisition rule
    • the current variance of the estimated posterior density (https://arxiv.org/abs/1805.09294)
    • minimizing the expected integrated variance of the approximate posterior, under a new simulation draw (https://arxiv.org/abs/1704.00520)