What?

A survey of simulation-based inference and identifying what can improve the field.

Why?

Simulators are omnipresent in science, with a progress in ML, we have new tools to improve the simulators → keep the science going.

How?

source: original paper

What is a simulator?

• A computer program;
• Takes parameters $\theta$ as input;
• Samples latent variables (internal states) $z \sim p_i(z_i \mid \theta, z_{<i})$;
  • parameters affect the transition probabilities ^^^.
  • latents heavily depend on the problem;
    • can be discrete or continuous;
    • have some semantics;
    • dimensions can vary greatly;
    • some simulators provide access to latents (others are black boxes)
• Produces a data vector $x \sim p(x\mid \theta, z)$as the output.
  • $x$ correspond to observations.

Inference

• Given observed data $x$, what are the parameters $\theta$ or latents $z$?
  • Calcluate the posterior $p(\theta \mid x) = p(x \mid \theta) p(\theta)/ \int{p(x\mid \theta')p(\theta')d\theta'}$.
  • The likelihood is intractable! (need to integrate over all the latents)

Traditional methods

• Approximate Bayesian Computation (ABC):
  • Draw $\theta$ from the prior;
  • Simulate with $\theta$ to get $x_\text{sim}$;
  • Reject if $\rho(x_\text{sim}, x_\text{obs})<\epsilon$, where $\rho$ is some distance;
  • You get your posterior.
  • Problems:
    • Needs a lot of samples;
    • Poor scaling to high-dimensional data (here you go, Jeremy Howard);
    • For new observations, requires rerunning the inference.
• Amortized likelihood (1E):
  • Similar to ABC, can call it "approximate frequentist computation";
  • Amortized! New data points can be efficiently evaluated.
  • Curse of dimensionality again! (Oh no =()
    • Both approaches require low-dimensional summary statistics (need feature extractors!)

Frontiers

• Shortcomings of traditional approaches:
  • sample efficiency;
  • quality of inference;
  • amortization;
• Main directions of progress:
  • Machine Learning
    • Neural Networks for the win;
    • Replace human feature extractors with networks;
    • Density estimation in high dimensions;
    • Normalizing flows;
    • GANs;
  • Active Learning
    • Sample parameters $\theta$ that increase our knowledge the most;
  • Automatic Differentiation
    • Treat the simulation as a white box;
    • Probabilistic programming;

Using the simulator directly during inference (A-D on the figure)

• Run the simulator with the parameters that are expected to improve the knowledge of the posterior the most.
• Inference controls all steps of the program execution and can bias each draw of latents to improve the data match.
• Probabilistic programming for the win;

Surrogate models (E-H on the figure)