AI_ML_DL’s diary


The frontier of simulation-based inference

The frontier of simulation-based inference

Kyle Cranmer, Johann Brehmer, and Gilles Louppe


Many domains of science have developed complex simulations to describe phenomena of interest.

While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems.

We review the rapidly developing field of simulation-based inference and identify the forces giving additional momentum to the field.

Finally, we describe how the frontier is expanding so that a broad audience can appreciate the profound influence these developments may have on science.


statistical inference | implicit models | likelihood-free inference | 

approximate Bayesian computation | neural density estimation


Mechanistic models can be used to predict how systems will behave in a variety of circumstances.

These run the gamut of distance scales, with notable examples including particle physics, molecular dynamics, protain folding, population genetics, neuroscience, epidemiology, economics, ecology, climate science, astrophysics, and cosmology.

The expressiveness of programming languages facilitates the development of complex, high-fidelity simulations and the power of modern computing provides the ability to generate synthetic data from them.

Unfortunately, these simulators are poorly suited for statistical inference.

The source of the challenge is that the probability density (or likelihood) for a given observation - an essential ingredient for both frequentist and Bayesian inference methods - is typically intractable.

Such models are often referred to as implicit models and contrasted against prescribed models where the likelihood for an observation can be explicitly calculated (1).

The problem setting of statistical inference under intractable likelihoodshas been dubbed likelihood-free inference - although it is a bit of a misnomer as typically one attempts to estimate the intractable likelihood, so we feel the term simulation-based inference is more apt.  






*ABCは、Approximate Bayesian Computationのこと。


Workflows for Simulation-Based Inference



推論手法は、ABCのように、推論中にシミュレーター自体を使用するものと、代理モデルを構築して推論に使用する方法に大きく分けることができます。最初のケースでは、シミュレーターの出力がデータと直接比較されます(図1 A–D)。後者の場合、シミュレーターの出力は、図1 E – Hの緑色のボックスに示すように、推定またはMLステージのトレーニングデータとして使用されます。結果の代理モデルは、赤い六角形で示され、推論に使用されます。






style=147 iteration=1


style=147 iteration=20


style=147 iteration=500