Likelihood-free methods perform parameter inference in stochastic simulator
models where evaluating the likelihood is intractable but sampling synthetic
data is possible. One class of methods for this likelihood-free problem uses a
classifier to distinguish between pairs of parameter-observation samples
generated using the simulator and pairs sampled from some reference
distribution, which implicitly learns a density ratio proportional to the
likelihood. Another popular class of methods fits a conditional distribution to
the parameter posterior directly, and a particular recent variant allows for
the use of flexible neural density estimators for this task. In this work, we
show that both of these approaches can be unified under a general contrastive
learning scheme, and clarify how they should be run and compared.

该研究探讨了两种不需要概率似然函数的方法来处理具有随机模拟器模型的参数推断问题，分别是通过分类器学习隐含的密度比例和构建条件分布进行参数后验的灵活神经密度估计。研究表明这两种方法可以共同运行于一种对比学习策略下，并详细解释了它们如何运行和相互比较。

对比学习用于无似然推断

On Contrastive Learning for Likelihood-free Inference

An explosion of high-throughput DNA sequencing in the past decade has led to
a surge of interest in population-scale inference with whole-genome data.
Recent work in population genetics has centered on designing inference methods
for relatively simple model classes, and few scalable general-purpose inference
techniques exist for more realistic, complex models. To achieve this, two
inferential challenges need to be addressed: (1) population data are
exchangeable, calling for methods that efficiently exploit the symmetries of
the data, and (2) computing likelihoods is intractable as it requires
integrating over a set of correlated, extremely high-dimensional latent
variables. These challenges are traditionally tackled by likelihood-free
methods that use scientific simulators to generate datasets and reduce them to
hand-designed, permutation-invariant summary statistics, often leading to
inaccurate inference. In this work, we develop an exchangeable neural network
that performs summary statistic-free, likelihood-free inference. Our framework
can be applied in a black-box fashion across a variety of simulation-based
tasks, both within and outside biology. We demonstrate the power of our
approach on the recombination hotspot testing problem, outperforming the
state-of-the-art.

该研究利用交换神经网络，实现了基于模拟数据的统计推断，旨在解决高维变量积分与数据置换不变性问题，取得了在重组热点测试问题上领先于现有技术的成果。

一种基于可交换神经网络的无似然推断框架，应用于人群遗传数据

A Likelihood-Free Inference Framework for Population Genetic Data using  Exchangeable Neural Networks

We consider the problem of parametric statistical inference when likelihood
computations are prohibitively expensive but sampling from the model is
possible. Several so-called likelihood-free methods have been developed to
perform inference in the absence of a likelihood function. The popular
synthetic likelihood approach infers the parameters by modelling summary
statistics of the data by a Gaussian probability distribution. In another
popular approach called approximate Bayesian computation, the inference is
performed by identifying parameter values for which the summary statistics of
the simulated data are close to those of the observed data. Synthetic
likelihood is easier to use as no measure of `closeness' is required but the
Gaussianity assumption is often limiting. Moreover, both approaches require
judiciously chosen summary statistics. We here present an alternative inference
approach that is as easy to use as synthetic likelihood but not as restricted
in its assumptions, and that, in a natural way, enables automatic selection of
relevant summary statistic from a large set of candidates. The basic idea is to
frame the problem of estimating the posterior as a problem of estimating the
ratio between the data generating distribution and the marginal distribution.
This problem can be solved by logistic regression, and including regularising
penalty terms enables automatic selection of the summary statistics relevant to
the inference task. We illustrate the general theory on canonical examples and
employ it to perform inference for challenging stochastic nonlinear dynamical
systems and high-dimensional summary statistics.

基于逻辑回归的比例估计方法作为参数统计推断的替代方法，以更丰富的总结统计信息来消除假设先验和卡方问题。

使用比值估计实现无似然推断

Likelihood-free inference by ratio estimation

Also known as likelihood-free methods, approximate Bayesian computational
(ABC) methods have appeared in the past ten years as the most satisfactory
approach to untractable likelihood problems, first in genetics then in a
broader spectrum of applications. However, these methods suffer to some degree
from calibration difficulties that make them rather volatile in their
implementation and thus render them suspicious to the users of more traditional
Monte Carlo methods. In this survey, we study the various improvements and
extensions made to the original ABC algorithm over the recent years.

这篇综述论文研究了近年来对原始 ABC 算法进行的各种改进和扩展，探讨了 ABC 方法在缺少可追踪度的似然问题中的解决方案，并且指出了它们存在的校准困难和不稳定性问题。