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

Neural density estimators are flexible families of parametric models which
have seen widespread use in unsupervised machine learning in recent years.
Maximum-likelihood training typically dictates that these models be constrained
to specify an explicit density. However, this limitation can be overcome by
instead using a neural network to specify an energy function, or unnormalized
density, which can subsequently be normalized to obtain a valid distribution.
The challenge with this approach lies in accurately estimating the normalizing
constant of the high-dimensional energy function. We propose the Autoregressive
Energy Machine, an energy-based model which simultaneously learns an
unnormalized density and computes an importance-sampling estimate of the
normalizing constant for each conditional in an autoregressive decomposition.
The Autoregressive Energy Machine achieves state-of-the-art performance on a
suite of density-estimation tasks.

Autoregressive Energy Machine 是一种高效的基于能量的神经网络模型，具备在无监督学习中广泛使用的灵活性，可以在不受概率密度限制的条件下计算归一化常数，实现在密度估计任务中的最优表现。

自回归能量机

Autoregressive Energy Machines

Likelihood-free inference provides a framework for performing rigorous
Bayesian inference using only forward simulations, properly accounting for all
physical and observational effects that can be successfully included in the
simulations. The key challenge for likelihood-free applications in cosmology,
where simulation is typically expensive, is developing methods that can achieve
high-fidelity posterior inference with as few simulations as possible.
Density-estimation likelihood-free inference (DELFI) methods turn inference
into a density estimation task on a set of simulated data-parameter pairs, and
give orders of magnitude improvements over traditional Approximate Bayesian
Computation approaches to likelihood-free inference. In this paper we use
neural density estimators (NDEs) to learn the likelihood function from a set of
simulated datasets, with active learning to adaptively acquire simulations in
the most relevant regions of parameter space on-the-fly. We demonstrate the
approach on a number of cosmological case studies, showing that for typical
problems high-fidelity posterior inference can be achieved with just
$\mathcal{O}(10^3)$ simulations or fewer. In addition to enabling efficient
simulation-based inference, for simple problems where the form of the
likelihood is known, DELFI offers a fast alternative to MCMC sampling, giving
orders of magnitude speed-up in some cases. Finally, we introduce
\textsc{pydelfi} -- a flexible public implementation of DELFI with NDEs and
active learning -- available at https://github.com/justinalsing/pydelfi.

本文使用神经密度估计器学习来自一组模拟数据集的似然函数，以及实时学习以适应性地获取最相关的参数空间区域的仿真，以展示 DELFI 在宇宙学案例研究中的应用。

利用神经密度估计器和主动学习的快速无似然宇宙学

Fast likelihood-free cosmology with neural density estimators and active  learning

Autoregressive models are among the best performing neural density
estimators. We describe an approach for increasing the flexibility of an
autoregressive model, based on modelling the random numbers that the model uses
internally when generating data. By constructing a stack of autoregressive
models, each modelling the random numbers of the next model in the stack, we
obtain a type of normalizing flow suitable for density estimation, which we
call Masked Autoregressive Flow. This type of flow is closely related to
Inverse Autoregressive Flow and is a generalization of Real NVP. Masked
Autoregressive Flow achieves state-of-the-art performance in a range of
general-purpose density estimation tasks.

使用 Masked Autoregressive Flow 构建自回归模型栈，提高神经密度估计的灵活性，达到最先进的性能表现。