We introduce a new amortized likelihood ratio estimator for likelihood-free
simulation-based inference (SBI). Our estimator is simple to train and
estimates the likelihood ratio using a single forward pass of the neural
estimator. Our approach directly computes the likelihood ratio between two
competing parameter sets which is different from the previous approach of
comparing two neural network output values. We refer to our model as the direct
neural ratio estimator (DNRE). As part of introducing the DNRE, we derive a
corresponding Monte Carlo estimate of the posterior. We benchmark our new ratio
estimator and compare to previous ratio estimators in the literature. We show
that our new ratio estimator often outperforms these previous approaches. As a
further contribution, we introduce a new derivative estimator for likelihood
ratio estimators that enables us to compare likelihood-free Hamiltonian Monte
Carlo (HMC) with random-walk Metropolis-Hastings (MH). We show that HMC is
equally competitive, which has not been previously shown. Finally, we include a
novel real-world application of SBI by using our neural ratio estimator to
design a quadcopter. Code is available at this https URL

我们引入了一种新的摊销似然比估计器，用于无似然模拟推理（SBI），引入了一种称为直接神经比率估计器（DNRE）的模型，对先前的方法进行了改进，并在文献中与其他估计器进行了比较，同时实现了一个新的导数估计器，使得我们可以比较无似然哈密顿蒙特卡洛（HMC）和随机行走 Metropolis-Hastings（MH），最后我们通过使用神经比率估计器设计四旋翼飞行器展示了该方法的现实应用。

直接摊销似然比估计

Direct Amortized Likelihood Ratio Estimation

Personalised interactive systems such as recommender systems require
selecting relevant items dependent on context. Production systems need to
identify the items rapidly from very large catalogues which can be efficiently
solved using maximum inner product search technology. Offline optimisation of
maximum inner product search can be achieved by a relaxation of the discrete
problem resulting in policy learning or REINFORCE style learning algorithms.
Unfortunately, this relaxation step requires computing a sum over the entire
catalogue making the complexity of the evaluation of the gradient (and hence
each stochastic gradient descent iterations) linear in the catalogue size. This
calculation is untenable in many real world examples such as large catalogue
recommender systems, severely limiting the usefulness of this method in
practice. In this paper, we derive an excellent approximation of these policy
learning algorithms that scale logarithmically with the catalogue size. Our
contribution is based upon combining three novel ideas: a new Monte Carlo
estimate of the gradient of a policy, the self normalised importance sampling
estimator and the use of fast maximum inner product search at training time.
Extensive experiments show that our algorithm is an order of magnitude faster
than naive approaches yet produces equally good policies.

本研究采用 Monte Carlo 梯度的新估计方法，结合 SNIS 重要性采样估计和快速的最大内积搜索方法，解决了离线最大内积搜索的问题，提出了一个新的策略学习算法。与传统算法相比，该算法在速度和性能方面均得到了优化。