Agent-based model calibration using likelihood-free inference

通常可以设计能够模拟复杂现象但不能很好地适用于标准统计方法的模拟器。当运行模拟器是直接的，但是相应的似然函数是难以处理的，这通常是由于需要对大量的潜在变量进行边际化以获得似然函数而引起的。一个关键的例子是基于主体的模型，这是一类灵活的模型，其中个体主体的行为被指定，然后相互作用经常产生复杂的紧急行为。最近，许多基于模拟的推理方法被开发出来，它们使用模拟来逼近感兴趣的函数，例如似然、后验或似然与证据的比率。通常，原始模拟器输出的维度太高，不能直接使用，因此使用一组汇总统计信息来执行推理。在大多数感兴趣的模型中，模拟器会被错误地指定，这意味着模拟器不能完美地复制真实的底层数据生成过程(对于任何一组参数)。这导致在逼近感兴趣函数时出现问题，例如在逼近似然时，观测数据(或汇总统计数据)可能远远落在似然的尾部，其中密度估计可能是不可靠的，特别是对于像归一化流量这样的强大方法(Papamakario等人，2021年)。原则性地处理误指定的困难阻碍了仿真器和基于仿真的方法的应用，该项目的总体目标是促进基于仿真的方法，并研究如何提高其对模型误指定的鲁棒性。目前，该项目将重点放在两个方面。该项目的第一个重点是调查梯度增强用于获得条件密度估计的使用(例如，可能性；Thomas等人，2018年)。梯度增强是一种从一组简单的基本学习算法构造集成模型的方法。使用助推框架的一个特别优点是，变量选择和模型拟合可以联合进行。在似然近似的情况下，这对应于自动选择用于预测条件分布参数的模拟器参数。第二个调查领域将是制定学习总结统计数据的方法，这些方法具有信息量大、对错误说明的抵抗力强的特点。实现这一点的一种选择是使用变分自动编码器，它已被广泛用于学习机器学习中的数据集的低维表示。为了提高对错误指定的稳健性，可以应用广义贝叶斯后验(Schmon等人，2020)或半模块推理(Carmona和Nicholls，2020)的想法来调整目标函数。

It is often possible to design simulators that are capable of modelling complex phenomena but are not well suited to standard statistical methods. This arises when running the simulator is straightforward, but the corresponding likelihood function is intractable, often due to a large number of latent variables which would need to be marginalised over to obtain the likelihood function. One key example are agent-based models, a flexible class of models where the behaviours of individual agents are specified, which then interact often producing complex emergent behaviour.Recently, many simulation-based inference methods have been developed, which use simulations to approximate a function of interest, for example the likelihood, the posterior, or the likelihood-to-evidence ratio. Often the raw simulator output is of too high dimension to be used directly, so inference is instead performed using a set of summary statistics. In most models of interest, the simulator will be somewhat misspecified, meaning that the simulator does not perfectly replicate the true underlying data generating process (for any set of parameters). This leads to issues when approximating the function of interest, for example when approximating the likelihood, the observed data (or summary statistics) may fall far in the tails of the likelihood where density estimation may be unreliable, particularly for powerful methods like normalising flows (Papamakarios et al., 2021). The difficulty of handling misspecification in a principled manner has hindered application of simulators and simulation-based methods.The overall aim of the project is to contribute to simulation-based methods and investigate ways to improve their robustness to model misspecification. Currently, this project will focus on two areas. The first focus of the project is to investigate the use of gradient boosting for obtaining conditional density estimates (e.g. the likelihood; Thomas et al., 2018). Gradient boosting is a method for constructing ensemble models from a set of simple base learning algorithms. A particular advantage of using a boosting framework is that variable selection and model fitting can be performed jointly. In the context of likelihood approximation, this corresponds to automatically selecting simulator parameters used to predict the conditional distribution parameters. The second area of investigation will be to develop methods for learning summary statistics that are informative and robust to misspecification. One option to achieve this could be to use variational autoencoders, which have been widely used to learn low dimensional representations of datasets in machine learning. To improve robustness to misspecification, ideas from generalised Bayesian posteriors (Schmon et al., 2020) or semi-modular inference (Carmona and Nicholls, 2020) could be applied to adapt the objective function.