Agent-based model calibration using likelihood-free inference

通常可以设计能够模拟复杂现象但不适合标准统计方法的模拟器。当运行模拟器是简单的，但相应的似然函数是棘手的，这往往是由于大量的潜在变量，这将需要被边缘化，以获得似然函数。一个关键的例子是基于代理的模型，一个灵活的模型类别，其中指定的个体代理的行为，然后相互作用，经常产生复杂的紧急behavior.Recently，许多基于模拟的推理方法已经开发出来，使用模拟来近似感兴趣的函数，例如似然，后验，或似然证据比。通常，原始模拟器输出的维度太高而不能直接使用，因此使用一组汇总统计数据来执行推断。在大多数感兴趣的模型中，模拟器会被错误地指定，这意味着模拟器不会完美地复制真实的底层数据生成过程（对于任何参数集）。这导致在近似感兴趣的函数时的问题，例如在近似似然时，观察到的数据（或汇总统计量）可能远远落在似然的尾部，其中密度估计可能不可靠，特别是对于像归一化流的强大方法（Papamakarios等人，2021年）。处理错误的原则性方式的困难，阻碍了模拟器和基于模拟的方法的应用。该项目的总体目标是促进基于模拟的方法，并研究如何提高其鲁棒性模型错误。目前，该项目将重点关注两个领域。该项目的第一个重点是研究使用梯度提升来获得条件密度估计（例如，似然;托马斯等人，2018年）。梯度提升是一种从一组简单的基础学习算法构建集成模型的方法。使用boosting框架的一个特别优势是变量选择和模型拟合可以联合执行。在似然近似的上下文中，这对应于自动选择用于预测条件分布参数的模拟器参数。调查的第二个领域将是制定学习汇总统计的方法，这些方法信息丰富，对错误说明具有鲁棒性。实现这一目标的一个选择是使用变分自编码器，它已被广泛用于机器学习中学习数据集的低维表示。为了提高对错误指定的鲁棒性，来自广义贝叶斯后验的想法（Schmon等人，2020）或半模块化推理（Carmona和Nicholls，2020）可以应用于调整目标函数。

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.