Mutual information maximization for amortized likelihood inference from sampled trajectories: MINIMALIST
Mutual information maximization for amortized likelihood inference from sampled trajectories: MINIMALIST
复制标题
从采样轨迹进行摊销似然推断的互信息最大化：极简主义
DOI：
10.1103/physreve.105.055309
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发表时间：
2022
影响因子：
2.4
通讯作者：
Walczak, Aleksandra M.
中科院分区：
文献类型：
--
作者：
Isacchini, Giulio;Spisak, Natanael;Nourmohammad, Armita;Mora, Thierry;Walczak, Aleksandra M.
即使在实践中无法计算模型的可能性，基于模拟的推理也可以学习模型的参数。一类方法使用用不同参数模拟的数据来推断似然证据比模型，或等效的后验函数。在这里，我们将推理任务定义为使用人工神经网络参数化的能量函数的估计。我们提出了一种名为 MINIMALIST 的直观方法，其中通过最大化模拟数据的似然来找到似然证据比的最佳模型。在这个框架内，基于模拟的推理任务和互信息最大化之间的联系是清晰的，并且我们展示了几种已知的后验估计方法如何与互信息的替代下界相关。这些不同的目标函数旨在相同的最佳能量形式，因此可以直接进行基准测试。我们比较了它们在模型参数推断方面的准确性，重点关注涵盖时间序列分析中常见挑战的四个动力系统：乘性噪声驱动的动力学、非线性相互作用、混沌行为和高维参数空间。
Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence ratio, or equivalently the posterior function. Here we frame the inference task as an estimation of an energy function parametrized with an artificial neural network. We present an intuitive approach, named MINIMALIST, in which the optimal model of the likelihood-to-evidence ratio is found by maximizing the likelihood of simulated data. Within this framework, the connection between the task of simulation-based inference and mutual information maximization is clear, and we show how several known methods of posterior estimation relate to alternative lower bounds to mutual information. These distinct objective functions aim at the same optimal energy form and therefore can be directly benchmarked. We compare their accuracy in the inference of model parameters, focusing on four dynamical systems that encompass common challenges in time series analysis: dynamics driven by multiplicative noise, nonlinear interactions, chaotic behavior, and high-dimensional parameter space.