BayesFlow：利用可逆神经网络学习复杂随机模型
BayesFlow: Learning complex stochastic models with invertible neural networks
AI总结：
BayesFlow提出一种基于可逆神经网络的全局摊销贝叶斯推断方法，通过模拟学习概率映射，无需额外训练即可推断完整后验，适用于复杂难处理模型。
摘要：
估计数学模型参数是几乎所有科学分支中的常见问题。然而，当过程和模型描述变得越来越复杂且没有显式似然函数时，这个问题会变得尤为困难。在这项工作中，我们提出了一种基于可逆神经网络的全局摊销贝叶斯推断新方法，称为BayesFlow。该方法利用模拟来学习从观测数据到潜在模型参数的概率映射的全局估计器。以这种方式预训练的神经网络，无需额外训练或优化，即可推断涉及同一模型族的任意多个真实数据集上的完整后验分布。此外，我们的方法还包含一个摘要网络，该网络被训练用于将观测数据嵌入到信息量最大的摘要统计量中。从数据中学习摘要统计量使得该方法适用于标准推断技术因手工设计的摘要统计量而失败的建模场景。我们在种群动态、流行病学、认知科学和生态学中具有挑战性的难处理模型上展示了BayesFlow的实用性。我们认为，BayesFlow为任何可以从数据模拟的前向模型构建摊销贝叶斯参数估计机器提供了一个通用框架。
英文摘要：
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks which we call BayesFlow. The method uses simulation to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pre-trained in this way can then, without additional training or optimization, infer full posteriors on arbitrary many real datasets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with hand-crafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.
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