可拓模型预测的鲁棒性
Robustness of Model Predictions under Extension
摘要：
现实世界的数学模型是复杂系统的简化表示。使用数学模型的一个警告是，预测的因果效应和条件独立性在模型扩展下可能不稳健，限制了此类模型的适用性。在这项工作中，我们考虑的条件下，定性模型的预测被保存时，两个模型相结合。在温和的假设下，我们展示了如何使用因果排序技术来有效地评估定性模型预测的鲁棒性。我们还描述了一个大类的模型扩展，保留定性模型预测。对于处于平衡状态的动力系统，我们展示了新的见解如何帮助选择适当的模型扩展和反馈回路的存在原因。我们用一个带有免疫反应的病毒感染模型来说明我们的想法。
英文摘要：
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting applicability of such models. In this work, we consider conditions under which qualitative model predictions are preserved when two models are combined. Under mild assumptions, we show how to use the technique of causal ordering to efficiently assess the robustness of qualitative model predictions. We also characterize a large class of model extensions that preserve qualitative model predictions. For dynamical systems at equilibrium, we demonstrate how novel insights help to select appropriate model extensions and to reason about the presence of feedback loops. We illustrate our ideas with a viral infection model with immune responses.
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