Identifiability of linear compartmental models: the effect of moving inputs, outputs, and leaks
Identifiability of linear compartmental models: the effect of moving inputs, outputs, and leaks
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DOI：
10.1080/03081087.2020.1812497
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发表时间：
2020-09-01
影响因子：
1.1
通讯作者：
Shiu, Anne
中科院分区：
文献类型：
--
作者：
Gerberding, Seth;Obatake, Nida;Shiu, Anne
如果一个数学模型的参数可以从数据中恢复出来，那么这个模型就是可识别的。在这里，我们研究线性区隔模型，当模型的部分-特别是输入，输出，泄漏和边缘-被移动，添加或删除时，是否保留（局部的，一般的）可识别性。我们的结果如下。首先，对于某些链线、循环和乳状模型，移动或删除泄漏保留了可识别性。其次，对于最多有一个泄漏的循环模型，移动输入或输出保持可识别性。因此，具有最多一个泄漏（以及至少一个输入和至少一个输出）的每个循环模型都是可识别的。接下来，我们给出了添加泄漏使循环模型无法识别的条件。最后，对于某些没有泄漏的循环模型，添加特定边缘再次保留可识别性。我们的证明本质上是代数和组合的，依赖于初等对称多项式的结果和线性隔室模型的输入-输出方程理论。
A mathematical model is identifiable if its parameters can be recovered from data. Here we investigate, for linear compartmental models, whether (local, generic) identifiability is preserved when parts of the model - specifically, inputs, outputs, leaks, and edges - are moved, added, or deleted. Our results are as follows. First, for certain catenary, cycle, and mammillary models, moving or deleting the leak preserves identifiability. Next, for cycle models with up to one leak, moving inputs or outputs preserves identifiability. Thus, every cycle model with up to one leak (and at least one input and at least one output) is identifiable. Next, we give conditions under which adding leaks renders a cycle model unidentifiable. Finally, for certain cycle models with no leaks, adding specific edges again preserves identifiability. Our proofs, which are algebraic and combinatorial in nature, rely on results on elementary symmetric polynomials and the theory of input-output equations for linear compartmental models.