ON THE EXISTENCE OF IDENTIFIABLE REPARAMETRIZATIONS FOR LINEAR COMPARTMENT MODELS
ON THE EXISTENCE OF IDENTIFIABLE REPARAMETRIZATIONS FOR LINEAR COMPARTMENT MODELS
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DOI：
10.1137/15m1038013
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发表时间：
2016-01-01
影响因子：
1.9
通讯作者：
Draisma, Jan
中科院分区：
文献类型：
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作者：
Baaijens, Jasmijn A.;Draisma, Jan
线性隔室模型的参数通常由实验输入输出数据估计。当无限多个参数值可以产生相同的结果时，问题就出现了；这样的模型被称为不可识别的。在这种情况下，可以搜索模型的可识别的重新参数化-一个减少参数数量的映射，从而减少的模型是可识别的。我们研究一类特定的模型，这些模型已知是不可识别的。利用代数几何和图论，将Meshkat和Sullivant给出的可识别尺度再参数化存在的判据转化为基于二部图的加权邻接矩阵秩的判据。这使我们能够推导出几个新的结构，以获得具有可识别的缩放再参数化的图。利用这些构造，得到了此类图的一个大子类。最后，我们提出了一种细分或删除边缘的方法，以确保模型具有可识别的缩放再参数化。
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case, one can search for an identifiable reparametrization of the model-a map which reduces the number of parameters such that the reduced model is identifiable. We study a specific class of models which are known to be unidentifiable. Using algebraic geometry and graph theory, we translate a criterion given by Meshkat and Sullivant for the existence of an identifiable scaling reparametrization to a new criterion based on the rank of a weighted adjacency matrix of a certain bipartite graph. This allows us to derive several new constructions to obtain graphs with an identifiable scaling reparametrization. Using these constructions, a large subclass of such graphs is obtained. Finally, we present a procedure for subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization.