Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate the impact of this decreasing quality of approximation of the summands on the approximation of the weighted sum. Our results indicate that these approximations remain on a reliable level, but their quality reduces when the weights of interactions of higher degrees do not decrease quickly.

中文翻译：

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用加性基因组关系的Hadamard幂近似相互作用模型。

可以通过基于加性基因组关系的哈达玛能力的基因组关系模型来近似具有不同基因座之间相互作用的全基因组上位模型。我们说明，当交互作用度d增大时，该近似值的质量会降低。此外，考虑定义为不同程度相互作用的加权和的关系模型，我们研究了递减的逼近质量的降低对加权和近似的影响。我们的结果表明，这些近似值保持在可靠的水平上，但是当较高程度的相互作用的权重没有迅速降低时，它们的质量会降低。