Modeling the properties of chemical mixtures is a difficult but important part of any modeling process intended to be applicable to the often messy and impure phenomena of everyday life, including food and environmental safety, healthcare, etc. Part of this difficulty stems from the increased complexity of designing suitable model validation schemes for mixture data, a fact which has been elucidated in previous work only in the case of binary mixture models. We extend these previously defined validation strategies for QSAR modeling of binary mixtures to the more complex case of general, $N$-ary mixtures and argue that these strategies are applicable to many modeling tasks beyond simple chemical mixtures. Additionally, we propose a method of establishing a baseline model performance for each mixture dataset to be in used in model selection comparisons. This baseline is intended to account for the statistical dependence generically present between the properties of mixtures that share constituents. We contend that without such a baseline, estimates of model performance can be dramatically overestimated, and we demonstrate this with multiple case studies using real and simulated data.

翻译：化学混合物性质的建模是日常生活中的食品与环境卫生、医疗保健等领域中常见且复杂的杂散现象建模过程中的重要环节，但也颇具难度。部分困难源于为混合物数据设计合适模型验证方案的复杂性增加，这一点仅在二元混合模型的先前研究中得到阐明。我们将此前针对二元混合物QSAR建模定义的验证策略扩展到更复杂的通用N元混合物情形，并论证这些策略不仅适用于简单化学混合物，还可用于更广泛的建模任务。此外，我们提出了一种方法，用于为每个混合物数据集建立基准模型性能，以用于模型选择比较。该基准旨在说明共享组分的混合物性质之间普遍存在的统计依赖性。我们主张，若缺乏此类基准，模型性能的估计可能被严重高估，并通过多个真实与模拟数据的案例研究证明了这一点。