"Interpretable ANOVA Approximation of High-Dimensional Scattered Data"Schmischke, MichaelWe present an approximation method based on the ANOVA (analysis of variance) decomposition and Grouped Transformations. For high-dimensional data, we have to find a way to circumvent the curse of dimensionality. Our answer to this lies in the variable interactions. We assume a low superposition dimension of the approximation, i.e., only few variables interact simultaneously. In a theoretical context, this can be related to the smoothness of a function. From an application standpoint, the sparsity-of-effects principle says that most real world systems are dominated by a small number of low complexity interactions. A major advantage of the method is that the approximation can be interpreted, i.e., we re able to rank the importance of the attribute interactions. Moreover, we are able to generate an attribute ranking to identify unimportant variables and reduce the dimensionality of the problem. Numerical experiments for synthetic and real data show that the method is on par with current machine learning methods and outperforms them in some cases. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Schmischke_2021-06_Online_ICCHA_2021.pdf |
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