Testing whether a sample of observations is statistically homogeneous, is fundamental for assessing the complexity of the underlying distribution. Moreover, it can help indetermining the model complexity (modelselection) in machine learning applications. Nevertheless, it is unfortunate that, as most statistical hypothesis testing methods, homogeneity testing also suffers from being only effective in very few dimensions.
We are specifically interested to measure the statistical power of such approaches, their scalability in the size of data, their adequacy to get easily recomputed (to get an updated result) when only small changes have taken place to the sample. Moreover, it is also interesting to try incorporating approaches related to histogram segmentation , k-modality testing, or other projection-based preprocessing. In terms of applications, we are planning to use such tests for kernel sparsification and/or data clustering.
epidemics, social interactions and behavior, diffusion control
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