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About this paper
Le Song, Alex Smola, Arthur Gretton, Karsten Borgwardt, Justin Bedo
BAHSIC applies HSIC to rank feature subsets by dependence on labels, providing a classifier-independent filter for classification and regression. It removes feature groups, adapting label kernels to the task. In a 22-feature synthetic XOR problem, BAHSIC and RELIEF recover the two relevant features at small sample sizes, unlike FOHSIC, Pearson correlation, and mutual information; this finding is limited to that setting.
Key insights
- HSIC provides a theoretically sound, unbiased, and statistically concentrated empirical estimator for general functional dependence, effectively detecting both linear and nonlinear relationships without relying on density estimation.
- The flexibility of kernel functions for the label space enables HSIC to serve as a universal criterion for feature selection across binary, multi-class, and regression problems, offering a unified and principled approach.
- Utilizing HSIC in a filter-based backward elimination scheme offers computational efficiency by decoupling feature selection from classifier training, while also enhancing the interpretability of selected features.
Summary by alphaXiv.
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