Sparse Modal Additive Model

doi:10.1109/TNNLS.2020.3005144

Sparse Modal Additive Model

2021-06-01

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DOI：10.1109/TNNLS.2020.3005144

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Sparse additive models have been successfully applied to high-dimensional data analysis due to the flexibility and interpretability of their representation. However, the existing methods are often formulated using the least-squares lass with learning the conditional mean, which is sensitive to data with the non-Gaussian noises, e.g., skewed noise, heavy-tailed noise, and outliers. To tackle this problem, we propose a new robust regression method, called as sparse modal additive model (SpMAM), by integrating the modal regression metric, the data-dependent hypothesis space, and the weighted l(q,1)-norm regularizer (q >= 1) into the additive models. Specifically, the modal regression metric assures the model robustness to complex noises via learning the conditional mode, the data-dependent hypothesis space offers the model adaptivity via sample-based presentation, and the l(q,1)-norm regularizer addresses the algorithmic interpretability via sparse variable selection. In theory, the proposed SpMAM enjoys statistical guarantees on asymptotic consistency for regression estimation and variable selection simultaneously. Experimental results on both synthetic and real-world benchmark data sets validate the effectiveness and robustness of the proposed model.

Keywords:

Additive models

data-dependent hypothesis space

generalization bound

modal regression

variable selection

Sparse Modal Additive Model

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