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Learning nonseparable sparse regularizers via multivariate activation functions
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AI
DOI：10.1016/j.neucom.2025.130853.png)
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Abstract
En 中文
Sparse regularization is a widely embraced technique in high-dimensional machine learning and signal processing. Existing sparse regularizers, however, are predominantly hand-crafted and often separable, making them less adaptable to data and potentially hindering performance. In this paper, we present a novel approach aiming at learning nonseparable (multivariate) sparse regularizers. We leverage the proximal gradient algorithm to transform the challenge of acquiring nonseparable sparse regularizers into the task of learning multivariate activation functions. We further establish the necessary conditions that these activation functions should satisfy. Our contribution culminates in the introduction of MAF-SRL, a deep network designed to learn multivariate activation functions within existing deep learning frameworks. To our knowledge, this research marks the first endeavor to learn nonseparable sparse regularizers. Extensive experiments conducted on benchmark datasets underscore the superiority of regularizers learned through MAF-SRL. They exhibit significantly enhanced performance in terms of both accuracy and sparseness compared to existing sparse regularizers.
Keywords:
sparse regularization
nonseparable regularizers
proximal gradient
multivariate activation functions
MAF-SRL