Efficient inexact proximal gradient algorithms for structured sparsity-inducing norm.

Area of Science:

• Machine Learning
• Optimization
• Statistical Learning Theory

Background:

• Structured-sparsity regularization is crucial for sparse learning, enabling the encoding of complex feature relationships.
• Existing methods, particularly for l1/l-infinity norm with arbitrary group overlap, face computational challenges due to complex proximal operators.
• The network-flow algorithm, while effective, proves time-consuming in high-dimensional scenarios.

Purpose of the Study:

• To develop a more efficient computational solution for l1/l-infinity group lasso with arbitrary group overlap.
• To address the computational bottleneck associated with solving the proximal operator in structured sparsity learning.
• To maintain or improve generalization performance compared to existing methods.

Main Methods:

• Development of an inexact proximal gradient method tailored for l1/l-infinity group lasso.
• The proposed algorithm requires only an inexact solution to the proximal sub-problem in each iteration, enabling efficient computation.
• Theoretical analysis to establish global convergence rates comparable to exact proximal methods.

Main Results:

• The inexact proximal gradient method demonstrates significantly improved efficiency compared to the network-flow algorithm.
• Experimental results confirm the computational advantages without compromising generalization performance.
• The algorithm effectively handles arbitrary group overlap in structured sparsity.

Conclusions:

• The proposed inexact proximal gradient method offers a computationally efficient and effective solution for l1/l-infinity group lasso with arbitrary group overlap.
• This advancement facilitates the application of structured sparsity regularization in high-dimensional settings.
• The method provides a practical alternative for researchers and practitioners in sparse learning.