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Nondegenerate piecewise linear systems: a finite Newton algorithm and applications in machine learning
Xiao-Tong Yuan1, Shuicheng Yan
1Department of Statistics, Rutgers University, NJ 08854, USA. xyuan@stat.rutgers.edu
Neural Computation
|November 19, 2011
Summary
We introduce PLS-DN, a damped Newton method for solving piecewise linear systems (PLS). This method offers a provably finite and efficient solution for optimization and learning problems.
Area of Science:
- Numerical Analysis
- Optimization Theory
- Machine Learning
Background:
- Piecewise linear systems (PLS) are crucial in solving linear complementarity problems.
- These problems model various learning and optimization tasks.
- Existing methods may lack efficiency for nondegenerate PLSs.
Purpose of the Study:
- To propose an effective damped Newton method for nondegenerate PLSs.
- To ensure exact solutions up to machine precision.
- To demonstrate the method's applicability in statistical learning.
Main Methods:
- Development of the PLS-DN algorithm, a damped Newton-type method.
- Analysis of the algorithm's convergence properties.
- Application to statistical learning problems like Lasso and SVMs.
Main Results:
- PLS-DN guarantees global convergence in a finite number of iterations.
- The method exhibits at least linear convergence before termination.
- Numerical results confirm the effectiveness and efficiency on synthetic and benchmark data.
Conclusions:
- PLS-DN provides an exact and efficient solution for nondegenerate PLSs.
- The method offers a novel perspective for modeling statistical learning problems.
- The algorithm is validated through comprehensive numerical experiments.
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