On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
Robust trainability of single neurons
Journal of Computer and System Sciences
Anti-Hadamard matrices, coin weighing, threshold gates, and indecomposable hypergraphs
Journal of Combinatorial Theory Series A
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A decision-theoretic generalization of on-line learning and an application to boosting
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems
Theoretical Computer Science
Linear Programming Boosting via Column Generation
Machine Learning
Feature Selection Via Mathematical Programming
INFORMS Journal on Computing
Use of the zero norm with linear models and kernel methods
The Journal of Machine Learning Research
On the hardness of approximating label-cover
Information Processing Letters
| Hi-index | 0.89 |
We consider the problem of minimizing the number of misclassifications of a weighted voting classifier, plus a penalty proportional to the number of nonzero weights. We first prove that its optimum is at least as hard to approximate as the minimum disagreement halfspace problem for a wide range of penalty parameter values. After formulating the problem as a mixed integer program (MIP), we show that common ''soft margin'' linear programming (LP) formulations for constructing weighted voting classsifiers are equivalent to an LP relaxation of our formulation. We show that this relaxation is very weak, with a potentially exponential integrality gap. However, we also show that augmenting the relaxation with certain valid inequalities tightens it considerably, yielding a linear upper bound on the gap for all values of the penalty parameter that exceed a reasonable threshold. Unlike earlier techniques proposed for similar problems (Bradley and Mangasarian (1998) [4], Weston et al. (2003) [14]), our approach provides bounds on the optimal solution value.