TY - GEN

T1 - Learning halfspaces with the zero-one loss

T2 - 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012

AU - Birnbaum, Aharon

AU - Shalev-Shwartz, Shai

PY - 2012

Y1 - 2012

N2 - Given α, ε, we study the time complexity required to improperly learn a halfs-pace with misclassification error rate of at most (1 + α)L*gamma + ε, where L *gamma is the optimal γ-margin error rate. For α = 1/γ, polynomial time and sample complexity is achievable using the hinge-loss. For α = 0, Shalev-Shwartz et al. [2011] showed that poly(1/γ) time is impossible, while learning is possible in time exp(Õ (1/γ)). An immediate question, which this paper tackles, is what is achievable if α ε (0, 1/γ). We derive positive results interpolating between the polynomial time for α = 1/γ and the exponential time for α = 0. In particular, we show that there are cases in which α = o(1/γ) but the problem is still solvable in polynomial time. Our results naturally extend to the adversarial online learning model and to the PAC learning with malicious noise model.

AB - Given α, ε, we study the time complexity required to improperly learn a halfs-pace with misclassification error rate of at most (1 + α)L*gamma + ε, where L *gamma is the optimal γ-margin error rate. For α = 1/γ, polynomial time and sample complexity is achievable using the hinge-loss. For α = 0, Shalev-Shwartz et al. [2011] showed that poly(1/γ) time is impossible, while learning is possible in time exp(Õ (1/γ)). An immediate question, which this paper tackles, is what is achievable if α ε (0, 1/γ). We derive positive results interpolating between the polynomial time for α = 1/γ and the exponential time for α = 0. In particular, we show that there are cases in which α = o(1/γ) but the problem is still solvable in polynomial time. Our results naturally extend to the adversarial online learning model and to the PAC learning with malicious noise model.

UR - http://www.scopus.com/inward/record.url?scp=84877735350&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84877735350

SN - 9781627480031

T3 - Advances in Neural Information Processing Systems

SP - 926

EP - 935

BT - Advances in Neural Information Processing Systems 25

Y2 - 3 December 2012 through 6 December 2012

ER -