TY - GEN

T1 - Learning and smoothed analysis

AU - Kalai, Adam Tauman

AU - Samorodnitsky, Alex

AU - Teng, Shang Hua

PY - 2009

Y1 - 2009

N2 - We give a new model of learning motivated by smoothed analysis (Spielman and Teng, 2001). In this model, we analyze two new algorithms, for PAC-learning DNFs and agnostically learning decision trees, from random examples drawn from a constant-bounded product distributions. These two problems had previously been solved using membership queries (Jackson, 1995; Gopalan et al, 2005). Our analysis demonstrates that the "heavy" Fourier coefficients of a DNF suffice to recover the DNF. We also show that a structural property of the Fourier spectrum of any boolean function over "typical" product distributions. In a second model, we consider a simple new distribution over the boolean hypercube, one which is symmetric but is not the uniform distribution, from which we can learn O(log n)-depth decision trees in polynomial time.

AB - We give a new model of learning motivated by smoothed analysis (Spielman and Teng, 2001). In this model, we analyze two new algorithms, for PAC-learning DNFs and agnostically learning decision trees, from random examples drawn from a constant-bounded product distributions. These two problems had previously been solved using membership queries (Jackson, 1995; Gopalan et al, 2005). Our analysis demonstrates that the "heavy" Fourier coefficients of a DNF suffice to recover the DNF. We also show that a structural property of the Fourier spectrum of any boolean function over "typical" product distributions. In a second model, we consider a simple new distribution over the boolean hypercube, one which is symmetric but is not the uniform distribution, from which we can learn O(log n)-depth decision trees in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=77952396391&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2009.60

DO - 10.1109/FOCS.2009.60

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:77952396391

SN - 9780769538501

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 395

EP - 404

BT - Proceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009

T2 - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009

Y2 - 25 October 2009 through 27 October 2009

ER -