TY - GEN
T1 - Error Exponent in Agnostic PAC Learning
AU - Hendel, Adi
AU - Feder, Meir
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - Statistical learning theory and the Probably Ap-proximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to ana-lyze learning problems and algorithms, and have been studied thoroughly. Uniform worst case bounds on the convergence rate have been well established using, e.g., VC theory or Radamacher complexity. However, in a typical scenario the performance could be much better. In this paper, we consider PAC learning using a somewhat different tradeoff, the error exponent-a well established analysis method in Information Theory-which describes the exponential behavior of the probability that the risk will exceed a certain threshold as function of the sample size. We focus on binary classification and find, under some stability assumptions, an improved distribution dependent error exponent for a wide range of problems, establishing the exponential behavior of the PAC error probability in agnostic learning. Inter-estingly, under these assumptions, agnostic learning may have the same error exponent as realizable learning. The error exponent criterion can be applied to analyze knowledge distillation, a problem that so far lacks a theoretical analysis.
AB - Statistical learning theory and the Probably Ap-proximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to ana-lyze learning problems and algorithms, and have been studied thoroughly. Uniform worst case bounds on the convergence rate have been well established using, e.g., VC theory or Radamacher complexity. However, in a typical scenario the performance could be much better. In this paper, we consider PAC learning using a somewhat different tradeoff, the error exponent-a well established analysis method in Information Theory-which describes the exponential behavior of the probability that the risk will exceed a certain threshold as function of the sample size. We focus on binary classification and find, under some stability assumptions, an improved distribution dependent error exponent for a wide range of problems, establishing the exponential behavior of the PAC error probability in agnostic learning. Inter-estingly, under these assumptions, agnostic learning may have the same error exponent as realizable learning. The error exponent criterion can be applied to analyze knowledge distillation, a problem that so far lacks a theoretical analysis.
UR - http://www.scopus.com/inward/record.url?scp=85202795789&partnerID=8YFLogxK
U2 - 10.1109/ISIT57864.2024.10619319
DO - 10.1109/ISIT57864.2024.10619319
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:85202795789
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 765
EP - 770
BT - 2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 IEEE International Symposium on Information Theory, ISIT 2024
Y2 - 7 July 2024 through 12 July 2024
ER -