A stochastic gradient descent algorithm for structural risk minimisation

פרסום מחקרי: פרק בספר / בדוח / בכנספרסום בספר כנסביקורת עמיתים

2 ציטוטים ‏(Scopus)

תקציר

Structural risk minimisation (SRM) is a general complexity regularization method which automatically selects the model complexity that approximately minimises the misclassification error probability of the empirical risk minimiser. It does so by adding a complexity penalty term ∊(m, k) to the empirical risk of the candidate hypotheses and then for any fixed sample size m it minimises the sum with respect to the model complexity variable k. When learning multicategory classification there are M subsamples mi, corresponding to the M pattern classes with a priori probabilities pi, 1 ≤ i ≤ M. Using the usual representation for a multi-category classifier as M individual boolean classifiers, the penalty becomes ∑Mi=1 pi∊(mi, ki). If the mi are given then the standard SRM trivially applies here by minimizing the penalised empirical risk with respect to ki, 1,..., M. However, in situations where the total sample size ∑Mi=1 mi needs to be minimal one needs to also minimize the penalised empirical risk with respect to the variables mi, i = 1,..., M. The obvious problem is that the empirical risk can only be defined after the subsamples (and hence their sizes) are given (known). Utilising an on-line stochastic gradient descent approach, this paper overcomes this difficulty and introduces a sample-querying algorithm which extends the standard SRM principle. It minimises the penalised empirical risk not only with respect to the ki, as the standard SRM does, but also with respect to the mi, i = 1,..., M. The challenge here is in defining a stochastic empirical criterion which when minimised yields a sequence of subsample-size vectors which asymptotically achieve the Bayes’ optimal error convergence rate.

שפה מקוריתאנגלית
כותר פרסום המארחAlgorithmic Learning Theory - 14th International Conference, ALT 2003, Proceedings
עורכיםRicard Gavalda, Klaus P. Jantke, Eiji Takimoto
עמודים205-220
מספר עמודים16
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 2003
פורסם באופן חיצוניכן
אירוע14th International Conference on Algorithmic Learning Theory, ALT 2003 - Sapporo, יפן
משך הזמן: 17 אוק׳ 200319 אוק׳ 2003

סדרות פרסומים

שםLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
כרך2842
ISSN (מודפס)0302-9743
ISSN (אלקטרוני)1611-3349

כנס

כנס14th International Conference on Algorithmic Learning Theory, ALT 2003
מדינה/אזוריפן
עירSapporo
תקופה17/10/0319/10/03

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