The Journal of Machine Learning Research (www.jmlr.org) is pleased to announce the availability of two new papers in electronic form: Tracking the Best Linear Predictor Mark Herbster and Manfred K. Warmuth Journal of Machine Learning Research 1(Sep):281-309, 2001 Prior Knowledge and Preferential Structures in Gradient Descent Learning Algorithms Robert E. Mahony, Robert C. Williamson Journal of Machine Learning Research 1(Sep):311-355, 2001 ---------------------------------------- Tracking the Best Linear Predictor Mark Herbster and Manfred K. Warmuth Journal of Machine Learning Research 1(Sep):281-309, 2001 Abstract In most on-line learning research the total on-line loss of the algorithm is compared to the total loss of the best off-line predictor u from a comparison class of predictors. We call such bounds static bounds. The interesting feature of these bounds is that they hold for an arbitrary sequence of examples. Recently some work has been done where the predictor u_t at each trial t is allowed to change with time, and the total on-line loss of the algorithm is compared to the sum of the losses of u_t at each trial plus the total ``cost'' for shifting to successive predictors. This is to model situations in which the examples change over time, and different predictors from the comparison class are best for different segments of the sequence of examples. We call such bounds shifting bounds. They hold for arbitrary sequences of examples and arbitrary sequences of predictors. Naturally shifting bounds are much harder to prove. The only known bounds are for the case when the comparison class consists of a sequences of experts or boolean disjunctions. In this paper we develop the methodology for lifting known static bounds to the shifting case. In particular we obtain bounds when the comparison class consists of linear neurons (linear combinations of experts). Our essential technique is to project the hypothesis of the static algorithm at the end of each trial into a suitably chosen convex region. This keeps the hypothesis of the algorithm well-behaved and the static bounds can be converted to shifting bounds. ---------------------------------------- Prior Knowledge and Preferential Structures in Gradient Descent Learning Algorithms Robert E. Mahony, Robert C. Williamson Journal of Machine Learning Research 1(Sep):311-355, 2001 Abstract A family of gradient descent algorithms for learning linear functions in an online setting is considered. The family includes the classical LMS algorithm as well as new variants such as the Exponentiated Gradient (EG) algorithm due to Kivinen and Warmuth. The algorithms are based on prior distributions defined on the weight space. Techniques from differential geometry are used to develop the algorithms as gradient descent iterations with respect to the natural gradient in the Riemannian structure induced by the prior distribution. The proposed framework subsumes the notion of "link-functions". ---------------------------------------- These papers and earlier papers in Volume 1 are available electronically at http://www.jmlr.org in PostScript, PDF and HTML formats; a bound, hardcopy edition of Volume 1 will be available later this year. -David Cohn, <[EMAIL PROTECTED]> Managing Editor, Journal of Machine Learning Research ------- This message has been sent to the mailing list "[EMAIL PROTECTED]", which is maintained automatically by majordomo. To subscribe to the list, send mail to [EMAIL PROTECTED] with the line "subscribe jmlr-announce" in the body; to unsubscribe send email to [EMAIL PROTECTED] with the line "unsubscribe jmlr-announce" in the body.
