Book Advert-CV,GCV, et al

[Grace Wahba]

   BOOK ADVERT - CV, GCV, DF SIGNAL, The BIAS-VARIANCE TRADEOFF
        	 AND ALL THAT ....

Spline Models for Observational Data  by G. Wahba
v 59 in the SIAM NSF/CBMS Series in Applied Mathematics

Although this book is written in the language of statistics
it covers a number of topics that are increasingly recognized 
as being of importance to the computational learning 
community. It is well known that models such as neural 
nets, radial basis functions, spline and other bayesian 
models that are adapted to fit the data very well may
in fact overfit the data, leading to large generalization 
error. In particular, minimizing generalization error, aka
aka the bias-variance tradeoff, is discussed 
in the context of smooth multivariate function estimation
with noisy data.
Here, reducing the bias (fitting the data
well) increases the variance (a proxy for the generalization
error) and vice versa.  Included is an in-depth discussion
of ordinary cross validation, generalized cross validation
and unbiassed risk as criteria for optimizing the bias-
variance tradeoff. The role of "degrees of freedom for signal"
as well as the relationships between Bayes estimation, 
regularization, optimization in (reproducing kernel)  
hilbert spaces, splines, and certain radial basis functions
are covered, as well as a discussion of the relationship
between generalized cross validation and maximum likelihood 
estimates of the main parameter(s) controlling the 
bias-variance tradeoff, both in the context of a well-
known prior for the unknown smooth function, and in the 
general context of (smooth) regularization.
....................
Spline Models for Observational Data, by Grace Wahba
v. 59 in the CBMS-NSF Regional Conference
Series in Applied Mathematics, 
SIAM, Philadelphia, PA, March 1990. 
Softcover, 169 pages, bibliography, author index.
ISBN 0-89871-244-0

List Price $24.75, SIAM or CBMS* Member Price $19.80
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