T. Hastie, R. Tibshirani and J. Friedman (2001) The Elements of Statistical
Learning: Data Mining, Inference, and Prediction.  New York: Springer.
533+xvi pages. $79.95.

In the full springtime of a field, it is rare that some of it's best
gardeners take the time to give us a report on what's blooming.  Statistical
learning is a grafting of offshoots of  artificial intelligence, now called
machine learning, to the statistical technology of classification,
prediction, and forecasting.  The authors aim to synthesize of the efforts
of these two communities with a view to predicting what types of growth are
likely to survive, perhaps with a bit of weeding along the way.

This book is important to the psychometric community for many reasons.  The
contemporary classification literature owes much to the algorithmic
approaches to data analysis that flourished here in the sixties and
seventies, as well as to the data analysis movement of that period where
some valuable lateral thinking by pioneers like Doug Carroll, Jan de Leeuw,
Joseph Kruskal, Roger Shepherd and Forrest Young open up approaches not
based on classical probability theory and mathematical statistics.  And we
may add to this the central role of classification, prediction, and what is
now called data mining, in the practice and in  research in the educational
and  behavioral sciences.  Perhaps it's time for to return to these issues
with new enthusiasm and insights, and this book might just be what we need.
The book builds in many ways on Brian Ripley's Pattern Recognition (1996)
but the unhappy omission of the Leiden group's Gifi volume (Gifi, 1990) from
the bibliography suggests that the statistical learning community has
something to gain, too.

The initial chapters, 1 to 6, contain an overview of statistical material on
linear methods for regression and classification.  Supervised learning is
defined as the use of training samples to develop promising models, followed
by the assessment of their performance on validation and test data.  Nearest
neighbor nonparametric approaches are also presented in order to compare
these older tools in terms of the inevitable tradeoff between bias and
sampling variance.  Basis function expansions of functions, regularization
or smoothing and kernel methods are also introduced to support the more
extensive use of functional or nonparametric methods in current research.

The next two chapters are pivotal; they deal with methods for comparing
model performances, assessing model dimensionality, and important algorithms
such as EM and MCMC.  The authors are right, too, to stress how important
model interpretability is to our client communities, something that is a
plus for tree-based approaches (Breiman, Friedman, Olshen, and Stone, 1984)
but a problem for local or kernel procedures.

Chapters 9 through 13 deal with the main business of the book.  Additive
(Hastie and Tibshirani, 1990) and tree models come first, along with bump
hunting and multivariate regression splines, perhaps because the authors
themselves are leading contributors in these areas.  Boosting methods for
enhancing tree-based classification are currently generating a lot of
excitement, and there are some important insights into how boosting works,
which is essentially by summing a sequence of models for residuals.  Neural
networks are considered next, and linked to projection pursuit models.
Support vector machines, nonparametric discriminant analysis, prototype and
nearest neighbor classification methods follow.  The final chapter reviews
unsupervised learning methods such as cluster analysis, self-organizing maps
and variants of principal components analysis, where there is no correct
classification or explicit outcome variables to guide model construction.

Well chosen data sets of a serious size and clear applied significance,
drawn from problems such as character recognition, prostate cancer
forecasting, spam detection and microarray analysis, are used in
illustrations.  The book pioneers the use of color graphics in textbook
publishing, and some of the displays are stunning.   These authors write
well, too.

What do we need to know to profit from this book?  A fair amount, in my
estimation.  It is a must for those already working in some of the areas
mentioned above, but some previous exposure to concepts such as trees and
additive models is also nearly essential since topics are often mentioned
and used in earlier chapters, well before they are defined and taken up in
detail later.  This rather casual attitude towards organization is apt to
make the book a tough read for total newcomers and for students.

These are not a complaints, however, since the immediacy of the treatment
and the excitement that comes with timeliness more than compensate for the
sacrifice of polish and exposition that we expect in texts on more mature
areas. This is a landmark volume, and this reviewer rates it as a Best Buy.

References

Breiman, L., Friedman, J, Olshen, R. and Stone, C. (1994) Classification and
Regression Trees,  Belmont, Calif.: Wadsworth.

Gifi, A. (1990) Nonlinear multivariate analysis, New York: Wiley.

Hastie, T. and Tibshirani, R. (1993) Generalized Additive Models, London:
Chapman and Hall.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge:
Cambridge University Press.