Pattern Recognition and Machine Learning
Solutions to the Exercises: Web-Edition
Markus Svens
´
en and Christopher M. Bishop
Copyright
c
2002–2007
This is the solutions manual (web-edition) for the book Pattern Recognition and Machine Learning
(PRML; published by Springer in 2006). It contains solutions to the
www exercises. This release
was created October 5, 2007. Future releases with corrections to errors will be published on the PRML
web-site (see below).
The authors would like to express their gratitude to the various people who have provided feedback on
pre-releases of this document. In particular, the “Bishop Reading Group”, held in the Visual Geometry
Group at the University of Oxford provided valuable comments and suggestions.
The authors welcome all comments, questions and suggestions about the solutions as well as reports on
(potential) errors in text or formulae in this document; please send any such feedback to
prml-fb@microsoft.com
Further information about PRML is available from
http://research.microsoft.com/∼cmbishop/PRML
Contents
Contents 5
Chapter 1: Pattern Recognition . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 2: Density Estimation . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 3: Linear Models for Regression . . . . . . . . . . . . . . . . . . 34
Chapter 4: Linear Models for Classification . . . . . . . . . . . . . . . . 41
Chapter 5: Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . 46
Chapter 6: Kernel Methods . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter 7: Sparse Kernel Machines . . . . . . . . . . . . . . . . . . . . . 59
Chapter 8: Probabilistic Graphical Models . . . . . . . . . . . . . . . . . 63
Chapter 9: Mixture Models . . . . . . . . . . . . . . . . . . . . . . . . . 68
Chapter 10: Variational Inference and EM . . . . . . . . . . . . . . . . . 72
Chapter 11: Sampling Methods . . . . . . . . . . . . . . . . . . . . . . . 83
Chapter 12: Latent Variables . . . . . . . . . . . . . . . . . . . . . . . . 85
Chapter 13: Sequential Data . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 14: Combining Models . . . . . . . . . . . . . . . . . . . . . . . 96
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