Pattern Recognition and Machine Learning
Solutions to the Exercises: Tutors’ Edition
Markus Svens
´
en and Christopher M. Bishop
Copyright
c
2002–2009
This is the solutions manual (Tutors’ Edition) for the book Pattern Recognition and Machine Learning
(PRML; published by Springer in 2006). This release was created September 8, 2009. Any future releases
(e.g. with corrections to errors) will be announced on the PRML web-site (see below) and published via
Springer.
PLEASE DO NOT DISTRIBUTE
Most of the solutions in this manual are intended as a resource for
tutors teaching courses based on PRML and the value of this resource
would be greatly diminished if was to become generally available. All
tutors who want a copy should contact Springer directly.
The authors would like to express their gratitude to the various people who have provided feedback on
earlier releases of this document.
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: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 2: Probability Distributions . . . . . . . . . . . . . . . . . . . . 28
Chapter 3: Linear Models for Regression . . . . . . . . . . . . . . . . . . 62
Chapter 4: Linear Models for Classification . . . . . . . . . . . . . . . . 78
Chapter 5: Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . 93
Chapter 6: Kernel Methods . . . . . . . . . . . . . . . . . . . . . . . . . 114
Chapter 7: Sparse Kernel Machines . . . . . . . . . . . . . . . . . . . . . 128
Chapter 8: Graphical Models . . . . . . . . . . . . . . . . . . . . . . . . 136
Chapter 9: Mixture Models and EM . . . . . . . . . . . . . . . . . . . . 150
Chapter 10: Approximate Inference . . . . . . . . . . . . . . . . . . . . . 163
Chapter 11: Sampling Methods . . . . . . . . . . . . . . . . . . . . . . . 198
Chapter 12: Continuous Latent Variables . . . . . . . . . . . . . . . . . . 207
Chapter 13: Sequential Data . . . . . . . . . . . . . . . . . . . . . . . . 223
Chapter 14: Combining Models . . . . . . . . . . . . . . . . . . . . . . . 246
5
