PREFACE ix Many people have helped by proofreading draft material and providing com- ments and suggestions,including Shivani Agarwal,Cedric Archambeau,Arik Azran, Andrew Blake,Hakan Cevikalp,Michael Fourman,Brendan Frey,Zoubin Ghahra- mani,Thore Graepel,Katherine Heller,Ralf Herbrich,Geoffrey Hinton,Adam Jo- hansen,Matthew Johnson,Michael Jordan,Eva Kalyvianaki,Anitha Kannan,Julia Lasserre,David Liu,Tom Minka,Ian Nabney,Tonatiuh Pena,Yuan Qi,Sam Roweis, Balaji Sanjiya,Toby Sharp,Ana Costa e Silva,David Spiegelhalter,Jay Stokes,Tara Symeonides,Martin Szummer,Marshall Tappen,Ilkay Ulusoy,Chris Williams,John Winn,and Andrew Zisserman. Finally,I would like to thank my wife Jenna who has been hugely supportive throughout the several years it has taken to write this book. Chris Bishop Cambridge February 2006PREFACE ix Many people have helped by proofreading draft material and providing com￾ments and suggestions, including Shivani Agarwal, Cedric Archambeau, Arik Azran, ´ Andrew Blake, Hakan Cevikalp, Michael Fourman, Brendan Frey, Zoubin Ghahra￾mani, Thore Graepel, Katherine Heller, Ralf Herbrich, Geoffrey Hinton, Adam Jo￾hansen, Matthew Johnson, Michael Jordan, Eva Kalyvianaki, Anitha Kannan, Julia Lasserre, David Liu, Tom Minka, Ian Nabney, Tonatiuh Pena, Yuan Qi, Sam Roweis, Balaji Sanjiya, Toby Sharp, Ana Costa e Silva, David Spiegelhalter, Jay Stokes, Tara Symeonides, Martin Szummer, Marshall Tappen, Ilkay Ulusoy, Chris Williams, John Winn, and Andrew Zisserman. Finally, I would like to thank my wife Jenna who has been hugely supportive throughout the several years it has taken to write this book. Chris Bishop Cambridge February 2006