Machinelearningis arapidlymaturing?eldthataims toprovidepracticalme- ods for data discovery, categorization and modelling. The She?eld Machine Learning Workshop, which was held 7-10 September 2004, brought together some of the leading international researchers in the ?eld for a series of talks and posters that represented new developments in machine learning and numerical methods. The workshop was sponsored by the Engineering and Physical Sciences - search Council (EPSRC) and the London Mathematical Society (LMS) through the MathFIT program,whose aim is the encouragementof new interdisciplinary research.AdditionalfundingwasprovidedbythePASCALEuropeanFramework 6 Network of Excellence and the University of She?eld. It was the commitment of these funding bodies that enabled the workshop to have a strong program of invited speakers,and the organizerswish to thank these funding bodies for their ?nancial support. The particular focus for interactions at the workshop was - vanced Research Methods in Machine Learning and Statistical Signal Processing. These proceedings contain work that was presented at the workshop, and ideas that were developed through, or inspired by, attendance at the workshop. The proceedings re?ect this mixture and illustrate the diversity of applications and theoretical work in machine learning. We would like to thank the presenters and attendees at the workshop for the excellent quality of presentation and discussion during the oral and poster sessions. We are also grateful to Gillian Callaghan for her support in the orga- zation of the workshop, and ?nally we wish to thank the anonymous reviewers for their help in compiling the proceedings.